The Pearson Complete Guide to the CAT 9788131774144, 9788131799574, 8131774147

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The Pearson Complete Guide to the

C AT Second Edition (According to the latest CAT pattern)

Nishit K. Sinha CAT Consultant

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The aim of this publication is to supply information taken from sources believed to be valid and reliable. This is not an attempt to render any type of professional advice or analysis, nor is it to be treated as such. While much care has been taken to ensure the veracity and currency of the information presented within, neither the publisher nor its authors bear any responsibility for any damage arising from inadvertent omissions, negligence or inaccuracies (typographical or factual) that may have found their way into this book. Copyright © 2012 Dorling Kindersley (India) Pvt. Ltd Licensees of Pearson Education in South Asia No part of this eBook may be used or reproduced in any manner whatsoever without the publisher’s prior written consent. This eBook may or may not include all assets that were part of the print version. The publisher reserves the right to remove any material present in this eBook at any time. ISBN 9788131774144 eISBN 9788131799574 Head Office: A-8(A), Sector 62, Knowledge Boulevard, 7th Floor, NOIDA 201 309, India Registered Office: 11 Local Shopping Centre, Panchsheel Park, New Delhi 110 017, India

To My Brothers and Sisters-in-law Mr Amit Kumar and Mrs Babita Sinha and Mr Vinit Kumar and Mrs Rashmi Verma

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Contents

Preface to the Second Edition Preface Acknowledgements CAT Demystified About the Book About the Author

vii viii xi xiii xvii xviii

PART 1 Quantitative Aptitude and Data Interpretation Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13

Number System Review Test 1 Average Percentage Ratio, Proportion and Variation Time and Work Time Speed and Distance Review Test 2 Geometry and Mensuration Review Test 3 Set Theory Equations Sequence and Series Function, Graphs and Maxima Minima Permutations, Combinations and Probability Miscellaneous Review Test 4

1.3 1.25 1.29 1.43 1.60 1.73 1.86 1.99 1.103 1.145 1.149 1.156 1.168 1.178 1.191 1.212 1.227

vi 

  Contents

Chapter 14

Data Interpretation Practice Exercise 1 Practice Exercise 2 Practice Exercise 3 Practice Exercise 4 Practice Exercise 5 Practice Exercise 6 Practice Exercise 7 Review Test 5 Section Test 1 Section Test 2

1.231 1.254 1.259 1.264 1.268 1.272 1.277 1.282 1.287 1.292 1.298

PART 2 Verbal and Logical Reasoning Chapter 1 Chapter 2 Chapter 3

Reading Comprehension English Usage Logical Reasoning Practice Exercise 1 Practice Exercise 2 Section Test 1 Section Test 2

2.3 2.51 2.158 2.173 2.177 2.180 2.187

PART 3 Cat Papers CAT 2002 CAT 2003 CAT 2004 CAT 2005 CAT 2006 CAT 2007 CAT 2008

3.3 3.35 3.69 3.99 3.125 3.145 3.165

PART 4 Full Length Tests Based on CAT 2011 Pattern Test Paper 1 Test Paper 2 Test Paper 3

4.3 4.19 4.34

Preface to the Second Edition

The CAT changed again in 2011—with the introduction of (a) 2–Section format instead of 3–section format and (b) Sectional time limit. This book caters to the changed CAT 2011 pattern fully. It is designed to brush up your fundamentals, give you opportunity to practice typical problems and then give you a feedback through the test papers. I have tried to maintain that every next question should bring some new learning or idea. Next it moves on to testing of that particular part. 1st two parts of the book will not only expose you to the sections Quantitative Aptitude + Data Interpretation and Verbal + Logical Reasoning, but also give you ample opportunity to test yourself through 5 Review Tests and 4 Section Tests if you are prepared for the next level of testing or not. 3rd part is dedicated to CAT papers—just have a feel of it, and try to solve these questions once you are through with the particular concept. 4th Part contains 3 Full Length Test papers based upon the CAT 2011 pattern—Take those as per the instructions given. These test papers also have indicative percentile—to tell you about your level of preparedness. Lastly, there is a CD containing Section Tests and Full Length Papers. In case of any query, you can share that with me at [email protected] Best of luck to all the future CXOs, for life.

Preface

HOW TO PREPARE FOR THE COMMON ADMISSION TEST (CAT): THE STORY OF MOVES Let me start with the famous story “Garry Kasparov Vs IBM Deep Blue computer”: During 1996–1997, computer Deep Blue developed by IBM played two series of matches with the then world chess champion Garry Kasparov. While the first series of six matches played in 1996 was won by Garry Kasparov (Wins–3, Draw–2, Loss–1), disapproving the IBM’s supremacy claim of machine over man, the second series played in May 1997 was won by the IBM’s machines. After this loss, Kasparov said that he sometimes saw deep intelligence and creativity in the machine’s moves, suggesting that during the second game, human chess players, in violation of the rules, intervened. As expected, IBM vehemently denied that it cheated, saying the only human intervention occurred between the games and not during the games. The rules provided for the developers to modify the program between the games, an opportunity they said they used to shore up the weaknesses in the computer’s playing prowess that were revealed during the course of the match. [Source - http://www.research.ibm.com/deepblue]

Cut to CAT Preparation Now What are the typical responses/reactions we have when we see a question? Some of those most frequently occurring are listed below: Responses/Reactions 1. Solution is clear end to end

2. Solution is somewhat clear

3. Not at all having any idea of the solution

Response/Reaction 1—I know where to start and how to reach to the final solution. So, it’s just a matter of a few seconds/minutes that I will have the solution. Response/Reaction 2—Solution is somewhat clear—I know how to start, but not absolutely sure if it will lead to the end solution. Response/Reaction 3—Not at all having any idea of the solution—How to approach or proceed is not clear? You may wonder why I started with Kasparov Vs IBM story and how it is linked to CAT preparation and the possible reactions. To answer this, I raise another question—human beings have the thinking capabilities, and so they can decide the moves on the basis of the changing situations and so they plays chess. How does a computer actually play chess?

Preface 

  ix

If we go through the Kasparov Vs Deep Blue story in flashback, we get to know that there were some chess grandmasters who were part of the IBM Deep Blue manufacturing team and supplying the most crucial information— the database of moves played across thousands of games. So while these moves created a repository of information inside the ‘brain’ of the computer, a complex modelling was done to decide which counter move is best for what move— something on the lines of decision tree analysis through probabilistic calculations. And here was the need for faster calculation. So, for ‘X’ move placed by Kasparov, the computer used to analyze how many times this move had been put and what probability respective countermoves had of leading to the winning position.

Cut Back to CAT Preparation This might have answered the most universal query of the students—why are we able to solve a particular question and not been able to solve another one? So it’s just about the moves—solution to every question involves some moves (loosely speaking, steps have the same connotation as moves). If we have the moves ready with us from the starting to the end of the solution, we have the 1st response/reaction. And so on 2nd or 3rd response that how many moves we have. Summarizing, we can solve a question if, either we have the moves already installed inside our brain, or else we would be required to generate them on our own at that very moment inside the examination hall. Probably this is the single most important reason why a question from ‘Function Chapter’ seems comparatively easier to a student who has gone through maths in X+2 as opposed to a student who has not gone through maths in X+2. So, how can a student who has not gone through maths can come at par with a student who is a maths graduate?

Generating the moves

Retaining the moves Re-using the moves

And how moves will be generated (the base of this triad)—By going through the concepts, and solving not just quantity of questions, but quality of questions too. Looking upon the pattern of CAT QA for the past years, one can be reasonably sure that fetching 40% marks in QA is sufficient to get approximate 97–98 percentile. This translates into 10 questions (as per CAT 2008). The idea is, if we can have the moves ready for 6 questions, for an example, then we would be required to generate moves only for 4 questions inside the examination hall, and this saves our considerable time that can be invested in other sections, including QA too. For example, there was a question in CAT 2008—What is the number of terms in the expansion of (a + b + c)20? I had put almost the same question in my QA book, which was published in 2006, in Miscellaneous chapter— What is the number of terms in the expansion of (a + b + c)10? I am not saying that our objective should be to match the question—that as a student I should have, done exactly the same question appearing in the CAT of that year before sitting in the CAT. Rather it’s about the thought process— retaining the moves used earlier while solving a question, and the ability to use the same in even slightly different situations. And what is true for QA is mostly true for other sections too.

x 

  Preface

Sectional Contribution in Result To understand the relative performance of students, making it to premier B-Schools, across different sections asked in the CAT and other tests, I conducted a survey. Following is the result of that survey conducted across the students of IIMs, XLRI, MDI Gurgaon and SP Jain: Case

%age of Respondents

QA

LR/DI

EU/RC

1

20

Excellent

Decent

Cleared cut-off

2

15

Cleared cut-off

Decent

Excellent

3

39

Decent

Decent

Cleared cut-off

4

22

Cleared cut-off +

Excellent

Cleared cut-off

5

 4

Excellent

Excellent

Excellent

Above table uses ‘excellent’ as the best level of preparedness, then ‘decent’ and then ‘cleared cut-off.’ Some of the observations that we can make out from the above survey table: 1. All the respondents were either excellent or decent in LR DI section. 2. Even if a student is not very good at QA or EU/RC, if the student can just clear the cut-off in these sections, and at the same time do well in LR/DI, overall good percentile can be achieved, resulting into the calls from IIMs and other premier B-School in the CAT and other examinations. 3. It also shows that if a student can prepare at excellence level in one particular section, and clears cut-off in other sections with some margin, calls can be get (as shown in case 4). To conclude with this section, I admit that these are not the exhaustive list of methods to crack the CAT or to get into IIMs. You may have your own combination or strategy to get into your desired B- School. However, remember the golden thumb rule—Doing the right things and then doing the things right. So know that which combination is good for you, and then decide what is the best method to achieve that.

Acknowledgements

Second edition of this book brought to me a God-sent opportunity to enrich this book with new ideas—mostly suggested by the users of this book. Besides, change in the CAT 2011 pattern was also a challenge for the CAT training industry stakeholders, including me, to provide a comprehensive preparation agenda to the MBA aspirants. Through this book, I have tried to do the same. Second edition of this book would not have been possible without the active suggestions from my friends in the coaching industry, including the ones at my last organization—Mr Hitesh Devalia, Mr Bhuvan Gupta, Mr Pardeep Kumar, Mr Dwijendra Srivastava, Ms Jaya Rughani, Mr Huzefa and Mr PC. A lot of thanks to the colleagues working with me at dueNorthAcademics—Ms Neha Kavi and Mr Dileep Kumar, Mr Tanay Kotriwala and Tinky-Inky for allowing me to take a day off as and when required. Thanks a lot to the editorial team of Pearson—Mr Rajesh Shetty, Mr Asad Shabir for helping me in maintaining the sanctity of the deadline of completing the whole project. Showick Thorpe, your guidance is much appreciated.

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CAT Demystified

CAT stands for the Common Admission Test. It is a test conducted by IIMs for admission into several programs offered by them. Besides IIMs, there are a good number of colleges which accept CAT score in their first round of selection process. As of now, there are 13 IIMs offering PGP at following places: Ahmedabad, Bangalore, Calcutta, Lucknow, Indore, Kozhikode, Shillong, Ranchi, Rohtak, Raipur, Udaipur, Trichy, Kashipur.

History of the CAT For last almost three decades, since the CAT has been started, it has changed its colours many a time in terms of number of questions, sections asked and orientation of those questions. Here we will discuss the pattern of CAT 2000 onwards. Chart 1 CAT 2000 CAT 2001 CAT 2002 CAT 2003 CAT 2004 CAT 2005 CAT 2006 CAT 2007 CAT 2008 CAT 2009 CAT 2010 CAT 2011

Number of sections 3 3 3 3 3 3 3 3 3 3 3 2

Total number of questions 165 165 150 150 123 90 75 75 90 60 60 60

Total Marks N.A. N.A. N.A. N.A. 150 150 300 300 360 450 (scaled score) 450 (scaled score) 450 (scaled score)

Time allowed 120 minutes 120 minutes 120 minutes 120 minutes 120 minutes 120 minutes 150 minutes 150 minutes 150 minutes 135 minutes 135 minutes 140 minutes

CAT 2011 has two sections: (a) Quantitative Ability & Data Interpretation (b) Verbal Ability & Logical Reasoning with 30 questions in each section. CAT 2011 also has sectional time limit of 70 minutes for each section. Before CAT 2004, the CAT did not mention how many marks one question carried? Marks carried per question were announced for the first time in CAT 2004.

xiv 

  CAT Demystified

Quite obvious from the above table that time allotted per question has risen sharply from CAT 2000 to CAT 2011. One possible conclusion drawn from here is that the CAT is focussing more on accuracy than speed, and secondly, it expects students to gain a certain level of competence across all the areas in a particular section. With the number of questions going down and time going up, students do not have much choice of questions to choose from. Chart 2 7LPHDOORWWHGSHU4XHVWLRQ  





   

  



  







&$7 &$7 &$7 &$7 &$7 &$7 &$7 &$7 &$7 &$7 &$7 &$7             7LPHDOORWWHGSHU4XHVWLRQ

Sectional Breakups and Getting an IIM Call One thing that has remained constant during this period of CAT 2000 - CAT 2010 is the number of sections and the way these sections have been joined—Quantitative Aptitude (QA), Logical Reasoning and Data Interpretation (LR/DI), and English Usage/Reading Comprehension (EU/RC). Though CAT 2011 changed it all: Chart 3 Year CAT 2000 CAT 2001 CAT 2002 CAT 2003 CAT 2004 CAT 2005 CAT 2006 CAT 2007 CAT 2008 CAT 2009 CAT 2010 CAT 2011

QA 55 50 50 50 35 30 25 25 25 20 20 30 (QA+DI)

LR DI 55 50 50 50 38 30 25 25 25 20 20

EU RC 55 50 50 50 50 30 25 25 40 20 20 30 (Verbal + LR)

Total no. of questions 165 150 150 150 123 90 75 75 90 60 60 60

One possible reason predicted for the 2-section format is the fact that the CAT is trying to emulate the standard global papers like the GRE/GMAT. However, past CAT trends show that a student is required to get around 70% marks to get at least one IIM call (with clearing the sectional cut-off). The following table and bar chart give us some clarity regarding the same:

CAT Demystified 

  xv

Chart 4 Year CAT 2000 CAT 2001 CAT 2002 CAT 2003 CAT 2004 CAT 2005 CAT 2006 CAT 2007 CAT 2008 CAT 2009 CAT 2010 CAT 2011

Total marks or questions 165 150 150 150 123 150 300 300 360 60 60 60

Marks/Qs required to get at least one IIM call 75 70 72 56 54 48 115 118 120 42 40 35

Following line chart gives questions solved or marks required as a percentage of total marks or total questions (as applicable): Chart 5 % marks or questions done to get one IIM call 70 46.7 45.5

66.66 58

48

43.9 37.3

39.3 32

38.3

33.3

CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Note: Above calculation is based upon the data collected from the students who got IIM calls in that particular year. So, to get at least one IIM call in CAT 2008, a student was required to get 33.33% marks out of the total with clearing the cut-off across the sections. Though in the online format of the CAT (since 2009), percentage questions to be done to get at least one IIM call has gone up, it is primarily because the exam is perceived to be easier in its totality than pen and paper based exams. A student might have got 10 easy questions out of 20 questions in a section. If we convert the requirement of marks to be obtained from the above line chart into questions to be done, we get the following table: Year CAT 2000 CAT 2001 CAT 2002 CAT 2003 CAT 2004 CAT 2005

No. of questions to be solved 85 80 81 60 42 38

Time allotted 120 minutes 120 minutes 120 minutes 120 minutes 120 minutes 120 minutes

Time invested per qn 1.4 1.5 1.5 2.0 2.9 3.2

xvi 

  CAT Demystified

Year CAT 2006 CAT 2007 CAT 2008 CAT 2009 CAT 2010 CAT 2011

No. of questions to be solved 33 33 34 42 40 35

Time allotted 150 minutes 150 minutes 150 minutes 135 minutes 135 minutes 135 minutes

Time invested per qn 4.5 4.5 4.4 3.2 3.3 3.8

Chart 6—For CAT 2000 to CAT 2008, at 90% accuracy with 1/4 negative marking, these are the approximate number of questions to be done. For CAT 2009 to CAT 2011, net of these many questions is to be done. To summarize this whole discussion till now, we will compare chart 2 with chart 6 and present them in a unified line chart given below (chart 7).

Time allotted vs Time that can be invested per Qn (in minutes) Time that can be invested/Qn

0.73 0.73 1.5 1.4

0.8 1.5

0.8 2

0.98 2.9

Time allotted per Qn

1.33 3.2

2

2

1.67

4.5

4.5

4.4

2.26 2.26 3.2

3.3

2.33 3.8

CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT CAT 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

This line brings to us an important information—For CAT 2006, CAT 2007 or CAT 2008, even if a student has taken approximately 4.5 minutes to solve a question with 90% accuracy, s/he has got enough marks to get at least one IIM call (provided s/he clears the sectional cut-off too). For online formats for CAT, it is around 3.3 minutes per question. So, it’s more about accuracy now than speed.

About the Book

SALIENT FEATURES OF THE BOOK 1. High on content—Special emphasis on areas where the CAT asks most of the question from 2. Sequential learning strategy—Building the fundamentals → Practising upon quality questions → Testing against the benchmark 3. Specially designed keeping in mind the requirements of working professionals—Crisp, compact and comprehensive 4. Balanced emphasis among the sections and within the sections 5. More than 2000 fully solved quality questions 6. Last 7 years’ solved CAT papers 7. Three full length test papers with indicative percentile list + four Section Tests 8. A CD containing Review Tests, Full Length Tests and Practice Exercises across the sections

About the Author

Nishit Sinha is a post-graduate from IIM Lucknow. For last 10 years, he has been training students for the CAT. Many of his students have now graduated from premier B-Schools across the globe. He is also the author of widely praised books Pearson Guide to QA DI for the CAT, Pearson Guide to Verbal LR for the CAT and Demystifying Number System. He is currently running the test prep organization dueNorth Academics, based at Dehradun.

PART

1

QUANTITATIVE APTITUDE AND DATA INTERPRETATION

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c h a p t e r

 1

Number System

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Numbers and their different types   Definitions and properties of those numbers   Concepts attached to these numbers   Kind of questions which are asked in the CAT   Method of solving questions

We are going to learn the following concepts in Number System: (i) LCM and HCF (iii) Number of divisors (v) Remainders (vii) Units digit

(ii)  Divisibility rules (iv)  Number of exponents (vi)  Base system

 CLASSIFICATION OF NUMBERS/ INTEGERS Natural Numbers Natural numbers are counting numbers, i.e., the numbers which we use to count any number of things. E.g., → 1, 2, 3,……….. The lowest natural number is 1.

Whole Numbers When zero is included in the list of natural number, then they are known as Whole numbers. E.g., → 0, 1, 2, ……. The lowest whole number is 0.

Integers Integers are whole numbers and negative of whole numbers. For example, 43 434235, 28, 2, 0, – 28, and – 3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and – 9.90 are not the integers.

Number Line The number line is used to represent the set of real numbers. Below is the brief representation of the number line:

1.4 

  Quantitative Aptitude and Data Interpretation

Opposites – 7 – 6 – 5 – 4 – 3

– 2 – 1 0 +1 +2

Negative integers

+3

+4

+5 +6 +6

Positive integers

Prime Numbers and Composite Numbers

Prime Numbers

for any number to be a prime number, it should be divisible by exactly one more number other than itself. Again as said above, Primes can be natural numbers only.

Among natural numbers, we can distinguish Prime numbers and Composite numbers. All the numbers which are having exactly two factors are known as Prime Numbers. In other words,

Prime numbers can also be seen as the building blocks. And we combine two or more than two same or distinct prime numbers to create numbers bigger than these prime numbers. E.g., → 3 × 2 = 6.

Number of prime numbers between every 100 numbers No.s from-to

1–100

No. of primes

25

101–200 201–300 301–400 401–500 501–600 601–700 701–800 801–900 901–1000 21

16

16

Composite Numbers A number is composite if it is the product of two or more than two distinct or same prime numbers. E.g., → 4, 6, 8, …. 4 = 22 6 = 21 ×31 Lowest composite number is 4.

Even and Odd numbers Suppose N is an integer. If there exists an integer P such that N = 2P + 1, then N is an odd number. If there exists an integer P such that N = 2P, then N is an even number. Putting in simple language, even numbers are those numbers which are divisible by 2 and Odd numbers are those integers which are not divisible by 2.

POINTS TO REMEMBER 1.  1 is neither prime nor composite. 2.  0 is neither positive nor negative.

17

14

16

14

15

14

Solution

Whatever kind of calculation we do with two even and two odd numbers, we will always get an even result. So, the answer is option 3. Example  2

If N, N+2 and N+4 are prime numbers, then the number of possible solutions for N is/are (CAT 2003) 1.  1 2.  2 3.  3 4.  None of these Solution

There is only one triplet of prime numbers where difference between any two prime number is 2, that is 3, 5 and 7. So, N = 3 is the only solution. Hence, the answer is 1.

 LCM AND HCF Example  1

Two of a, b, c and d are even and two are odd, not necessarily in order. Which of the following is definitely even? 1.  a + b + c – 2d 2.  a + 2b – c 3.  a + b – c + d 4.  2a + b + c – d. 0

Meaning of LCM The least common multiple (LCM) of two numbers is the smallest positive number that is a multiple of both. Multiples of 3 → 3, 6, 9, 12, 15, 18, 21, 24 ,……………… Multiples of 4 → 4, 8, 12, 16, 20, 24, 28 ,……………….

Number System  So, LCM of 3 and 4 will be 12, which is the lowest common multiple of 3 and 4. Now we will define the method of finding out LCM of two or more than two positive integers. Example  3

Find the LCM of 35, 45, 55.

  1.5

Meaning of HCF (Highest Common Factor) Factors are those +ve integral values of a number, which can divide that number. HCF, which is known as GCD(Greatest Common Divisor) also, is the highest value which can divide the given numbers. Factors of 20 – 1, 2, 4, 5, 10, 20. Factors of 30- 1, 2, 3, 5, 6, 10, 15, 30. So, 10 will be the HCF of 20 and 30. Important: HCF of (na – 1) and (nb – 1) = (nHCF of a and b – 1)

Solution

LCM of 35,45,55. First of all, find out LCM of 35 and 45.

Standard formula

Now 35 = 51 × 71 and 45 = 32 × 51. So, it can be observed here that 35 is not having 32 in it, so we will multiply 35 by 32. So, LCM of 35 and 45 = 35 × 32.(You can start with 45 also to find out the missing factors of 35 in 45.) Now, we will find out LCM of 35 × 32 and 55 = 51 × 111 55 = 51 × 111 Now, 111 is not there with 35 × 32. So, we will multiply 35 × 32 with 111. So, finally LCM = 35 × 32 × 111 = 3465.

1. LCM × HCF = Product of two numbers. This formula can be applied only in case of two numbers However if the numbers are relatively prime to each other then this formula can be applied for any no. of nos. 2. LCM of fractions = LCM of numerator of all the fractions/HCF of denominator of fractions 3. HCF of fractions = HCF of numerator of all the fractions/LCM of denominator of fractions 4. HCF of (sum of two numbers and their LCM) = HCF of numbers.

Example  4

Find out the LCM and HCF of 16, 12, 24. Solution

Number



Multiples

Factors

16

16, 32, 48, 64, 80, 96, 112, 128 ,…….

1, 2, 4, 8, 16

12

12, 24, 36, 48, 60, 72, 84, 96, 108 ,….

1, 2, 3, 4, 6, 12

24

24, 48, 72, 96, 120, 144, 168, 192 ,….

1, 2, 3, 4, 6, 8, 12, 24

Common Multiple



48, 96.....



Lowest common multiple



Common Factor 1, 2, 4 Highest common factor

48

Divisibility Rules (For decimal system) Divisibility rules are quite imperative because with the help of these, we can infer if a particular number is divisible by other number or not, without actually dividing it. Divisibility rules of numbers are specific to that particular number only.

4

Divisibility Rules For 2– I f unit digit of any number is 0, 2, 4, 6 or 8, then that number will be divisible by 2. For 3– I f sum total of all the digits of any number is divisible by 3, then the number will be divisible by 3. (e.g., 123, 456 etc.)

1.6 

  Quantitative Aptitude and Data Interpretation

Example  5

Solution

How many values of A are possible if 3245684A is divisible by 3?

Sum of digits of number is 8+9+7+6+5+A+4+B=39+A+B. So, A + B should be 6 or 15. Next value should be 24 but since A and B are digits so it can not be more than 18. Possible pairs of A and B are: B A 0 6 1 5 4 2 3 3 2 4 5 1 6 0 8 7 8 7 6 9 6 9 Since B is even, six possible set of values of A and B are there.

Solution

Sum total of the number = 32 + A For this number to be divisible by 3, A can take three values namely 1 or 4 or 7. (No other values are possible since A is the unit digit of the number) For 4 – If the last two digits of a number is divisible by 4, then that number will be divisible by 4. (Example, 3796, 248, 1256, etc.) For 5 – If the last digit of the number is 5 or 0, then that number will be divisible by 5. For 6 – If last digit of the number is divisible by two and sum total of all the digits of number is divisible by 3, then that number will be divisible by 6. For 7 – The integer is divisible by 7 if and only if the difference of the number of its thousands and the remainder of its divisible by 1000 is divisible by 7. For 7 – If the difference between the numbers of tens in the number and twice the unit digits divisible by 7 then the given number is divisible by 7.

Example 6

For 11– A number is divisible by 11, if the difference between the sum of the digits at the even places and the sum of the digits at the odd places is divisible by 11. Example: 6595149 is divisible by 11 as the difference of 6 + 9 + 1 + 9 = 25 and 5 + 5 + 4 = 14 is 11. For 12– If the number is divisible by 3 and 4, then the number will be divisible by 12. Example: 144,348.

Let us take the number 795. The units digit is 5 and when it is doubled we get 10. The remaining part of the number (i.e., the tens) is 79. If 10 is subtracted from 79 we get 69. Since this result is not divisible by 7, the original number 795 is not divisible by 7.

For 13– (A + 4B), where B is the unit’s place digit and A is all the remaining digits. Example – Checking the divisibility of 1404 by 13: Here A = 140 and B = 4, then A + 4B = 140 + 4 ×4 = 156. This 156 is divisible by 13 so 1404 will be divisible by 13.

For 8– I f the last 3 digits of number is divisible by 8, then the number itself will be divisible by 8. E.g., 128,34568,76232 etc.

For 14– If the number is divisible by 2 and 7 both, then the number will be divisible by 14.

For 9– I f the sum of digits of the number is divisible by 9, then the number will be divisible by 9. E.g., 129835782. 1+2+9+8+3+5+7+8+2=45. Since 45 is divisible by 9, number will be divisible by 9. Example  7

How many pairs of A and B are possible in number 89765A4B if number is divisible by 9, given that last digit of number is even?

For 15– A number is divisible by 15, if the sum of the digits is divisible by 3 and unit digit of the number is 0 or 5. Example: 225, 450, 375 etc. For 16– A number is divisible by 16, if the number formed by the last 4 digits of the given number is ­divisible by 16. Example: 12578320 is divisible by 16, since last 4 digits of the number, 8320 is divisible by 16. For 17– (A – 5B) Where B is the unit’s place digit and A is all the remaining digits.

Number System 

  1.7

For 18– The number should be divisible by 9 and 2 both.

Example  10

For 19– (A+2B), where B is the unit’s place digit and A is all the remaining digits. If the sum of the number of tens in the number and twice the unit digit is divisible by 19, then the number is divisible by 19. For example, let us take the number 665. the units digit is 5 and when it is doubled, we get 10. The remaining part of the number is 66. If 10 (which is the unit digit doubled.) is added to 66 we get 76. Since this result 76 is divisible by 19, it means the original number 665 is also divisible by 19.

Find the total number of even and prime divisors of N = 420.

For 20– The number should be divisible by 4 and 5.

Solution

N = 420 = 22 × 31 × 71× 51 Odd divisors will come only if we take zero power of 2 (since any number multiplied by any power(≥1) of 2 will give us an even number. So, odd divisors will come if we take N1 = 20 × 31 × 71× 51 So, number of odd divisors = (0+1)(1+1)(1+1)(1+1) = 8 So, total number even divisors = Total number of divisors – number of odd divisors = 24 – 8 = 16

Process to find out the divisibility rule for Prime numbers

Alternatively, we can also find out the number of even divisors of N = 420 directly (Or, in general for any number.)

We are creating the divisibility rule for P, a prime number.

420 = 22 × 31 × 71× 51

Step 1 – Find the multiple of P of the form 10K+1 or 10K –1. Step 2 – If it is 10 K –1, then the divisibility rule will be A + KB, and if it is 10 K +1, then the divisibility rule will be A – KB, where B is the unit’s place digit and A is all the remaining digits.

To obtain the factors of 420 which are even, we will not consider 20, since 20 = 1 So, number of even divisors of 420 = (2) (1 +1) (1+1)(1+1) =16 (We are not adding 1 in the power of 2, since we are not taking 20 here, i.e., we are not taking one power of 2) Prime divisor = 4 (namely 2, 3, 5 and 7 only)

Example 8

Finding out the divisibility rule of 23: Lowest Multiple of 23, which is closest to any multiple of 10 = 69 = 7 × 10 –1 So, rule is A + 7 B.

Example  11

Find the set of co-prime factors of the number N = 720. Solution

Number of Divisors To find out number of divisors of any number, we can use following formula: If N is any number which can be factorized like N = ap q × b × cr ×...…, where a, b and c are prime numbers. No. of divisors = (p +1) (q +1) (r +1)…………….. Example  9

Find the number of divisors of N = 420. Solution

N = 420 = 22 × 31 × 71× 51 So, No. of divisors = (2+1) (1+1) (1+1) (1+1) = 24

720 = 24 × 32 × 51 Using the formula for three prime factors [(p+1) (q+1) (r +1) – 1 + pq + qr + pr + 3pqr] [This is a standard formula if the number is having 3 prime factors] We get, [(4+1) (2+1) (1 +1) – 1 + 4.2 + 2.1 + 4.1 + 3.4.2.1] = 67

Sum of Divisors Like number of divisors of any number, we can find out the sum of divisors also. If N is any number which can be factorized like N = ap × bq × cr ×...…, where a, b and c are prime numbers. Then sum of all the divisors =

(ap+1–1) (bq+1–1) (cr+1–1) (a–1) (b–1) (c–1)

1.8 

  Quantitative Aptitude and Data Interpretation

REMAINDERS

Remainder Theorem

Dividend = Quotient × Divisor + Remainder 17 = 5 × 3 + 2 ⇒ dividend = 17, Quotient = 5, Divisor = 3, Remainder = 2 [ We are dividing 17 by 3 ].

The product of any two or more than two natural numbers has the same remainder when divided by any natural number as the product of their remainders. Lets understand this through an example:

Concept of Negative Remainder

12 × 13 156 = Remainder =2 7 7 Normal way of doing this is — Product →→→ Remainder Theorem method–Remainder →→→ Product →→ → Remainder So, first of all we will find out the remainders individually of each number and then we will multiply these individual remainders to find out final remainder.

As obvious from the name, remainder implies that something has been left out or something remain there. So, the remainder simply can never be negative. Its minimum value can be zero only and not negative. Example  12 9 Example 

What is the remainder when –50 is divided by 7?

Remainder

Remainder 12/7 = 5

Solution Solution

Remainder 13/7 = 6

50/7 = (–56+6)/7; which gives a remainder of 6. Or, when we divide –50 by 7, we get –1 as the remainder. Now, since remainder has to be non-negative, so we add 7(quotient) to it which makes final remainder as→ –1 + 7 = 6.

Remainder der 30/7 = 2

12 × 13 = Remainder (5 × 6)/ 7 = Remain7

Example  14 11 Example 

There are two methods to find out the remainder of any expression:

What is the remainder obtained when (1421 × 1423 × 1425) is divided 12? (CAT 2000 )

1. Cyclicity Method 2. Theorem Method

Solution Solution

Remainder of 1421/12 = 5 Remainder of 1423/12 = 7

Cyclicity Method For every expression of remainder, there comes attached a specific Cyclicity of remainders.

Example  Example  13 10 What is the remainder when 41000 is divided by 7?

To find the Cyclicity, we keep finding the remainders until any remainder repeats itself. It can be understood with the following example: → →

41 4

42 2

43 1

44 4

45 46 2 1

Remainder (1421 × 1423 × 1425)/12 = Remainder (5 × 7 × 9)/12 = Remainder (5 × 63)/12 = Remainder (5 × 3)/12 = 3

Derivations

Solution Solution

No./7 Remainder

Remainder of 1425/12 = 9

47 48 4 2

    Now, 4 4 gives us the same remainder as 41, so the Cyclicity is of 3 (Because remainders start repeating themselves after 43.)     So, any power of 3 or a multiple of 3 will give remainder of 1. So, 4999 will give 1 as the remainder. Final remainder = 4

(A+1)N will always give 1 as the remainder. (For all natural A values of A and N)

1.

Example  15 12 Example 

What is the remainder when 9100 is divided by 8? Solution Solution

For A = 8, it satisfies the above condition. So, remainder = 1 Alternatively, we can apply either of cyclicity or theorem method to find the remainder.

Number System  AN when N is even, remainder is 1 and when N is A+1 odd, remainder is A itself. 2.

Example  16 13 Example 

  1.9

Unit Digit (Any even number)4n = ………………….6 It means that any even number raised to a power, which is a multiple of 4, will give 6 as the unit digit. (Any odd number)4n = …………..……….1

What is the remainder when 210 is divided by 3?

It means that any odd number raised to a power, which is a multiple of 4, will give 1 as the unit digit.

Solution Solution

Exception – 0, 1, 5, 6 [these are independent of power, and unit digit will be the same respectively]

Since here N is even, so remainder = 1 3. i.  (an + bn) is divisible by (a + b), if n is odd.  Extension of the above formula – (an + bn + cn) is divisible by (a + b + c), if n is odd and a, b, c are in Arithmetic Progression.  Similarly, the above situation can be extended for any number of terms. ii.  (an – bn) is divisible by (a + b), if n is even. iii. (an – bn) is divisible by (a ­— b), for n being either odd or even.

Example  19 16 Example 

Find the unit digit of 256782345. Solution Solution

Unit digit of 256782345 = Unit digit of 845 (To find out unit digit, we need to have unit digits only. And similarly, to find out tens digit we need to have the tens and units digit only. In the present case, we are considering only last two digits of the power because divisibility rule of 4 needs only the last two digits of the numbers) 845 = 844+1 = 844 × 81 = (………6) × 8 = …….8

Example  17 14 Example 

Example  20 17 Example 

What is the remainder when (1523 + 2323) is divided by 19? (CAT 2004, 2 marks)

What is the unit digit of 323232? Solution Solution

Solution Solution

It can be observed that (15 + 23 ) is divisible by 38, so it will be divisible by 19 also. Hence, remainder = 0. 23

23

    Alternatively, this problem can be done either by cyclicity method or theorem method.

Example  18 15 Example 

What is the remainder when (163 +173+183+193) is divided by 70? (CAT 2005, 1 mark) Solution Solution

We know, this is a basic multiplication and division question. But using the above approach makes it a lot simple.    We know that (an + bn) is divisible by (a + b), if n is odd. Taking cue from this we can say that (an + bn + cn) is divisible by (a + b + c), if n is odd and similarly (an + bn + cn + dn) is divisible by (a + b + c + d). Now 16+17+18+19 = 70, so remainder is zero.

32 is an even numbers which is having a power of the form 4n. So, it will give 6 as the unit digit. Example  21 18 Example 

What is the last non-zero digit of the number 302720? (CAT 2005, 2 marks) Solution Solution

302720 = 32720 × 102720 Last Non-zero digit of 302720 = Unit Digit of 32720 =........1

Number of Exponents In simple terms, exponents are also known as Power. Exponent of any prime number P in n! =

n n n n + 2 + 3 + ................... + x , p p p p

  Quantitative Aptitude and Data Interpretation

1.10 

where n ≥ px and [.] denotes the greatest integer value i.e., we have to consider only the integral value. Let us find out exponent of 5 in 1000! = 1000/5 + 1000/52 +1000/53 + 1000/54 = 200 + 40 + 8 + 1 = 249 Example  22 Example 

19

What is the highest power of 5 which can divide N = (22! +17894!)?

Solution Solution

Number of times this number is divisible by 5 is same as number of zeroes at the end of this number. Since 22! have 4 zeroes at its end, so N will also be having only four zeroes at its end. Hence, highest power of 5 which can divide N is 4.

Base System In our decimal system of writing the numbers, we use 10 digits (0-9). In this system, largest number of single digit = 9, and the moment we have to form a number bigger than this number, we are needed to take resort to two-digit numbers starting from 10. Similarly, largest numbers of two digits = 99 and after this we have 100, a numbers of three digits. Now let us assume a system of writing where we use only 6 digits (0-5). Largest single digit number in this system will be 5 and next to this will be 10. Similarly, largest two digit number will be 55 and next to this is 100. This whole procedure can be summed up in the following table:

(0-9)10

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

(0-8)9

0

1

2

3

4

5

6

7

8

10

11

12

13

14

15

16

17

18

(0-7)8

0

1

2

3

4

5

6

7

10

11

12

13

14

15

16

17

20

21

(0-6)7

0

1

2

3

4

5

6

10

11

12

13

14

15

16

20

21

22

23

(0-5)6

0

1

2

3

4

5

10

11

12

13

14

15

20

21

22

23

24

25

(0-3)4

0

1

2

3

10

11

12

13

20

21

22

23

30

31

32

33

100

101

(0-2)3

0

1

2

10

11

12

20

21

22

100

101

102

110

111

112

120

121

122

Questions from this concept are asked in the following different ways:

So, (74)10 = (112)8

1.  (Base)10 to any other base and vice versa.

Converting (74)10 to the base of ( )7:

2. (Base)x to (Base)y and vice versa; none of x and y being equal to 10 but x and y will be given. 1. (Base)10 to any other base and vice versa.

Base

74

7

10

Remainder 4

7

1

3

Converting (74)10 to the base of ( )9: Base

74

9

8

Remainder 2

1

So, (74)10 = (134)7 Converting (74)10 to the base of ( )6:

So, (74)10 = (82)9 Converting (74)10 to the base of ( )8: Base 8

74

8

1

9

Quotient

Remainder 2 1

74

Base 6

12

Remainder 2

6

2

0

Quotient

So, (74)10 = (202)6

Number System  2. (Base)x to (Base)y and vice versa; none of x and y being equal to 10 but x and y will be given:

(345)8→→→→→→( )9 We will do this problem with the help of creating a bridge of base 10 between base 8 and base 9. Step 1 –  Convert (345)8 into base 10. 345 = 3 × 8 + 4 × 8 + 5 × 8 = (229)10 2

Decimal Calculation So far, we have seen the calculations involving natural numbers only. Let us now work with decimals.

Converting decimal system numbers to any other system

Base 10

→ → → →

→ → → →

Converting (345)8 to the base of ( )9:

  1.11

1

0

Suppose (12.725) is a numbers in decimal system which is required to be converted into octal system(8 digits) We will first convert 12 into octal system. (12)10 = (14)8 Now to convert (0.725)10 into ( method:

)8, we will apply following

Step 2 –  Now convert this no. in base 10 into base 9. (229)10 = 2 × 92 + 7 × 91 + 4 × 90 = (274)9

0.725 × 8 = 5.8

Take out integral part from here.

0.8 × 8 = 6.4

Take out integral part from here.

However, if new base is a power of old base and vice versa, then it can be converted directly also in the new base i.e., we are not needed to go to base 10 for these kind of conversions.

0.4 × 8 = 3.2

Take out integral part from here.

0.2 × 8 = 1.6

Take out integral part from here.

Example–(Base)2 to (Base)4 or (Base)2 to (Base)8 conversion does not require a bridge of base 10. Converting (101110010)2 to Octal ( )8 system: Firsty, we will club three digits of binary number into a single block and then will write the decimal equivalent of each group(left to right).

And keep doing this till the moment we get decimal part as zero i.e., the product should be an integer. (0.725)10 = (0.5632……)8 So, (12.725) = (14.5632……)8

Converting any other system numbers to decimal system

So, (101110010)2 is now (101)2(110)2(010)2

Now suppose if (15.453)7 is to be converted into decimal system, then the process is as follows:

Now, (101)2 = 1 × 22 + 0 + 1 × 20 = 5

We will first convert (15)7 into decimal system.

(110)2 = 1 × 22 + 1 × 21 + 0 × 20 = 6

(15)7 = 1 × 71 + 5 × 70 = (12)10

(010)2 = 0 × 22 + 1 × 21 + 0 × 20 = 2

Now (0.453)7 = 4 × 7-1 + 5 × 7-2 + 3 × 7-3 = 0. 6822.... So, (15.453)7 = (12.6822....)10

So, (101110010)2 = (562)8

  EXERCISE  1 1. A number is doubled and 6 is added to it. The resultant so obtained is multiplied by four, it becomes 96. What is the number? 1.  8 4.  13

2.  9 5.  None of these

3.  12

2. By what number should 3150 be multiplied to make it a perfect square? 1.  36 4.  210

2.  14 5.  None of these

3.  84

3. When 1 is added to both the numerator and denominator of certain fraction it becomes half and when 1 is subtracted from both the numerator and denominator it becomes 1/3. Find the original fraction. 1.  5/9 4.  3/7

2.  4/9 5.  None of these

3.  4/7

4. The least number which leaves remainders 2, 3, 4, 5 and 6 on dividing by 3, 4, 5, 6 and 7 is 1.  420 4.  414

2.  419 5.  None of these

3.  389

1.12 

  Quantitative Aptitude and Data Interpretation

5. What is the unit digit of 27257× 58549? 1.  8 4.  4

2.  9 5.  None of these

15. What is the units digit of 1! + 2! + 3! + ... + 2003!? 3.  6

6. What is the unit digit of 8778 - 7887?

1.  0 4.  3

2.  2 5.  None of these

3.  1

7. How many times does the digit 7 occur from 20 to 600?

16. Each of 8 boxes contains one or more marbles. Each box contains a different number of marbles, except for two boxes which contain the same number of marbles. What is the smallest total number of marbles that the 8 boxes could contain?

1.  120 4.  60

1.  28 4.  36

1.  8 4.  4

2.  9 5.  None of these 2.  118 5. None of these

3.  7

3.  58

8. If N is prime number, then how many different unit digits can (N2 + 1) have? 1.  8 4.  4

2.  9 5.  None of these

3.  7

9. What is the largest number that will always divide the sum of the cubes of any three consecutive natural numbers? 1.  8 4.  4

2.  9 5.  None of these

3.  7

10. LCM of two distinct natural numbers is 103. What will be their HCF? 1.  1 4.  7

2.  103 3.  11 5.  Cannot be determined

11. In a test of 20 questions, 5 marks are given for each correct answer and 2 are deducted for each incorrect answer. Amar did all the questions and scored 58. How many correct answers did he have? 1.  10 4.  16

2.  12 5.  None of these

3.  14

2.  31 5.  61

3.  41

13. Julie typed a 6-digit number into a faulty computer in which the 1 (one) key was broken. The number appearing on the screen was 2003, possibly with some blank spaces. How many different 6-digit numbers could have Julie typed? 1.  10 4.  25

2.  15 5.  None of these

3.  20

14. A whole number between 1 and 99 is not greater than 90, not less than 30, not a perfect square, not even, not a prime, not divisible by 3 and its last digit is not 5. How many such numbers are possible? 1.  0 4.  3

2.  2 5.  None of these

3.  35

17. The whole number N is divisible by 7. N leaves a remainder of 1 when divided by 2, 3, 4, or 5. What is the sum of the digits of smallest value of N? 1.  4 4.  3

2.  2 5.  None of these

3.  7

18. A person cashes a cheque at the bank. By mistake, the teller pays the number of paise as rupees and the number of rupees as paise. The person spent Rs 3.50 before realizing the mistake, and then on counting the money finds there is exactly double the amount of his actual cheque amount. For what was the actual amount (Rs) for the cheque made out? 1.  24.56 4.  32.68

2.  14.32 5.  None of these

3.  27.42

19. A and B are two natural numbers, each divisible by 5. Which of the following is not necessarily true? 1.  A+B is divisibly by 5 2.  A + B is divisible by 10 3.  A – B is divisible by 5

12. The sum of six consecutive positive odd integers starting with n is a perfect cube. Find the smallest possible n. 1.  21 4.  51

2.  29 5.  None of these

3.  1

4.  A2 – B2 is divisible by 5 5.  All of these are definitely true. 20. If n² is a perfect cube, then which of the following statement is always true? 1.  n is odd 2.  n is even 3.  n³ is a perfect square 4.  n is a perfect cube 5.  None of these 21. If (5x + 11y) is a prime number for natural number values of x and y, then what is the minimum value of (x + y)? 1.  2 4.  5

2.  3 5.  6

3.  4

Number System  22. What is the unit’s digit of 213 x 212 x 347 x 468 × 778? 1.  4 4.  2

2.  8 5.  None of these

3.  6

23. If the unit’s digit in the product (47n × 729 × 345 × 343) is 5, what is the maximum number of values that n may take? 1.  9 4.  5

2.  3 5.  4

3.  7

24. If a, b, c and d are consecutive odd numbers, then (a² + b² + c² + d²) is always divisible by 1.  5 4.  4

2.  7 5.  6

3.  3

25. Four bells toll at intervals of 14, 21 and 42 minutes respectively. If they toll together at 11.22 am, when will they toll together for the first time after that? 1.  11.56 am 4.  11.48 am

2.  12.04 pm 3.  12.06 pm 5.  None of these

26. When x is divided by 6, remainder obtained is 3. Find the remainder when x4 + x3 + x2 + x + 1 is divided by 6. 1.  3 4.  5

2.  4 5.  2

3.  1

Direction for questions 27 to 37:  Find the remainder in each of the questions when numerator is divided by denominator. 27. 9090 /13

1.  2 4.  4

2.  1 5.  None of these

3.  3

2.  11 5.  None of these

3.  9

29. 10200/8 2.  1 5.  None of these

3.  3

1010 +10100 +101000 +1010000000000 30. 7 1.  2 4.  4 44 22 33

5 1.  1 4.  4

1.  9 4.  8 33.

2.  10 5.  None of these

1 !1 + 2 !2 + 3 !3 + ......................... + 100 !100 23 × 3 × 5

1.  3 4.  4 34.

2.  1 5.  None of these

3.  5

1 !1! + 2 !2! + 3 !3! + .........................1000 !1000! 23 × 51

1.  5 4.  24 35.

3.  12

2.  7 5.  None of these

3.  15

21 + 41 + 61 + ................ + 100 ! 24

1.  21 4.  24 20 30

10 36. 2 11

2.  25 5.  None of these 64 36 44

3.  33

33 44

22 18 –5 +3 23 19

1.  4 4.  4

2.  8 5.  None of these

3.  3

2 3 1 1 + 22 + 33 1 37. 4 1.  1 4.  2

2.  0 3.  3 5.  Cannot be determined

1.  2 4.  4

2.  0 5.  6

3.  3

39. Find the unit digit of (325)5! × (2242)282 × (4291) 5!-3!.

1.  0 4.  4

11 31. 7

1 ! + 2 ! + 3 ! + .........................+ 100 ! 23 × 31

38. Find the unit digit of (2568 × 2!)180! × (3252 × 5!)200! × (3256) 5!.

28. 3202/101 1.  8 4.  7

32.

  1.13

2.  5 5.  None of these

2.  1 5.  None of these

3.  0

Direction for questions 40 to 42:  Read the passage given below and solve the questions based on it. 3.  8

2.  2 5.  None of these

1.  2 4.  4

3.  3

i. A, B, C, D and E are positive integers. ii. A + B + C is odd and D × E is even. 40. How many of the above numbers, at the most, could be odd? 1.  5 2.  2 3.  3 4.  4 5.  Cannot be determined

1.14 

  Quantitative Aptitude and Data Interpretation

41. How many of the above numbers at least, are odd? 1.  1 4.  4

46. How many factors of N = 1020 will be divisible by 15 but not by 5?

2.  2 3.  3 5.  Cannot be determined

1.  6 4.  0

42. Which of the following is definitely false?

3.  12

47. How many factors of N = 1020 will be divisible by 5 but not by 15?

I.  AB + AC is odd II.  AB + AD is odd III.  AD + AE is even 1.  (I) alone 2.  (II) alone 3.  (III) alone 4.  (I) and (II) 5.  None of these

1.  6 4.  0

2.  3 5.  2

3.  12

48. What is the largest number x such that (2004!)! is

divisible by (((x!)!)!)?

43. A 4-digit number is multiplied by N and the resultant such obtained is the same 4-digit number repeated to form an 8-digit number. Which of the following is true about N?

1.  3 4.  0

1.  N is divisible by 73 2.  N is divisible by 137 3.  N is divisible by both 73 and 137 4.  N is divisible by 13 5.  None of these

2.  4 5.  2

3.  6

49. How many zeroes will be there at the end of 25 × 235 × 40 × 50 × 60 × 165? 1.  6 4.  7

2.  24 5.  None of these

2.  8 5.  4

3.  5

50. N = 23 × 53. How many sets of two factors of N are co-prime to each other?

44. What is the total number of factors of N = 1020? 1.  12 4.  16

2.  3 5  2

1.  12 4.  11

3.  36

2.  24 5.  None of these

45. How many factors of N = 1020 will be odd? 2.  24 5.  None of these

ANSWER KEYS

1.  12 4.  16

3.  8

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

4

4.

2

5.

3

6.

3

7.

2

8.

4

9.

2

10.

1

11.

3

12.

2

13.

2

14.

3

15.

4

16.

2

17.

1

18.

2

19.

2

20.

4

21.

4

22.

1

23.

4

24.

4

25.

2

26.

3

27.

2

28.

3

29

1

30.

2

31.

2

32.

1

33.

5

34.

5

35.

5

36.

5

37.

2

38.

2

39.

3

40.

4

41.

1

42.

1

43.

3

44.

2

45.

3

46.

4

47.

1

48.

1

49.

1

50.

2

3.  23

Number System 

  1.15

HINTS AND EXPLANATIONS 1. (2)  Let number be x   4(2x + 6) = 96 or, 8x = 96 – 24 = 72

∴×=9

2. (2)  Factors of 3150 are 5² × 3² × 2× 7   So multiplication by 14 make it a perfect square. 3. (4)  Let the original fraction = x+1

1

= – 2 y + 1

x Y

⇒ 2 x – y = – 1 and

13. (2) There are 6 places in which to type two 1’s, the remaining 4 places being filled with 2003.  Hence, there are 6 choices for the place of the first 1 and then 5 for the second 1, a total of 30. But only half of these look different from each other so there are 15 possibilities. 14. (3)  Number is in between 30 and 90.   Using second information it is odd and not 49 or 81.

x+1 y+1

1

= – ⇒3 x – y = 2 3

So, × = 3 and y = 7. Alternatively, going through the options is the best way of solving such questions.

 Also it is not prime, so 31, 37, 41, 43, 47, 53, 57, 59, 61, 67, 71, 73, 79 83, 87 and 89 are also excluded.  Now it is not divisible by 3 or 5, 33, 35, 39, 45, 51, 55, 63, 65, 69, 75, 85 are also excluded.  The only remaining possibility is 77. Hence, there is only one such number.

4. (2)  Here, 3 – 2 = 1, 4 – 3 = 1, 5 – 4 = 1 and so on

15. (4) Since 5! and n! for all n > 5 are divisible by 10, the required units digit is the units digit of 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33. Hence the answer is 3.

 So, required no. = (LCM of 3, 4, 5, 6, 7) –1 = 420 – 1 = 419

16. (2) Put the smallest possible number of marbles in each box.

5. (3)  Unit digit of 27257 = Unit digit of 757

 Box 1 = Box 2 = 1 marble. Now put 2 marbles in box 3, 3 marbles in box 4, and so on. mallest total number of marbles is 1+ 1 + 2 + 3 + 4 + 5 + 6 + 7 = 29 marbles.



  757 = 756 × 7 = .....1 × 7 = ......7

17. (4)  METHOD 1: Using the concept of LCM

  Unit digit of 58549 = Unit digit of 849

  849 = 848 × 8 = .........6× 8 = .......8

  Final unit digit = ............7 × .......8 = .................6 6. (3)  8778 = 8776 × 872 = (.................9) = (............9)  (78)87 = (78)(4×21+3) = (78)4×19 (78)3 = (.................2) = (............2)

(.............. 1) × (.............. 6) ×

 So the unit digit of 8778 – 7887 = (………….9) – (……….2) = 7 7. (2) All the digits from 1-9 occur 10 times at units place and 10 times at tens place in between any 100 consecutive natural numbers.   So, Number of times 7 occur in between 1 to 100 = 20

 N leaves a remainder of 1 when divided by 2, 3, 4, or 5. Suppose we subtract 1 from N. The result is a multiple of 2, 3, 4, and 5. The least common multiple of all four numbers is 60.  Moreover, all common multiples of 2, 3, 4, and 5 are multiples of 60. Then N is 1 more than a multiple of 60. N is in the set {61, 121, 181, 241, 301, 361, …}. Divide each of these by 7. The smallest of them that is a multiple of 7 is 301. The smallest value that N can be is 301.  METHOD 2:  Determine the units digit and then the possible multiples of 7.  N leaves a remainder of 1 when divided by 5, so N has a unit digit of 1 or 6. N leaves a remainder of 1 when divided by 2, so N is odd. Therefore the unit digit is 1. The multiples of 7 that have a unit digit of 1 are the product of 7 and a number with a units digit of 3; i.e., 7 × 3, 7 × 13, etc. Then N is one of the numbers in the set {21, 91, 161, 231, 301,371, …}.

  →Number of times 7 occur in between 1 to 600 = 120

 The smallest of these that leaves a remainder of 1 when divided by 3 or 4 is 301.

  → Number of times 7 occur in between 20 to 600 = 120 – 2 = 118

18. (2) Cheque is $14.32; received = $32.14; spent = $3.50 Remaining = $32.14 - $3.50 = $ 28.64

8. (4)  Unit digit of the N (prime number) = 1, 2, 3, 5, 7, 9

19. (2) Take values and check using options. Option 2 is not definitely true.

  Unit digit of N = 1, 4, 9, 5 2

  Unit digit of (N2 + 1) = 2, 5, 0, 6. 10. (1) 103 is a prime number. LCM of two natural numbers = 103 is possible only if the numbers are 1 and 103. Hence HCF = 1

27. (1) 

(91 – 1) 90

=

13

0+1

91 90 13 1

11. (3) Suppose Amar solved n questions correctly. Then 58 = 5n − 2(20 − n) = 7n − 40, so 7n = 98 and therefore n = 14.

 

12. (2) Sum of six consecutive odd integers starting with n = n+(n+2) +(n+4)+ (n + 6) + (n + 8) + (n + 10) = 6n + 30 = 6(n + 5).

28.

 It can be seen now that smallest cube of the form 6 (n + 5) occurs when n + 5 = 36, so n = 31

Remainder obtained

=

13 3202 101

=

–

13

3100  × 3100 × 32 101 3100 101

= 1.

( – 1) 90 13

  Quantitative Aptitude and Data Interpretation

1.16 

3×3 101

9 101

=

7

31. Remainder of = 2 11

44 22 33



5

=

40. A, B and C would all be odd. Either D or E could also be odd. (One of these, namely, either E or D, must be even). Hence four numbers, at the most, could be odd. 41. We are trying to arrive at the minimum possible value of odd numbers. Only one number among A, B and C need be odd. Both D and E could be even. (That is, neither D, nor E, need to be be odd.) Hence at least one number is odd.

7

5

=

7



= 9 (Remainder)

4 + 4 + 4 ...................10 times

30. We can write 40

So unit digit of (2568 × 2!)180! × (3252 x 5!)200! × (3256) 5! = 0

= 5 (remainder) 7 11

44 22 33

5

2 (4 n + 3) even 5

= Remainder of

2 11

44 22 33

43. Assume a four digit number abcd.

5

2 (4 n + 1) = 5

N=

abcdabcd

abcd

= 10001 ⇒ N = 10001 = 73 × 137

44. 1020 = 171 × 31 × 51 × 22

Put n = 1 ⇒ Remainder = 2

Total number of factors = (1+1) (1+1) (1+1) (2+1) = 24

32. (4!)  Onwards remainder obtained will be 0.

45. To obtain odd factors, we would consider only 171 × 31 × 51 = (1+1) (1+1) (1+1) = 8

  So we will be considering only till 1! + 2! + 3! = 9

46. Its not possible.

9   = remainder 9 24

47. 1020 = 171 × 31 × 51 × 22

34. See the solution of Q. 32. 37. Ideally, in these types of questions, we divide each component in the numerator separately. 11

1

2 3

33



1 power of 3 (0)

divided by 4 ⇒ Remainder = 0

1 power of 5 (1)

[= (-1)odd] divided by 4 ⇒ Remainder = 3

1+0+3 4

=

So factors will come from 171 × 30 × 51 × 22. So we can use – 2 powers of 17 (0 and 1)

divided by 4 ⇒ Remainder = 1

22

To make the factor divisibly by 5 and not divisible by 15, we will not consider any power of 3.

3 powers of 2 (0, 1 and 2) So number of factors = 2 × 1 × 1 × 3 = 6

4 4

38. Unit digit of (2568 x 2!)

180!

48. (1)  Answer would be same if the question is ⇒ (2004!) is divisible by ((x!)!) or

=6

(2004) is divisible by (x!). Now use the options.

Unit digit of (3252 x 5!)200! = 0 Unit digit of (3256) 5! = 6

  EXERCISE  2 1. Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12? 1.  0 4.  6

2.  9 5.  2

3.  3

2. The integers 34041 and 32506, when divided by a threedigits integer n, leave the same remainder. What is the value of n? 1.  289 4.  307

2.  367 5.  313

3.  453

3. The left most digit of an integer of length 2000 digits is 3. In this integer, any two consecutive digits must be divisible by 17 or 23. The 2000th digit may be either x or y. What is the value of x + y? 1.  6 4.  12

2.  7 5.  5

3.  8  

__

 

________

4. What is the smallest integer n such that ​ √  n ​ +​ √  n + 2005 ​  is an integer?

1.  217

4.  45988

2.  4568 5.  None of these

3.  39204

Number System 

  1.17

5. How many numbers between 1 to 550 are divisible by 5 but not by 9?

14. What is the smallest natural number that can be expressed as a sum of 10 consecutive natural numbers as well as the sum of 9 consecutive natural numbers?

1.  98 4.  99

1.  145 4.  115

2.  97 5.  None of these

3.  101

6. A and B are two distinct digits greater than zero. If the sum of the two-digit numbers formed by using both the digits is a perfect square, what is the value of (A + B)? 1.  9 4.  17

2.  11 5.  21

3.  13

7. A number has exactly 15 composite factors. What can be the minimum number of prime factors of this number?

1.  2 4.  5

2.  3 5.  1

3.  4

8. A number has exactly 15 composite factors. What can be the maximum number of prime factors of this number? 1.  2 4.  5

2.  3 5.  6

3.  4

9. How many number of zeroes will be there at the end of 12! expressed in base 6? 1.  4 4.  7

2.  5 5.  8

3.  6

2.  135 5.  105

3.  125 51

15. Find the last two digits of 4950 . 1.  01 2.  41 3.  09 4.  49 5.  61 16. Let S be the set of integers x such that I.  100 < × P and R > S.

X+ 4020 – 2 (x -4522) = 2910, x=10154

Q   P   R   S

Number of males in Chota Hazri = 10154-4522 = 5632

4  

2   3   1

37. From II, b=2d

2  

1   4   3

Hence, b=10, d=5 or b=4, d=2

The distribution of coins can be of two types in both the cases, S gets an odd number. 29. Option (2) is the answer as it is one of the conditions mentioned in the question itself.

From III, e+a = 10 or e+a=4 From I, a+c= e or e-a=c From III and and I, we get 2e=10+cor 2e=4+c

  1.23

Number System  c

e = 5 + ​ _2 ​ ..... (i)

40. All the factors which are divisible by 50 but not divisible by 100 will have at least two powers of 5, and one power of 2.

c

Or e=2+ ​ _2 ​ ..... (ii)

And its format will be 21 × 52+y.

From (I), we can take c=2,4,6,10.

So number of divisors = 1 × 6 × 5 × 9 = 270

For c = 2, e = 6

41. Since there are five persons in the group, so possible no. of friends is 0, 1, 2, 3, 4. It seems here that everybody is having different number of friends, so the answer is zero. But anybody having four friends ensures that nobody is having 0 friends. So, at least two persons must have same number of friends.

C = 4, e = 7 (Not possible) C = 6, c = 8 (Not possible) C = 10, e = 10 (Not possible since both c and e cannot be10)

43. 123456………..125126 = 123……….125× 1000 + 126 5625 = 625 × 9

From (ii), we have c = 2, 4,6,10.

123……….125× 1000 is divisible both by 625 and 9.

For c = 2, e = 3 (Not possible)

So remainder obtained = 126

C = 4, e = 4 (Not possible)

44. Answer is LCM (1, 2, 3, 4, 5, 6, 7) = 420

C = 6, e = 5 (Possible)

45. Sum of integers from 1 to 10 = 55

C = 10, e=7 (Not possible)

Sum of integers from 21 to 20 = 155

Considering the possibility from B that c = 6 and e = 5 means e + a = 4, a = – 1 (not possible) Hence ,only possibility is b = 10, d = 5, c = 2, e = 6. e + a= 10, a=4 38. Let the number of five-rupee, two rupee and one-rupee coins be x, y and z respectively. x + y + z =- 300

Sum of integers from 21 to 30 = 255, Sum of integers from 1 to 30 = 465 We will add now few more numbers to reach 575.

31

32

33

34

496

528

561

595

5x + 2y + = 960 5x + y + 2z = 920

If we add till 34, sum exceeds beyond 575. Hence number added twice = 595 – 575 = 20

y z = 40



And x+2y = 340

46. There will be 19 Nine’s, 1 Eight and 1 Three.

Use the answer choices now.

47. It can be observed that unit digit of 332 = 1. Now any number having 1 as the unit digit will always give 2 at the unit place when divided by 50.

If x=140, y=100 and z=60, this satisfies the given conditions.

So, the answer is 2. 39. Let the total number of pages in the book be n. n

Let page number x be repeated. Then n (n + 1)

x + = 1000

2

Thus,

Since

n + x = 1000 Σ i=1

n (n + 1) 2 n (n + 1) 2

Hence x= 10.

48. Let us assume that there are N digits in this system of writing. So, (30)N = 3 × N1 + 0 × N0 = 24 ⇒ 3N = 24 ⇒ N = 8 So, this system of writing has 8 digits.

≤ 1000 gives n=44

990 ( for n = 44)

In this system, 3×4×5 = 60 will be written as 74. (60 = 7 × 81 + 4 × 80) Alternatively, since this system is having 6 as one of its digits, so minimum value of N will be 7. Again, 24 is written as 30 in this system, so N is less than 10. Now use hit and trial for N = 7 or 8 or 9 to find out N in 24 = (30)N.

1.24 

  Quantitative Aptitude and Data Interpretation

49. Remainder obtained from N = 18 Remainder obtained from P = 11 Remainder obtained from N + P = 4, however, it should have been 18 + 11 = 29 So, the divisor = 29 – 4 = 25

50. Number of one rupee coins = 158. Possible arrangements of coins are listed as 1, 2, 4, 8, 16, 32, 64 and 31. Number of bags = 8. So the least number of bags required = 8.

r e v i e w

t e s t

 1

Number System This review test

based on the following chapter

  Number System

  INSTRUCTIONS 1. This test contains 20 questions. You have forty-five minutes to complete the test. 2. All questions carry four marks each. Each wrong answer will attract a penalty of one mark. 3. Do your rough work only on the Test Booklet and not on the Answer Sheet. 1. It is a fact that every natural number can be LCM for a set of numbers. For example, consider 24. LCM of 8, 3 = 24 LCM of 12,24 = 24 LCM of 2, 8, 24 = 24 and so on. In this case, we have atleast three sets of distinct numbers [1st set (8,3), 2nd set (12,24), 3rd set (2, 8, 24)] for which LCM = 24. How many natural numbers from 1 to 100 can be the LCM of two or more than two distinct natural numbers in only one way (consider x, y = y, x ⇒ interchangeability of numbers is not allowed)? 1.  0 4.  25

2.  1 5.  26

3.  24

2. f(n) = Sum of digits of n until single digit is obtained. Find f(19101). 1.  0 4.  8

2.  3 5.  1

3.  6

3. Integers from 1 to 33 are written side by side one after the other as follows:  123456...........33. What is the remainder when this number is divided by 9? 1.  0 2.  1 3.  3 4.  6 5.  7 4. Natural numbers starting from 5 till N are written side by side one after the other to form a big number P = 5678910111213...............................N. If 78 < N < 85, how many values of N are possible so that when this number P is divided by 9, remainder obtained is 0? 1.  0 2.  1 3.  2 4.  3 5.  4 5. LCM of two distinct natural numbers = 263. How many different value/s of HCF is/are possible for these two distinct natural numbers? 1.  0 2.  1 3.  2 4.  3 5.  4 6. What is the tens place digit of 12626×12525? 2.  3 3.  7 1.  0 4.  9 5.  1 7. If n² is a cube, then which of the following statements is always true? 1.  n is odd 2.  n is even 3.  n³ is square 4.  n is a cube 5.  None of these 8. (1721 + 1921) is not divisible by 1.  36 4. 18

2. 8 5.  2

3. 9

1.26 

  Quantitative Aptitude and Data Interpretation

9. A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? 1. 17 2. 35 3. 59 4. 37 5.  19 10. What is the remainder when 1044 × 1047 × 1050 × 1053 is divided by 33? 1. 13 4. 8

2. 22 5.  20

3. 30

11. A natural number P is divided by another natural number Q. P and Q both have R as the common factor between them. Which of the following is definitely true (R ≠ 0)? 1.  When P is divided by Q, remainder obtained = R 2. When P is divided by Q, remainder obtained can never be equal to R 3. When P is divided by Q, remainder obtained has to be a multiple of R 4. When P is divided by Q, remainder obtained has to be a factor of R 5.  None of these 12. In a 50 digit positive number, all the digits are 4 except for the nth digit. This number is divisible by 13 for some choice of that nth digit. How many possible values can n have? 1. 13 2. 17 3. 21 4. 24 5.  29 13. What is the number of positive integer triplets(a, b, c) that satisfy abc = 4(a + b + c) with a < b < c? 1. 1 4. 7

2. 3 5.  9

3. 5

16. There is a string of 2003 beads which is to be cut between two beads as close to the middle as possible resulting into two strings, one with 1001 beads and one with 1002. The beads are glued onto the string so they won’t slide off. After this, shorter string of the two is taken and cut into two as close to the middle as possible and then keep repeating the process, at each step choosing a shorter string. Either of the strings can be chosen if they are equal. Cutting the strings is known as jump. How many jumps are required to have a string with only one bead? 1.  5 4.  10

2.  5 5.  11

3.  9

17. In the above question, how many strings would be there if the original string had 999,999 beads? 1.  15 4.  23

2.  18 5.  25

3.  20

18. How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine? 1.  40 4.  38

2.  37 5.  41

3.  39

19. A positive whole number M less than 100 is repre sented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals 1.  31 4.  91

2.  63 5.  None of these

3.  75

14. If n2 = 12345678987654321, what is n?

20. The number of positive integers n in the range 12≤ n≤ 40 such that the product (n—1)(n—2)...3.2.1 is not divisible by n is

1.  12344321 4.  1111111

1.  5 4.  14

RoI/minute

% Accuracy

Section Test   1

Marks

1.  y(x-z)2 is even 2.  y2(x-z) is odd 3.  y(x-z) is odd 4.  z(x-y)2 is even 5.  None of these

3.  13

Wrong



Right

15. Let x, y and z be distinct integers x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?

2.  7 5.  9

Attempts

2.  1235789 3.  111111111 5.  None of these

ANSWER KEYS

Review Test 1  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

5

3.

3

4.

3

5.

2

6.

1

7.

4

8.

2

9.

4

10.

3

11.

3

12.

4

13.

3

14.

3

15.

1

16.

4

17.

3

18.

3

19.

4

20.

2

  1.27

HINTS AND EXPLANATIONS 1. We need to find out the prime numbers from 1 to 100 in this case ⇒ total 25 prime numbers.

6. We know that for tens place digit, our concern should be only for the last two digits (rightmost two digits) of the number.

2. We have to find out the sum of digits of the number 19101 till we get a single digit.



So tens place digit of 12626×12525 = Tens place digit of 2626×2525



Now we will find out the tens place digit of 26 26 and 25 25 one by one.



For 2525 – All the powers of 2525 will end up with ‘25’ as the last two digits.



For 2626 – For every power equal to greater than 262, last two digits = 76 (Can be seen by actual multiplication)



Alternatively, last two digits of any number is going to be same as the remainder obtained when divided by 100.



Remainder (2626/100 ) = Remainder (67613/100 ) = Remainder (7613/100 ) = Remainder (57766×76/100 ) = Remainder (767/100 ) = 76 (Finally)



So tens place digit of 12626×12525 = Tens place digit of 2626×2525 = Tens place digit of 25 × 76 = 1900



Sum of digits of 19 = 1 + 9 = 10 ⇒ Sum of digits of 10 = 1 + 0 = 1



Hence Sum of digits of 19101 = Sum of digits of 1101 = 1

3. When numbers are written one after the other (as given in the question), to check the divisibility of that number by 9, we are simply required to find the sum of all the numbers (and not the digits in the number).

So, sum of the integers from 1 to 33 = 33×34/2 = 3317



When this number is divided by 9, remainder obtained = 3

4. When numbers are written one after the other (as given in the question), to check the divisibility of that number by 9, we are simply required to find the sum of all the numbers (and not the digits in the number).

So, sum of the integers from 5 to 79 (79 is the 1st possible value for N) =3150 = Divisible by 9



To find out the next value of N, we just have to keep looking that which next number gives sum of digits 9 or a multiple of 9.



Till 80 – Numbers till 79 (divisible by 9) + 8 + 0 = Numbers till 79 (divisible by 9) + 8 = Not divisible



Till 81 – Numbers till 79 (divisible by 9) + 8 + 0 + 8 + 1= Numbers till 79 (divisible by 9) + 17 = Not divisible



Till 82 – Numbers till 79 (divisible by 9) + 8 + 0 + 8 + 1 + 8 + 2 = Numbers till 79 (divisible by 9) + 27 = Divisible by 9



7. Assume values and try to refute the options. 8. This number will be divisible by all the factors of 36 (17 + 19). 9. When twice the original number is divided by the same divisor, remainder should have been twice

24 = 48, but it is 11 in this case. Hence the divisor = 48 – 11 = 37

10. Instead of dividing 1044 × 1047 × 1050 × 1053 by 33, we will divide the numbers by 11 and 3 (33 = 11 × 3) separately, which is considerably easier than dividing a number by 33.

1044 × 1047 × 1050 × 1053/3

Till 83 – Numbers till 82 (divisible by 9) + 8 + 3 = Numbers till 82 (divisible by 9) + 11 = Not Divisible by 9



1050 is divisible by 3, hence remainder obtained when 1044 × 1047 × 1050 × 1053 is divided by 3 is 0.



Till 84 – Numbers till 82 (divisible by 9) + 8 + 3 + 8 + 4 = Numbers till 82 (divisible by 9) + 23 = Not Divisible by 9



Remainder obtained when 1044 × 1047 × 1050 × 1053 is divided by 11:



Hence value of N = 79, 82 = Two values



Remainder obtained when 1044/3 = 10



Remainder obtained when 1047/3 = 10 + 3 = 13 = 2 Remainder obtained when 1050/3 = 10 +6 = 16 = 5



Remainder obtained when 1053/3 = 10 + 9 = 19 = 8

5. 263 is a prime number. LCM = 263 for two distinct natural number is possible only if the numbers are 1, 263 (other possible way is 263, 263 for same numbers). Hence there can be only one HCF.

  Quantitative Aptitude and Data Interpretation

1.28 



So, remainder obtained when 1044 × 1047 × 1050 × 1053 is divided by 11 = Remainder obtained when 10 × 2 × 5 × 8 is divided by 11 =8 Final remainder will be same as a number which when divided by 11 gives remainder 8 and is divisible by 3 = 30



Jump 9 gives 10 strings, shortest length 3.



Jump 10 gives 11 strings, shortest length 1.

17. Lowest power of 2 ≥ 106 is to be calculated.

Since 210 = 1024, 220 > 106 and 219 < 106

11. Assume some values and go through the options.



So the answer is 20.

14. 12 = 1

18. There are 101 integers in all, of which 51 are even.



11 = 121



From 100 to 200, there are 14 multiples of 7, of which 7 are even.



111 = 12321



There are 11 multiples of 9, of which 6 are even.



Hence the square root of the number given is 111111111 (1 written 9 times).



But, there is one integer (i.e., 126) that is a multiple of both 7 and 9 and also even.

15. Assume some values for x, y and z, and go through the options.



Hence, the answer is (51 – 7 – 6 + 1) = 39

16. Jump 1 gives 2 strings, shortest length 1001.

19. Since the last digit in base 2, 3 and 5 is 1, the number should be such that on dividing by either 2, 3 or 5 we should get a remainder 1. The smallest such number is 31. The next set of numbers are 61, 91. Among these only 31 and 91 are a part of the answer choices.

2

2



Jump 2 gives 3 strings, shortest length 500.



Jump 3 gives 4 strings, shortest length 250.



Jump 4 gives 5 strings, shortest length 125.





Among these, (31)10 = (11111)2 = (1011)3 = (111)5 Thus, all three forms have leading digit 1.

Jump 5 gives 6 strings, shortest length 62.



Hence the answer is 91.



Jump 6 gives 7 strings, shortest length 31.



Jump 7 gives 8 strings, shortest length 15.

20. From 12 to 40, there are 7 prime numbers, i.e., 13, 17, 19, 23, 29, 31, 37, which is not divisible by



Jump 8 gives 9 strings, shortest length 7.



(n- 1)!

c h a p t e r

 2

Average

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   What is Average and its various interpretations   Definitions and properties   Applications of Average in different cases   Different cases of Mixtures and Alligation   Method of solving question

  AVERAGE Traditionally, average is calculated by dividing the sum of all the numbers by the number of numbers.   Sum of numbers Number ofnumbers Let us find the average of four numbers 214, 215, 219, 224. 214 + 215 + 219 + 224 = 218 Average = 4 Average =

Central Value meaning of Average Average can also be seen as the central value of all the values given. Applying this definition for the above written numbers; let us assume the central value of all the given numbers= 214

Now find deviations of all the nos. from 214: 214 215 219 224 When assumed central value is (214): 0 +1 +5 +10 Now finding the average of deviation gives us 0 + 1 + 5 + 10 16 =4 = 4 4 So Average = Assumed central value + average of deviations = 214 + 4 =218 In the similar fashion, we can assume any value to be the assumed average and then finding the average of all the deviations will give us average. And when we are adding all the nos. and dividing it by number of numbers, then unintentionally we have assumed 0 to be the central value.

1.30 

  Quantitative Aptitude and Data Interpretation

Example  1 1 Example 

Average age of A, B, and C is 84 years. When D joins them average of A, B, C and D becomes 80 years. Now a new person E, whose age is 4 years more than D, replaces A and average age of B, C, D and E becomes 78 years. What is the age of A? Solution Solution

Since average age of A, B and C is 84 years so we can very safely assume that age of each of A, B, and C is 84 years. A = 84 years B = 84 years C = 84 years After D has joined them, the whole situation can be seen as: A B C D

Initially 84  yrs 84  yrs 84  yrs …..

finally 80  yrs 80  yrs 80  yrs 80  yrs

Decrease in the age of A, B, and C can be attributed to the increase in the age of D. so now after getting 12 years in total (4 years each from A, B, and C) D is at 80 years. So original age of D= 80- 12= 68 years. So age of E = 72 years Now average age of A, B, C, and D = 80 years; A + B + C + D = 320 And average of B, C, D, and E = 78 years: B + C + D + E = 312 (Since the average difference between the ages of A and E is 2 years,) Difference (A – E) =2 x 4 = 8 years Since E = 72 years, so A = 80 years Best part of using central value method of averages lies in the fact that with help of this method, every question of average can be done by mental calculation only.

Example  2 Example 

2

Average score of Rahul Dravid after 25 innings is 46 runs per innings. If after the 26th inning his average runs increased by 2 runs, then what is his score in the 26th inning? Solution Solution

Runs in 26th inning = Runs total after 26 innings – Runs total after 25 innings = 26×48 – 25×46 = 98

Alternatively, we can do this question by above given central value meaning also. Since the average increases by 2 runs per innings, so we can assume that 2 runs have been added to his score in each of the first 25 innings. Now, total runs added in these innings have been contributed by runs scored in 26th inning which must be equal to 25 × 2 = 50 runs. And after contributing 50 runs, his score in the 26th inning is 48 runs. Hence, Runs scored in 26th inning = New Average + old innings × change in average = 48 + 25 × 2 = 98. To have a mental mapping, we can see the whole situation as: Number of innings

Average in 1st 25 innings

Average in 1st 26 innings

Addition

1

46

48

2

2

46

48

2

3

46

48

2

…

…

…

..

…

…

…

..

…

…

…

..

25

46

48

2

26

48

Properties of average 1. Average always lies in between maximum and minimum value. It can be equal to the maximum or minimum value only in case of all the numbers being equal. Example: A1, A2, A3, and A4 are four numbers given where A1>A2>A3>A4. Average of these four numbers will always lies in between A1 and A4. However, if all the four numbers are equal (A1=A2=A3=A4) then the average will be equal to each of these numbers. Average = A1=A2=A3=A4. 2. Average is the resultant of net surplus and net deficit, as used in Central Tendency method. 3. When weights of different quantities are same, then we use simple method to find the average However, when we take different weights of different quantities, then it is known as weighted average and we use the method of weighted average to find the average.

Average  Example: Assume per capita income of India is USD 500 and per capita income of US is USD 200. Now if we merge India and US into one country then it can be seen that per capita income of this new country will not be equal to = USD 350 4. If the value of the each quantity is increased or decreased by the same value S, then the average will also increase or decrease respectively by S. 5. If the value of each quantity is multiplied by the same value S. Then the average will also be multiplied by S. 6. If the value of each quantity is divided by the same value S(S≠0) then the average will also be divided by S.

1.  Average involving Time Speed and Distance Total distance

Average age of 5 members of a family is 20 years. The youngest member of the family is 4 years old. At the time of birth of this youngest member, average age of rest of the members of the family was N years. What is the average age of the family (in terms of N) excluding the youngest member? Solution Solution

Sum of ages of all the members of the family = 100

So, the average age of all the members of the family excluding the youngest number = 96/4 = 24 = N So is the average age of the family (in terms of N) excluding the youngest member = N + 4

Total time

However, while solving the questions involving Time Speed and Distance, we should ideally assume some distance, preferably the LCM of all the speeds given. Example  3 Example 

5

Sum of ages of all the members of the family excluding the youngest number = 100 – 4 = 96

Some special Cases

Average speed =

Example  4 Example 

  1.31

4

Lovely goes to Patna from New Delhi at a speed of 40 kmph and returns with a speed of 60 kmph. What is her average speed during the whole journey?

Weighted Average We have seen that Average can be used only if the weights of all the factors, for which average is to be calculated, is same. So, we can see Weighted Average as a more generalized form of Average. This can be further understood with the following illustration: Class A

Class B

Solution Solution

No. of students

10

10

Let us assume that the total distance between Patna and New Delhi is 120 km (LCM of 40 and 60).

Average age

12 years

16 years

So, total time taken (Patna – New Delhi and New Delhi – Patna) = 3 + 2 = 5 hours

Now, if we combine both these classes, then average age of

So, Average Speed =

12 + 16

28 = 14 years. And this is 2 2 one standard example of Average.

240 = 48 kmph 5

all the students =

=

Let us see another example:

2.  Average involving Age If the average of a group of n persons is given at any point of time and we are required to find out the average of same group consisting same n persons, then it is done in the following way: 5 years back

10 years back

Now

10 years later

5 years later

N–5

N –10

N

N + 10

N+5

Class A

Class B

No. of students

12

16

Average age

10 years

14 years

Now, if we combine these two classes now, then average cannot be calculated as the above mentioned method, since this is an example where weights attached to different averages are different.

1.32 

  Quantitative Aptitude and Data Interpretation

Expression for Weighted Average

Example  5 Example 

11

Group No. No. of members Average age of group

In a mixture of 420 litres, the ratio of milk and water is 6 : 1. Now, 120 litres of the water is added to the mixture. What is the ratio of milk : water in the final mixture?

G1

   N1

   A1

G2

   N2

   A2

Solution Solution

If we combine both the groups, then average age of all the members = (N1 × A1 + N2 × A 2)/ (N1 + N2) = Aw We write this in the Conventional Criss-cross method as given below: Lower value (Average A1)

Higher value (Average A2) Weighted Average Aw

Quantity (at Average A1)    (n1)

Quantity (at Average A1)    (n2)

A2 – Aw n1 And we write this as:  n = Aw – A1 2 i.e.,

Quantity ( Lower. Priced) Higher Price – Averge Price = Quantity (Higher. Priced) Average Price – Lower Price

It is quite obvious from here that ratio of number of persons/items in different groups is proportionate to the deviations of their average from the average of all the people combined. This average of all the members combined is known as Weighted Average, and is denoted by Aw. This process of mixing two groups is also referred as Alligation.

Mixtures When two or more than two pure substances/mixtures are mixed in a certain ratio, it create a mixture. For the CAT preparation, we will confine ourselves mostly with homogenous mixtures.

Volume of milk = 360 litres and volume of water = 60 litres. When 120 litres of water is added, volume of water = 180 litres So, ratio of milk : water = 2 : 1

Example  6 Example 

6

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk? 1.  2 : 3 2.  1 : 2 3.  1 : 3 4.  3 : 4 Solution Solution

Ratio of milk and water = 80 : 20 When ¼ th of this mixture is sold, total volume of mixture will reduce by 25%, so 25% of milk and water both will reduce (this is nothing but the quantity of water and milk being sold out when 25 liters of mixture is being sold out). So, volume of milk and water after selling out ¼ th of mixture = 60 liters and 15 litres respectively. Addition of 25 litres of water will finally give us the following: Volume of milk = 60 litres and volume of water = 40 litres. Hence, the ratio of Water and Milk = 40 : 60 = 2 : 3. Hence option 1 is answer.

Example  7 Example 

7

How many litres of fresh water should be mixed with 30 litres of 50% milk solution so that resultant solution is a 10% milk solution? Solution Solution

Method 1:  Using Alligation 0%

Mixing without replacement In this particular type of mixing two or more than two substances, we mix one with other without any part of any mixture being replaced.

50% 10%

40

10

Average 

  1.33

Solution  7 7 Solition 

Example  9 Example 

So, ratio of fresh water added: milk solution = 4 : 1 Hence 120 litres of fresh water should be added.

I went to a hotel along with 12 friends of mine. I paid Rs 145 and all the others paid an equal amount. In the end when we did some calculations, we found that the average sum paid by all of us was Rs 5 more than what was originally paid by each of my friends. How much money did each of my friends pay? 1  Rs 120 2  Rs 100 3  Rs 80 4  Rs 70

Method 2: Principle of constant volume of one component Since we are adding fresh water, volume of milk will be constant. Now volume of milk = 15 litres = 10% of the new mixture So, 100% of the new mixture = 150 litres So, volume of fresh water added = 150 – 30 = 120 litres Method 3:  Principle of Inverse proportion We know that concentration is inversely proportional to the volume of solute added. So, in this case 30 × 50% = 10% × (30 + x), where x is the volume of water added.

9

Solution Solution

Assume that each of my friends paid = Rs x, hence total money paid = Rs 145 + 12 x Average money paid by all of us = (145 + 12x)/13 According to the question, (145 + 12x)/13 – 5 = x Solving this, we get x = 80. Hence option 3.

So, x = 120 litres Method 4:  Using equation In the final mixture, Milk = 10% = 15 litres 30 + x Total So, x = 120 litres Some more worked out examples:

Example  10 Example 

10

The average of eight numbers is 25, that of the first two is 20 and of the next three is 26. The sixth number is less than the seventh by 4, and less than the eighth by 6. the last number is 1.30 2.32 3.40 4.36

Example  8 8 Example 

Solution Solution

Neo is going to NDLS from PNBE by his car at a speed of 40 kmph. While coming back, he returns with a speed of x kmph. What should be the value of x so that his average speed during the whole journey is 80 kmph?

Sum of all the numbers = 200 Sum of 1st two numbers = 40 Sum of next three numbers (No.3, No.4, No.5) = 78 Hence sum of 1st five numbers = 118, so sum of 6th, 7th and 8th number = 82 -------------(1) Assume that sixth number = x, hence 7th no. = x + 4, 8th no. = x + 6 So, x + x + 4 + x + 6 = 82 ⇒ 3x + 10 = 82 ⇒ x = 24 So, last number (8th no.) = 30. Hence option 1.

Solution Solution

Maximum average speed cannot be more than or equal to twice the lower speed in any direction. Hence the average speed < 80 kmph. So, it is not possible.

1.34 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  1 1. The average age of 11 players of a team is 23 years. If the captain’s age is included, the average age increases by 1.5 years. The age of the captain is

8. The average age of 24 students and the class teacher is 16 years. If the class teacher’s age is excluded, the average is reduced by one year. Find the age of the class teacher.

1.  36 years 5 months 2.  38 years

1.  40 years 4.  56 years

3.  41 years

9. A vessel of 70 litres is filled with milk and water. 75 per cent of milk and 25 per cent of water is taken out of the vessel. It is found that the vessel is vacated by 60 per cent. Find the initial quantity of water.

4.  42 years 6 months 5.  None of these 2. Krishna’s father was five times as old as Krishna 5 years ago. After 10 years, he will be three times as old as Krishna. What is the average age of Krishna and his father today? 1.  10 years 4.  25 years

2.  20 years 5.  50 years

3.  30 years

3. The average age of 32 boys in a class is 17 years. If the age of two boys, each 20 years aged are excluded and the teachers age is included the average decreases by two. What is the teacher’s age? 1.  27 4.  49

2.  039 5.  51

3.  43

4. The average weight of 5 apples is 100 g and the average weight of 4 oranges is 80 g. If 2 apples and 2 oranges are picked from them then average weight is found to be 85 g. What is the average weight of the remaining apples and oranges? 1.  88 g 4.  95 g

2.  90 g 5.  92 g

3.  96 g

5. A person bought 20 kg of rice at Rs 10.50 per kg and 30 kgs at Rs 12 per kg. He mixed the two and sold the mixture at Rs 11.40 per kg. What was the gain in this deal (in Rs)? 1.  0 4.  75

2.  20 5.  5

3.  100

6. The average weight of 6 women decreases by 3 kg when one of them weighting 80 kg is replaced by a new woman. The weight of the new woman is 1.  62 kg 4.  72 kg

2.  60 kg 5.  None of these

3.  70 kg

7. Rs 4000 is divided into two parts such that one part is put out at 3% and the other at 5%. If the annual interest earned from both the investments be Rs 144, find the first part. 1.  Rs 4000 4.  Rs 3500

2.  Rs 2800 5.  Rs 2600

3.  Rs 3800

1.  21 litres 4.  32 litres

2.  38 years 5.  None of these

2.  25 litres 5.  None of these

3.  50 years

3.  27 litres

10. How many litres of fresh water should be mixed with 30 litres of 50% milk solution so that resultant solution is a 10% milk solution? 1.  120 litres 4.  60 litres

2.  25 litres 5.  160 litres

3.  150 litres

11. Average of 10 two digit positive integer is Z. However, one number AB is taken as BA, then the average increases to Z + 2.7. What is the value of |B – A|? 1.  1 4.  4

2.  2 5.  5

3.  3

12. In the above question, how many set of values for A and B are possible? 1.  5 4.  8

2.  6 5.  0

3.  7

13. How many runs did Rahul score in his 32nd match? A.  For the first 30 matches his average was 36. B.  His average run score is 32 till 31st match. C. The average till 31st match is greater than his score in 32nd match.

1.  A and B together are sufficient 2.  A and C together are sufficient 3.  B and C together are sufficient 4.  All A, B and C together are necessary 5.  All A, B and C even together are not sufficient.

14. How much water should be added to a mixture so that water may be 20 per cent of the final mixture? A.  The mixture of milk and water measures 80 litres. B.  It contains 5 per cent water initially. C.  It contains 76 litre milk initially.

1.  A alone is sufficient 2.  B and C together are sufficient 3.  Any two of the three are sufficient. 4.  A, B and C all the three together are necessary 5.  All the three even together are not sufficient.

Average  15. There is a sequence of 11 consecutive odd numbers. If the average of first 7 numbers is X, then find the average of all the 11 integers. 1.  X + 3 4.  X + 7

2.  X + 4 5.  X

3.  X + 5

Direction for questions 16 to 19:  Read the passage below and solve the questions based on it. There are two brands of TVs, Onida and Videocon in the market. Onida is an old brand launched in 1990 and Videocon is a new brand launched in 1997. For both these brands, 20% of the TVs purchased every year are disposed off as out-dated exactly two years later. It is known that 10 Onida TVs were disposed off in 1997. The following table gives us the no. of TVs in operation at the end of the year from 1996 to 2000.

Onida Videocon

1995

1996

1997

1998

1999

2000

120

162

182

222

236

236

0

0

30

80

124

134

16. What is the average number of Videocon TVs disposed every year off by 2000? 1.  4 4.  10

2.  12 5.  7

3.  8

17. What is the average number of Onida TVs purchased every year till 1995? 1.  20 4.  32

2.  24 3.  28 5.  Cannot be determined

18. For which of the following years, average of Onida and Videocon disposed maximum? 1.  1997 4.  2000

2.  1998 3.  1999 5.  Cannot be determined

19. What is the average number of Videocon TVs purchased every year by 2000? 1.  33.5 4.  35

2.  37.5 5.  None of these

3.  40

20. Mohit was conducting an experiment in which the average of 11 observations came to be 90. Average of first five observations was 87, and that of the last five was 84. What was the measure of the 6th observation? 1.  165 4.  135

2.  150 5.  125

3.  145

21. There are five delegates attending the meeting. The weight of the first delegate is 200 kg and the weight of the 2nd delegate is 20% higher than the weight of the third delegate, whose weight is 25% higher than the 1st delegate’s weight. The fourth delegate at

  1.35

350 kgs is 30% lighter than the fifth delegate. Find the average weight of all the five delegates. 1.  310 4.  240

2.  320 5.  None of these

3.  300

22. In an exam the average was found to be p marks. After deducting typographical error the average marks of 94 students reduced from 84 to 64. Due to this the average came down by 18.8 marks. What was the number of students who took the exam? 1.  100 4.  120

2.  90 5.  None of these

3.  110

23. During an ODI match, Agarkar, Saurav, Sachin, Dravid and Ganguly scored an average of 39 runs. Dravid scored 7 more than Ganguly. Ganguly scored 9 fewer than Agarkar. Saurav scored as many as Dravid and Ganguly combined and Saurav and Sachin scored 110 runs between them. How many runs did Sachin score? 1.  47 4.  57

2.  51 5.  None of these

3.  53

24. The average temperature of Khammam in the first four days of a month was 58o C. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifty day of Khammam? 1.  240o C 4.  46 o C

2.  232 o C 5.  None of these

3.  64 o C

25. An airplane flies along the four sides of a square field at the speeds of 200, 400, 600 and 800 km/h. The average speed of the plane around the field in km/h is 1.  384 4.  284

2.  400 5.  432

3.  500

26. Three years ago, the average age of A and B was 18 years. With C joining them, the average age becomes 22 years. How old is C now? 1.  24 years 4.  30 years

2.  27 years 5.  42 years

3.  28 years

27. The average of three numbers is 135. The largest number is 180 and the difference of the other numbers is 25. The smallest number is 1.  130 4.  100

2.  125 5.  None of these

3.  120

28. Tanuj Johri travels from X to Y at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for the whole journey? 1.  36 kmph 4.  50 kmph

2.  45 kmph 3.  48 kmph 5.  None of these

1.36 

  Quantitative Aptitude and Data Interpretation

29. A worker is paid x rupees for painting every 10 metres of a wall and y rupees for painting every extra metre. During one week, he painted 10 metres on Monday, 13 metres on Tuesday, 12 metres on Wednesday, 11 metres on Thursday and 12 metres on Friday. What is his average daily earning in rupees for the five day week?

4.  5x + 8y 5.  None of these 30. Average of ten positive numbers is X . If each number increases by 10 per cent then X

ANSWER KEYS

1.  x + (8/5)y 2.  (5x + 9y)/5 3.  10 x + (8/5)y

1.  Remains unchanged 2.  Is increased by 10% 3.  May decrease 4.  May either increase of decrease 5.  Cannot be determined

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

5

3.

2

4.

3

5.

1

6.

1

7.

2

8.

1

9.

1

10.

1

11.

3

12.

2

13.

5

14.

3

15.

2

16.

1

17.

5

18.

5

19.

2

20.

4

21.

2

22.

1

23.

4

24.

3

25.

1

26.

1

27.

4

28.

3

29

1

30.

2

HINTS AND EXPLANATIONS 1. (3)  Captain’s age = 12 × (23 + 1.5) – 11×23



  So, weight of 3 apples and 2 oranges remaining = (500 + 320 – 340) g = 480 g



  Average weight = 480/5 = 96 g.

  = 294 – 253 = 41 years.

2. (5) Let Krishna’s present age be x years and his father’s present age be y years.

  Now, 5(x – 5) = (y – 5) ⇒ 5x – y = 20 ...(i)



  Again, 3 (x + 10) = y + 10 ⇒ 3x – y = – 20..... (ii)



  From eqn. (i) and (ii) we get



  x = 20, y = 80



  So, present average age = 50 years

5. (1)  Gain = 50 × 11.40 – (20 × 10.5 + 30 × 12) = 0 6. (1)  80 – 3 × 6 = 62 kg 7. (2)  Average rate =

144 4000



  Ratio = 14 : 6 = 7 : 3



  So, first part =

3. (2)  Total age of boys in the class is 32 × 17 = 544

7 10

× 100 = 3.6

× 4000 = Rs 2800



  Excluded age of two boys means (544 – 2 × 20) = 504

8. (1)  Class teacher’s age = 25 × 16 – 24 × 15



  The age of (32 – 2) = 30 boys





  Now, teacher's age = 504 – (30 + 1) × (17 - 2)

10. (1)  Using Alligation



  = 504 – 31 × 15 = 504 – 465 = 39 years

  = 400 – 360 = 40 years

0%

4. (3)  Weight of 5 apples = 500 g

  Weight of 4 apples = 320 g



  Weight of 2 applies and 2 oranges picked = 340 g

50% 10%

40

10

Average 

  1.37



  So, ratio of fresh water added: milk solution = 4 : 1



With respect to scoring runs



  Hence 120 litres of fresh water should be added.



Dravid = Ganguly + 7



Ganguly = Agarkar – 9



Saurav = Dravid + Ganguly



Saurav + Sachin = 110



⇒ Agarkar, Dravid, Ganguly, Saurav and Sachin scored 32, 30, 23, 53 and 57 runs respectively.

11. (3) AB is taken as BA, then the average increases to Z + 2.7 → BA – AB = 2.7 × 10 = 27

  BA – AB = 9 (B – A) = 27 → B – A = 3

12. (2) Total such sets possible = (4,1), (5,2), (6,3), (7,4), (8,5), (9,6) [(3,0) is not admissible as the numbers are of two digits] 14. (3)  Milk in the mixture = 80 – 4 = 76 litre

  If water will be 20%, then milk = 100 – 20 = 80%



  Given that 80% = 76 litre



Suppose Temperature on 1st day = 7K



Suppose temperature on 5th day = 8K





So, temperature on M + T + W + Th = 232

  So, Added water = 95 – 80 = 15 litre



Average Temperature on T + W + Th + F = 240



232 – 7 K = 240 – 8K ⇒ K = 8



Temperature on 5th day = 64º.

 

24. (3)

∴ 100% =

76 80

× 100 = 95 litre

15. (2) 

Average of first 7 numbers will be the 4th number = X (Given)



Average of all the 11 numbers will be the 6th number, i.e., X + 4.

16. (1)  Total number of TVs disposed by 2000 = 20% of TVs purchased (in 1997 + in 1998)

25. (1)

Let each side of the square field be x km



Videocon purchased in 1997 = 30 ⇒ Disposed off = 6



So, average speed of the plane



Videocon purchased in 1998 = 50 ⇒ Disposed off = 10



=



Total disposed off = 16 ⇒ Average Disposed off/year = 4

17. We don’t have any data regarding which year before 1995 how many TVs were purchased? Data given pertaining to any year is the combination of—i. Purchased previous years, ii. Purchased same year, iii. (negative) disposed off.

So cannot be determined.

19. Total number of existing Videocon TVs in 2000 = 134

Total purchased = Total number of existing + Disposed off = 134 + 16 (from Q16) = 150



So, average purchased = 37.5/year

x 800

+

x 600

4 × 2400

3 + 4 + 6 + 12



= 384

+

=

x 400

+



(A – 3) + (B – 3) = 36 ⇒ A + B = 42



Also A + B + C = 66 ⇒ C = 24.

27. (4)

Let the three numbers be X, Y and Z.



∴

X+Y+Z 3

= 135 ⇒ X + Y + Z = 405



Let X be the largest number



Weight of 4th delegate = 350 kg ⇒ weight of 5th delegate = 350/0.7 = 500 kg



∴ X = 180 ⇒ Y + Z = 225

Average weight = 1600/5 = 320 kg









(Agarkar + Saurav + Sachin + Dravid + Ganguly) make = 39 × 5 = 195.

200

25

Weight of 3rd delegate = 250 kg ⇒ weight of 2nd delegate = 300 kg

23. (4)

=

9600



22. Number of students = (84 – 64) × 94/18.8 = 100

x

26. (1)

20. 11 × 90 – 5 × 87 – 5 × 84 = 900 – 435 – 420 = 135. 21. Weight of 1st delegate = 200 kg

4x

Y – Z = 25 ⇒ Y = 125, Z = 100 (smallest number)

28. (3)

Let the distance between X and Y be x km.



Time taken from X to Y @ 40 km/h =

x 40

hours

1.38 

  Quantitative Aptitude and Data Interpretation

Time taken from Y to X @ 60 km/h = Average speed =

29. (1)

x 40

2x +

x

x 60

hours

= 48 km/h.

60



On Wednesday, the payment = Rs (x + 2y)



On Thursday, the payment = Rs ( x + y)



On Friday, the payment = Rs (x + 2y)



Average daily earning during the five-day week = 5x + 8y

On Money, the payment = Rs x

On Tuesday, the payment = Rs (x + 3y)



5

=x+

8y 5

.

30. (2)

  EXERCISE  2 1. Four gallons are drawn from a case full of wine. It is then filled with water. Four gallons of mixture are again drawn and the cask is again filled with water. The ratio of quantity of wine now left in the cask to that of mixture in it is 36 : 49. How much does the cask hold? 1.  30 gallons 4.  28 gallons

2.  25 gallons 3.  35 gallons 5.  None of these

2. There is a vessel holding 40 litres of milk. Initially, 4 litres of milk is taken out from the vessel and 4 litres of water is poured in. After this, 5 litres of mixture is replaced with 5 litres of water. And finally, 6 litres of mixture is replaced with 6 litres of water. How much of the milk (in ltrs.) is there in the vessel now?

1.  26.775 4.  27.42

2.  29.16 5.  None of these

3.  24.72

3. There is a vessel holding 40 litres of milk. Initially, 4 litres of milk is taken out from the vessel and 5 litres of water is poured in. After this, 5 litres of mixture from this vessel is replaced with 6 litres of water. And finally, 6 litres of mixture from this vessel is replaced with 7 litres of water. How much of the milk (in ltrs.) is there in the vessel now? 1.  22.42 4.  29.42

2.  27.09 5.  None of these

3.  24.72

4. There is a vessel holding 40 litres of milk. Initially, 4 litres of milk is taken out from the vessel and 5 litres of water is poured in. After this, 6 litres of mixture from this vessel is replaced with 7 litres of water. And finally 8 litres of mixture from this vessel is replaced with 9 litres of water. How much of the milk (in litres.) is there in the vessel now? 1.  22.82 4.  24.87

2.  20.92 5.  None of these

3.  26.78

5. To find three consecutive odd numbers, which of the following statements is/are sufficient? A. The average of four consecutive odd numbers starting from the last of the given odd numbers is 12.5

B. The difference of the highest and the lowest number is 4. C.  Sum of the squares of the three numbers is 251.

1.  A alone is sufficient 2.  B alone is sufficient 3.  Either A or C is sufficient 4.  A, B and C together are necessary 5.  C alone is sufficient

Direction for questions 6 and 7: Answer the questions based on the following information. A, B and C are three numbers. Let @ (A,B) = Average of A and B, / (A,B) = Product of A and B, and × (A,B) = The result of dividing A by B. 6. The sum of A and B is given by 1.  /(@ (A,B),2) 4.  @(×(A,B),2)

2.  ×(@(A,B)2) 3.  @(/(A,B),2) 5.  None of these

7. Average of A, B and C is given by 1.  @(/@/(@/(B,A),2),C),3) 2.  ×@((/@(B,A), 3,C), 2) 3.  /(×(×(@(B,A,), 2),C),3) 4.  /(×(@(/(B,A)2),3),2 5.  None of these 8. Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is 1.  n 2.  n+1 3.  k×n, where k is a function of n 2 7 5.  None of these 4.  n +

Average  9. For a 800 miles trip, a car travelled half the distance at 80 miles per hour and the other half at 100 miles per hour. What was the average speed of the car? 1.  18

2.  180

3.  90

8 5.  None of these 9 10. Having scored 98 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings? 4.  88

1.  28 4.  22

2.  26 5.  20

3.  24

11. In an examination, Hari’s average marks was 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How papers were there in the examination? 1.  8 4.  11

2.  9 5.  12

3.  10

12. During a year, a batsman played 20 innings. In the first four innings, he scored an average of 20.8 runs; in the next six, he scored an average of 33 runs; in the next seven innings, he scored an average of 17.5 runs and in the last three, he scored average zero. What was his average per innings for the year? 1.  20.19 4.  23.95

2.  21.3 5.  22.01

3.  23.9

13. Three classes x, y and z take an algebra test. The average score in class x is 83. The average score in class y is 76. The average score in class z is 85. The average score of all students in classes x and y together is 79. The average score of all students in classes y and z together is 81. What is the average for all the three classes? 1.  81 4.  84.5

2.  81.5 5.  None of these

3.  82

14. A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35 7 . What was the number erased? 17 1.  7 2.  8 3.  9 4.  6

5.  None of these

  1.39

Direction for questions 15 to 16:  Answer the questions based on the passage given below. The batting average (BA) of a hitter is computed from the runs scored, innings played, completed innings and incomplete innings. R1 =  Number of home runs scored in complete innings. N1 =  Number of complete innings. R2 = Number of home runs scored in incomplete innings. N2 = Number of incomplete innings. R1 + R 2 BA = N1 To accurately assess a hitter’s accomplishment, two other statistical computations called the MBA1 and the MBA 2 are also devised, which are defined as follows. R1 R1 N2 R max 0, 2 MBA1 = + N1 N1 N2 N1 MBA2 =

R1 + R 2

N1 + N2

15. Based on the above information, which of the following is true? 1.  MBA1 < BA < MBA2 2.  BA < MBA2< MBA1 3.  MBA2 < BA < MBA1 4.  BA < MBA2 5.  None of these 16. An experienced cricketer with no incomplete innings has BA of 50. The next time he bats, the innings is incomplete and he scores 45 runs. It can be inferred that 1.  BA and MBA1 will both increase 2.  BA will increase and MBA2 will decrease 3. BA will increase and not enough data is available to assess change in MBA1 and MBA2 4.  BA will increase and MBA1 will decrease. 5.  None of these Direction for questions 17 to 19:  Read the passage below and solve the questions based on it. Ten different samples of milk solution—A, B, C, D, E, F, G, H, I and J are taken and the concentration of each sample (total quantity of milk as a percentage of total quantity of solution) was found out and the results were tabulated as follows: Sample A B C D E F G H I J Concentration 78 57 82 84 98 66 34 87 79 71 (%)

1.40 

  Quantitative Aptitude and Data Interpretation

17. If two samples of milk are taken and it is required to form a sample whose concentration is more than 80 per cent, then a maximum of how many distinct pairs of samples are there, which will never give the desired result for any ratio of their volumes?

1.  2491 4.  2591

1.  30 4.  15

In the entrance examination of IIMs, there were 200 questions each of which carried the same marks. A correct answer gets 2 marks and there is a negative marking of 100%. A total of 70 candidates took the exam and it was later found that the average marks obtained by these 70 candidates was 240. The candidates were not required to attempt all the questions. None of the candidates got more number of incorrect answers than correct answers.

2.  48 5.  16

3.  12

18. A triplet is a set of three distinct samples taken in some ratio of their volumes. How many such distinct triplets are there, which when mixed can give a sample with more than 80 per cent concentration? 1.  50 4.  200

2.  100 5.  210

3.  150

19. How many distinct samples are there such that if two or more than two such samples are mixed in any ratio, the resulting solution is always a sample of more than 80% concentration? 1. 4 4.  10

2.  6 5.  12

3.  8

20. There are three containers C1, C2 and C3 having milk and water solutions in the ratio a:b, where a ε (1, 2, 3) and b ε (4, 5, 6). Containers C1, C2 and C3 can take any value of a and b. For how many different set of values of concentrations of containers C1, C2 and C3, the resultant mixture will have ratio of milk and water as 1:1? 1.  12 4.  1.

2.  0 5.  None of these

3.  Infinite

21. In the above question, a ε (1, 2, 6) and b ε (4, 5, 3). Containers C1, C2 and C3 can take any value of a and b. For how many different set of values of concentrations of containers C1, C2 and C3, the resultant mixture will have ratio of milk and water as 1:1? 1.  12 4.  1

2.  0 5.  None of these

3.  Infinite

22. Average weight of a class of 25 students is 30 kg. Average weight of girls is 5 kg more than that of the boys. If the class teacher’s weight, which is between 64 kg and 106 kg, is included, the average weight of the male members of the class equals that of the female members. If the average weight of the boys (in kg) is an integer, then what is the number of girls in the class? 1.  20 4.  18

2.  15 3.  10 5.  Cannot be determined

23. A succession of numbers is said to be in Arithmetic Progression (AP) if the difference between any term and the previous term is constant throughout. In a AP n1, n2, n3, ….,n47, the sum of odd numbered terms n1, n3, n5, ….,n47 is 1272. What is the sum of all the 47 terms of this AP?

2.  2500 5.  None of these

3.  2400

Direction for questions 24 to 26: Read the passage below and solve the questions based on it.

24. Which of the following is always true? 1. None of the applicants had a net score less than 240 2. The net scores would always be an even integer. 3. The net scores of any candidate would always be a positive integer. 4. The net scores of the topper could be exactly 24% more than the average of the entire group. 5. None of these 25. If the topper had a net score of 380 and the sixth ranker had a net score of 370 and the net scores of the top six rankers were distinct, then what would be the average net score of the 64 students who got ranks from the seventh of the last? 1.  225 4.  290

2.  245 5.  None of these

3.  275

26. When the scores of the top four students are deleted, the average score of the remaining 66 students falls by 6 marks. Assume that it is possible for two or more students to have the same net score. What is the minimum score possible for the fourth ranking student if no student got a net score of more than 352? 1.  280 4.  320

2.  300 5.  340

3.  308

27. The average marks of the girls in a class is equal to the number of boys and the average marks of boys is equal to the number of girls. If the class average is 4 less than the average of the boys’ average marks and the girls’ average marks, which of the following could be the number of students in the class? 1.  24 2.  48 3.  50 4.  64 5.  54 28. In the above question, what can be the minimum number of students in the class? 1.  0 4.  2

2.  2 5.  None of these

3.  8

Average  29. A, B, C, D, E are five consecutive integers and the average of these five numbers is less than

1 4

ANSWER KEYS

30. Find the difference between the average of first n even numbers and the average of all the even numbers up to n (n is an even number). n n–1 n+1 1.  2.  3.  2 2 2 4.  n 5.  Cannot be determined

of A. Then A is

1.  positive 2.  negative 4.  data inconsistent 5.  None of these

  1.41

3.  even

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

1

3.

2

4.

4

5.

3

6.

1

7.

4

8.

2

9.

4

10.

2

11.

4

12.

1

13.

2

14.

1

15.

5

16.

4

17.

4

18.

2

19.

2

20.

2

21.

3

22.

2

23.

1

24.

2

25.

5

26.

2

27.

3

28.

5

29

1

30.

3

HINTS AND EXPLANATIONS 5. (3)  Using statement A

  Let, the numbers be x, x + 2 x + 4



  A⇒



  Or, x + 5.5 =12.5 ⇒ x = 7



  ⇒ Numbers are 7, 9, and 11.



  Using statement C



  Suppose the numbers are x, x + 2, x + 4



  Then x² + (x + 2)² + (x + 4)² = 251



  or, x² + 4x – 77 = 0



 Neglecting the –ve value, we have x = 7 ⇒ The numbers are 7, 9, 11



 Statement B just rewrites the same information. So cannot be solved using statement B alone.

(x + 4) + (x + 5) + (x + 6) + (x +7) 4

= 12.5

7. Use choices. Put some values and check the consistency. 8. Use any 7 consecutive numbers to check the answers. n=

(1 + 2 + 3 + 4 + 5) 5

k=



So k = n + 1.

=4

5

Alternately, the average of the first 5 terms is the middle term which is third term, and the average of the first 7 terms is the middle term which is the fourth term. Hence, it is one more than the previous average. 9. (4) The distance of 800 miles was covered in 5 + 4 = 9 hours.

6. Assume some values of A and B and substitute in the options to get the answer.



(1 + 2 + 3 + 4 + 5 + 6)



= 3, average of 7 integers is

Average speed = 10. (2)

800 9

= 88

8 9

miles per hour.

Let the average score of the 1st 18 innings be n 18 n + 98 = 19 ( n + 4)⇒ n = 22 So, Average score after 19th innings = x + 4 = 26. 11. (4) 12. (1)

4 × 20.8 + 6 × 33 + 7 × 17.5 + 3 × 0

= 20.19 20 13. Let the number of students in classes X, Y and Z be a, b and c respectively. Then Total of X = 83a

1.42 

  Quantitative Aptitude and Data Interpretation

Total of Y = 76b

17. Any combination of two samples out of A, B, F, G, I and J will not give rise to a sample of concentration of more than or equal to 80%, be what the ratio of their volumes. So, it is 6C2 = 15. It can be counted also without using Permutation and Combination also:

Total of Z = 85c And Also

83a + 76b

= 79, i.e., 4a = 3b

a+b 76a + 85c

= 81, i.e., 4c = 5b

a+b 4

Hence , b=

a, c

3

5 4

4

=

3

×

4

5

a=

3

3

a

n (n + 1) Then

2 ( n + 1)

978

=

12

= 81.5

7 17

=

602 17

Hence, n = 69 and x = 7 satisfy the above conditions. 16. BA = 50 where there is no incomplete innings means r 2 = n2 = 0, MBA1 =

r1 n1

r1

+

n1 n1 = 50+0=50 BA =

r 1 + r2

MBA2 =

n1

=

r 1 + r2 n1 + n 2

max 0,

r2

r1

n2

n1

50n1 + 45 n1 =

GI, GJ



IJ.

So, possible combinations are – CD, CE, CH, DE, DH, EH

20. The various ratios possible are – 1 : 4, 1 : 5, 1 : 6, 2 : 4, 2 : 5, and so on. Since all these ratios are having less than 50% concentration of milk, so we cannot form a mixture having 1 : 1 (50% concentration of milk) ratio of milk and water. 21. Since we are having here concentration more than 50%, we can form the mixture having the ratio of milk and water as 1 : 1. Now, we can form mixtures of various concentrations by mixing two different mixtures (of different concentration), so finally infinite possibilities can be there. 23. Average = 1272/24 = 53

= 50 n2





a

5

= 35

FG, FI, FJ

5 3

+x



19. Mixing the samples C, D, E and H in any ratio will give rise to a sample of concentration more than 80%.

a a+ 3 3 14. Let the highest number be n and x be the number erased. a+

AB, AF, AG, AI, AJ BF, BG, BI, BJ

a+b+c

a + 85 ×

4

4

83a + 76b + 85c

Average of X, Y and Z= 83a + 76 ×

5

b=



24. All the additions in the net score would be in the multiple of 2 and similarly all the subtractions will also be in the multiple of 2. Hence net scores will also be a multiple of 2. 26. Sum of scores of top four students = 1356

= 50+

45 n1

50n1 + 45 n1 + 1

Hence, BA will increase, MBA1 will decrease.

> 50

Maximum possible score possible for top three students = 352 × 3 = 1056 Hence the minimum possible score for the 4th student = 300 n  30. Answer = (n + 1) –  + 1  2 

c h a p t e r

 3

Percentage

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   What is Percentage?   Definitions and properties   Its applications—Profit and Loss, Discount and Interest   Usage of percentage as a calculation device   Method of solving questions

Percentage is a way to express a number as a fraction of 100 (per cent meaning “per hundred”).

Student in America gets 100 marks out of 1000 marks. If we convert the marks obtained on a base of 100, then it becomes 10. According to the definition of percentage, this student has obtained 10% marks.

It is denoted by using the sign “%”. For example, 45% (read as “forty-five per cent”) is equal to 45/100, or 0.45.

In fact, we use percentage as a common platform of 100 to compare the given values.

  WHAT IS PERCENTAGE?

To understand percentage better, let us see this table: Student in Marks Total Marks obtained/100 marks country obtained Marks

America

100

1000

10%

India

25

25

100%

China

45

300

15%

France

50

100

50%

Basic Statements Basic Statement 1:  What is x % of y?

x×y 100

⇒ _____ ​   ​ 

It can also be seen that x % of y = y % of x

1.44 

  Quantitative Aptitude and Data Interpretation

Example Example

4% of 2,000 = 2,000 % of 4 Using this, we can see that if we have to calculate 24% of 25 (or any other calculation of similar nature), it is better to find out 25% of 24 =​ __ ​ 14 ​   ​× 24 = (24/4) = 6.

(  )

Basic Statement 2: What percentage of x is y?

y × 100

⇒ _______ ​  x ​   

Basic Statement 3: Change Change a. Percentage change = __________ ​ Initial value   ​  × 100 b. Successive Percentage change A quantity is to be increased successively by 20% and 30%. Ideally, this should be done by taking 100 as the initial value and then changing this initial value first by 20% and then by 30%. It can be seen below: 100 –→ 20%↑ –→ 120 → 30%↑–→ 156

Market share

2002–03

2003–04

Maruti

40%

48%

Honda

30%

26%

Percentage change in the market share of Maruti over the years 48 –  40  = ​ ______ ​× 100 = 20% 40   Percentage point change in the market share of Maruti over the years = 48 % – 40% = 8% Similarly, if we have to increase any quantity N by S%, S    ​) and when the same quantity then it is equal to N (1 + ​ ___ 100

N is to be decreased by S%, then final quantity S = N (1 – ___ ​ 100   ​). 

Observations i. An increase of 100% is equal to the final amount becoming 200% of initial value or twice the initial value. ii. A decrease of 100% is equal to the final amount becoming zero. Hence 0% of initial value. iv. Its worth mentioning here that

So, net percentage increase = 56%

100 → 20%↑→ 100 × 1.2 = 120 100 → 20%↓→ 100 × 0.8 = 80

This is known as Straight Line method of solving the problems.

150 → 30%↑→ 150 × 1.3 = 195 150 → 30%↓→ 150 × 0.7 = 105

600 Using this formula, 20 + 30 + ​ ___ 100 ​ = 56%

210 → 27%↑→ 210 × 1.27 = 266.7 210 → 27%↓→ 210 × 0.73 = 153.3 So, if final value and percentage increase or percentage decrease is given and we have to find out the Initial Value, then it can be done in the similar way.

Note- If there is % decrease instead of % increase, then we take ‘–’ (Negative) sign.

Using S → 30%↑→ S × 1.3 = 195; where S is the initial value

For example,

So, if final value 195 and 30%↑ is given, then initial value

Successive % change if a% ↑ and then b% ↓

195 S = ___ ​ 1.3 ​  = 150

Alternatively, we can use successive change formula also:

( 

)

ab ​ a +b + ___ ​ 100  ​  ​%

a(–b) = a + (–b) + _____ ​  100 ​ 

(  )

ab = (a–b –​ ___ ​ 100  ​  ​% c. Percentage point change It is the numerical difference between the values for which we have to calculate change. Let us assume some values to understand the above written concept:

[In the above examples, ↑ represents increase and ↓ represents decrease.] If initial value (= x ) is increased by R%, then final value R   ​) ​ 100 = x ( 1+ ___ If initial value (= x) is decreased by R%, then final value R   ​)  = x (1– ___ ​ 100

Percentage  Example  1 Example 

1

What is 50% of 40% of Rs 1200? Solution

Solution

50 ___ 40 ​ ___ 100  ​ × ​ 100  ​ × 1200 = Rs 240 Alternatively, 1st calculate 50% of 40 = 20 and then 20% of 1200 = 240 It can be seen that 50% of 40% of Rs 1200 = 40% of 50% of Rs 1200. Example  2

Example  2

A student multiplies a number X by 5 instead of dividing it by 5. What is the percentage change in the result due to this mistake? Solution Solution

  1.45

Alternatively, we can use successive change formula also: ab (a + b + ___ ​ 100  ​)%   = 40%, where a = Percentage increase in price, b = Percentage increase in consumption. b 6 ​ 5  ​= __ ​ 5 ​  b = 20 Putting the value of a = 20%, we get b + __ Hence b = 16.66% Example  4

Example  4

42% of a number is subtracted from 61% of the same number and the resulting value is 38. What is that number? Solution Solution

Let us assume that the number = N So, 0.61N – 0.42 N = 38, or, 0.19 N = 38, Hence N = 200

Let us assume X = 100 So, actual result should have been 100 ÷ 5 = 20 But the result obtained = 100 × 5 = 500 So, percentage change = (500 – 20) × 100/20 = 2400% (It can be very well observed that if we take base as 500, percentage change = 96%. What we should primarily take care of – with comparison to which number are we calculating percentage change?) Example  3

Example  3 Price of sugar has increased by 20%, however expenses in sugar has increased by 40%. By what percentage has the consumption of sugar increased?

Solution Solution

We know that Price × Consumption = Expenditure Assume that initially, the price was Rs 10/kg and consumption was = 10 kg Hence initial expenditure = 10 × 10 = 100 New price = 12, and new expenditure = 140 Hence New consumption = 140/12 = 11.66 Hence percentage increase in consumption 11.66 – 10 = _________ ​  10 ​    × 100 = 16.66%

Example  5 Example 

5

The length and breadth of a rectangle are increased by 20% and 10% respectively. Which of the following is the percentage increase in its perimeter? 1.  32% 2.  13% 3.  15% 4.  16% 5.  Cannot be determined Solution Solution

Since the exact value of length and breadth are not given, hence we cannot calculate the percentage increase in the perimeter of rectangle. Hence option (5) is the answer. Understand that percentage change is not a function of summation or subtraction, as in the case of perimeter of a rectangle.

Example  6

Example  6 The length and breadth of a rectangle are increased by 10% and 10% respectively. Which of the following is the percentage increase in its area? 1.  17% 2.  13% 3.  21% 4.  16% 5.  Cannot be determined

1.46 

  Quantitative Aptitude and Data Interpretation

Solution Solution

Solution Solution

Method 1: Let us assume that the length of rectangle = breadth of rectangle = 10 units (Square is nothing but a special case of rectangle having length = breadth)

Let us assume that the length = A and breadth = B Old perimeter = 2 (A+B) New perimeter = 2 ( 1.2 A + 1.1B)

Initial area = Length × Breadth = 10 × 10 = 100 sq. units

2 (1 .2 A + 1.1B) = 2 (A+B) × X (New perimeter = X times new perimeter)

New length = New breadth can be calculated as follows:

Simplifying it we get,

10 → 10%↑→ 10 × 1.1 = 11

+ 1.1B   __________ =X ​ 1.2A A + B ​ 

Hence new area = 11 × 11 = 121

0.2A + 0.1B Or, 1 +__________ ​  A + B ​  =   X is the increase in perimeter due

Percentage change in area = 21%

to increase in length and breadth. Now going through the options,

Method 2: Successive percentage change formula There are two factors bringing a change in the area of rectangle namely length and breadth. Each of these are contributing by 10% increase in the area of new reactangle.

0.2A + 0.1B   = 0.17, hence A : B Checking option (A), ​ __________ A + B ​  = 7 : 3, so possible. 0.2A + 0.1B   = 0.13, hence A : B Checking option (B), ​ __________ A + B ​  = 3 : 7, so not possible.

Using successive percentage change formula

0.2A + 0.1B   = 0.15, hence A : B Checking option (C), ​ __________ A + B ​  = 1 : 1, so possible.

ab   = (10 + 10 + 1) % = 21% (a + b + ​ ___ 100  ​)%

0.2A + 0.1B   = 0.16, hence A : B Checking option (D), ​ __________ A + B ​  = 3 : 2, so possible.

Method 3: Successive percentage change method Assume initial area = 100 sq. units Final area = 100 –→ 10%↑ –→ 110 → 10%↑–→ 121 So, net percentage increase in area = 21%

Alternatively, this question can be done with the method of Alligation also. Breadth

Length

10%

20%

Example  7

17%

The length and breadth of a rectangle are increased by 20% and 10% respectively. Which of the following cannot be the percentage increase in its perimeter? (Assume length is more than breadth). 1.  17

2.  13

3.  15

4.  16

5.  All are possible

3%

7%

For Breadth : Length = 3 : 7, it is possible to have 17% increase in perimeter of rectangle.    Similarly, other percentage increases can be checked if possible or not.

Percentage 

  1.47

Cost Price (CP)

It can be understood in this way—Suppose CP of an article is Rs 100 and shopkeeper wants to earn a profit of 20%, i.e., he wants to have a profit of Rs 20. Now, he anticipates that any customer who is coming to him will ask for some discount and if he fixes the SP at Rs 120, then he won’t be able to give any discount to the customer. So, he now marks up his price over Rs 120 so that he can give some discount to his customer.

This is the price which a person pays to purchase something or cost incurred while manufacturing something.

Remember that if nothing else is stated, then Mark up % is always calculated over CP.

  APPLICATIONS OF PERCENTAGE Profit, Loss and Discount Basic Terminology

Types of Cost

MP

1. Fixed cost– As obvious from the name, it is that kind of cost which is fixed in all the cases. 2. Variable cost– Variable costs are those costs which vary according to the no. of units produced.

Total Units Produced

Per Unit Cost

Unit Variable Costs

Total Units Produced

Total Fixed Costs Total Costs

Total Costs

Total Variable Costs

Fixed Costs

Total Units Produced

Unit Fixed Costs Per Unit Cost

Variable Costs

Total Units Produced

% decrease

Example  8 Example 

SP

% profit % loss

CP

8

After selling an article at a discount percentage of 50%, profit percentage obtained is 20%. What is the mark–up over CP? Let us assume that CP = Rs 100. So, SP = Rs 120. Now, after giving a discount of 50% over MP, Rs 120 is the SP. Using product stability ratio, 50%↓ = 100%↑ So, MP = 100%↑ over SP = Rs 240

( 

)

_______   ​×100  ​% Hence percentage mark–up = 140% ​ ​ 240–100 100   

Alternatively, 0.5 MP = 1.2 CP MP/CP = 1.2/0.5 = 2.4 MP ​ – 1) × 100 = (2.4 – 1) × So, percentage Mark–up = (​ ___ CP 100 = 140% Further, we know that:

3. Semi variable cost– Semi variable costs are those costs which are fixed in one particular strata, but the costs varies among the different stratas.

If SP > CP, then there will be a profit and if SP < CP, then there will be a loss.

Selling Price (SP) – This is the price at which something

CP – SP = Loss

SP – CP = Profit

is sold.

Profit % = Profit/CP × 100

Marked price Or Mark–up price (MP) – This is the price which the shopkeeper fixes in anticipation of some discount being asked by customer.

Loss % = Loss/CP × 100

List price or Tag price – As obvious from the name, this is the price which is printed on the tag of the article.

For our calculations related to the concept of Profit and Loss, till the moment nothing is stated in the questions, we won’t see much difference between Marked Price and List price.

Profit% or Loss % is always calculated upon CP, unless something else is mentioned. It can be seen that whenever there is a profit, then MP ≥ SP > CP. However, when there is a loss, then we may not have some definite relationship between the above written three quantities (MP, SP and CP).

1.48 

  Quantitative Aptitude and Data Interpretation

Margin

Ratio of CP1 : CP2 = (100+y) : (100 + x)

When we calculate profit percentage as a percentage of SP, then it is known as Margin. So, Margin =​ _____ ​ Profit      ​×100  ​%

ii. First one is sold at a profit of x% and second one is sold at a loss of y%.

( 

)

SP

Calculating CP/SP when profit% or loss% is given If we say that there is a profit of 20%, then CP × 1.2 = SP So, if CP = Rs 120, then SP = Rs 120 × 1.2 = Rs 144 Or, if SP = Rs 144, then CP = 144/1.2 = Rs 120 (Needless to say that if there is a profit of 30%, then we will take 1.3 at the place of 1.2, and if there is a loss of 27%, then we will take 0.73 at the place of 1.2) So, if there is a profit of R%, and SP = C, then CP = _______ ​ 100C+R    ​  ×100 C ×100 And in case of loss of R%, CP = ​ _______ 100 – R ​  Alternatively, we can use Product–Stability Ratio also to find out SP if CP is given.

Ratio of CP1 : CP2 = (100 – y) : (100 + x) iii. First one is sold at a loss of x% and second one is sold at a loss of y%. Ratio of CP1 : CP2 = (100 – y) : (100 – x) iv. First one is sold at a loss of x% and second one is sold at a profit of y%. Ratio of CP1 : CP2 = (100 + y) : (100 – x) v. If SPs of two articles are same, and one is sold at a profit of x% and another is sold at a loss of x%, then in that case there will be loss always. And loss percentage x2  ​ % = ___ ​ 100

Example  10

Example  10

Example  9

Example  9 Two shopkeepers sell some article for Rs 4000 each. A shopkeeper calculates his profit % on his CP and another calculates his profit % wrongly on SP. What is the difference in their actual profit if both claim to have a profit of 20%?

SPs of two articles are same. One is sold at a loss of 20% and another one at a profit of 20%. What is the net loss/ profit in the whole transaction?

Solution Solution

Solution Solution

In 1st case,

In 2nd case

20 2 = 4% Method 1: Using (v) above Loss % = 100

SP = Rs 4000

SP = Rs 4000

Method 2: Assume that SPs of each of the article = Rs 100

Profit = 20% of CP Profit = 20% of SP CP = Rs 3333.33 ​ = ____ ​ 4000 ​  ​ CP = Rs 3200 1.2   

( 

Profit = Rs 666.66

)

Profit = Rs 800

So, difference in profit = Rs 133.33

So, CP1 (For the article which is sold at a loss of 20%) = 100/0.8 = Rs 125 CP2 (For the article which is sold at a profit of 20%) = 100/1.2 = Rs 83.33 So, net CP = Rs 125 + Rs 83.33 = Rs 208.33 As we can observe now that SP < CP, so, there is a loss. Loss % = (8.33/208.33) × 100 = (1/25) × 100 = 4%

Some important results

When SPs of two articles are same i. First one is sold at a profit of x% and second one is sold at a profit of y%.

Alternatively, if SPs of two articles are same, and one is sold at a profit of x% and another is sold at a loss of x%, then in that case there will be loss always. And loss 2 x2  ​ % = ___ percentage = ___ ​ 100 ​ 20 100  ​% = 4%

Percentage  Example  11 Example 

11

  1.49

Example  13

Example  13

Two articles are sold at Rs 12,000 each. One is sold at a profit of 20% and another one at a loss of 20%. What is the net loss?

A shopkeeper sells his articles at his CP but uses a faulty balance which reads 1000 gm for 750 gms. What is his actual profit percentage?

Solution Solution

Solution

SP1 = Rs 12,000

This question can be solved by several methods

CP1 = Rs 12,000/1.2 = Rs 10,000

Method 1 – Since while selling, 750 g = 1 kg

SP2 = Rs 12,000

So, 250 gms = 1/3 kg

CP2 = Rs 12,000/0.8 = Rs 15,000 So, Total CP = Rs 25,000 and total SP = Rs 24,000 So, loss = Rs 1000.

So, profit = 1/3 = 33.33% Method 2 – While selling, since the shopkeeper is branding 750 grams as 1 kg, so 1000 grams will be branded as 1000/750 = 1.33 kg. And while purchasing, he has paid for just 1000 grams. So, net profit = (1.33 – 1) = 0.33 kg

Alternatively, since there is a loss of 4%. So, for every Rs 100 invested, Rs 96 is coming back and Rs 4 is lost. In our case, 96% = Rs 24,000; so, 4% = Rs 1000. Example  12 Example 

10

due North Inc. is worldwide number 1 idea developer company. One day, they sold Idea 1 to CL and Idea 2 to AMS at a profit percentage of 20% and 30% respectively. If the sum of developing Idea 1 and Idea 2 is Rs 25000, what is the developing cost of Idea 1? Solution Solution

Ratio of Developing cost of Idea 1 : Idea 2 = 130 : 120 130 ___   25000 = Rs 13000 So, Developing cost of Idea 1 = 250 ​   ​×

So, profit percentage = 0.33/1 × 100 = 33% (approx) General Expression: ______ % Profit =​(  ​ 1000–x ​ × 100 )​% x   

Where x = quantity (grams) sold at the place of 1000 grams. This formula is valid only if the article is sold at CP. Example  14

Example  14

A shopkeeper sells his goods at its CP only. But still he manages to gain a profit of 40% because he has manipulated his weights. How many grams shopkeeper is the actually selling in place of 1000 grams? Solution Solution

To earn a profit of 40%, shopkeeper needs to make 1.4 kg 1000 out of 1 kg. So, he will be selling ____ ​ 1.4 ​    grams = 714.28 grams at the place of 1 kg.

Faulty Weight Typical faulty weight conditions occur when a shopkeeper sells quantity other than what he professes to sell. Let us understand this with the help of an example—A shopkeeper sells 900 grams instead of 1000 grams—in this case shopkeeper will earn profit due to goods of less weight given to customer. However, if 1100 grams goes in place of 1000 grams, then there will be loss.

Simple Interest and Compound Interest Interest is defined as the “Time value of money.” As the time passes on, value of money keeps on changing. The basic difference between Simple Interest and Compound Interest lies in the fact that while in case of Simple interest, Principal as well as interest (per period

1.50 

  Quantitative Aptitude and Data Interpretation

reckoned, for example, per year) remain same for the whole period given, in case of Compound Interest, after a certain period both Principal and Compound Interest keep on changing. Let us understand this with the following example:  

T=0

T=1

T=2

T=3

SI

Principal = 100

100

100

100

 

Interest (Rate = 10 %pa)

10

10

10

 

 

 

 

 

CI

Principal = 100

100

110

121

 

Interest (Rate = 10 %pa)

10

11

12.1

R n R ___ It can be seen that P(1 + ​ ___ 100   ​)  is nothing but P(1 + ​ 100   ​)  R   ​)  …….n times, which is simply the application (1 + ___ ​ 100 of Successive Percentage Change. According to the standard terminologies of interest, Amount = Principal + Interest. However, at some places, terms like initial amount and final amounts are also used to indicate the principal and (principal + interest) respectively. In all the cases, the term ‘sum’ or ‘initial sum’ is used to indicate the principal.    When rate of interest is different for the different years: If 1st year rate of interest = R1, 2nd year rate of interest = R2, and 3rd year rate of interest = R3, then CI =

( 

) ( 

) ( 

)

R1 R3 R2 ___ ___ P ​ 1 +​ ___ 100  ​  ​​ 1+​ 100  ​  ​ ​ 1+​ 100  ​  ​–P

Simple Interest In case of Simple Interest, interest is reckoned at a flat rate for the entire period of time for the sum borrowed/lent. P ×(R × T) So, Simple Interest (I) = ​ __________   100 ​  Example  15

Example  15

Example  16 Example 

16

Difference between two years of Compound Interest and Simple Interest at 10% over Rs X is Rs 10. What is the value of X? Solution Solution

A sum of money becomes 2 times in 5 years at SI. What is the interest rate per annum? At the end of 1st year Solution Solution

SI

CI

10%

10%

At the end of 2nd year 10%

10% + 10% of 10%= 11%

=20% = 21%

If principal = X, then amount = 2X, hence interest = X P ×(R × T)   Using the formula, (I) = ​ __________ 100 ​ 

So, 1% = Rs 10

X×R×5 X = _________ ​  100 ​  , hence R = 20%

It is pertinent here to understand that if the rate of Interest = R% per annum for both CI and SI, then the difference between CI and SI for 2 years will be equal to (R% of R)% = (R 2/100)% of Principal

Alternatively, if a sum of money gets doubled in X years at 100 SI, then the rate of interest per annum = ___ ​  X ​ %

Compound Interest In case of Compound Interest, interest is reckoned on the interest of previous years also apart from reckoning it on the current year. R n Compound Interest = P(1 + ​ ___ 100   ​)  – P R   ​) n Amount = P(1 + ___ ​ 100

⇒ 100% = Rs 1000

In the above case, R = 10%, so the difference between CI and SI for 2 years = 1%

Compound Interest reckoned Half–yearly or Quarterly If rate of interest is R% annually and CI is compounded half yearly for n years, then the expression for Compound Interest

( 

)

2n __ ​ R  ​   2   ​ –P = P ​ 1 + ​ ___ 100  ​– 

Percentage  If Rate of Interest is R% annually and CI is compounded quarterly, then the expression for Compound Interest 4n __ ​ R  ​   4 = P ​ 1 +​ ___ 100  ​   ​ – P

( 

)

Example  17 Example 

17

A sum of money becomes after two years Rs 1875 and after three years Rs 2343.75 at compound interest. What is the rate of interest per annum?

Solution Solution

Amount after three years = Amount after two

( 

)

r   ​  ​ ​ 100 years × ​ 1 + ___ r   ​  ​= 2343. 75/1875 = 1.25 (​ 1 + ​ ___ ) 100 Hence r = 25%

  1.51

1.52 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  1 1. If x is 30% greater they y, then y is by what percentage less than x? 1  ​ % 1  ​ % 1.  30% 2.  23 ___ ​ 13 3.  29 ___ ​ 13 4.  42 __ ​ 67 ​  % 5.  None of these 2. Reema’s income is 75% of Sanjeev’s income. Anil’s income is 60% of Reema’s income. To find the income of Anil, which of the following statement(s) is/are sufficient/necessary? a. The ratio of Reema’s income and Anil’s income is 5 : 3. b. The sum of the income of both Anil and Reema is Rs 7200. c. The difference between the income of Sanjeev and Reema is Rs 1500. 1.  Only B alone is sufficient 2.  Either B or C is sufficient 3. Any of the three is sufficient 4.  All together are necessary 5.  All even together are not sufficient.

1.  Rs 650 4.  Rs 800

2.  Rs 750 5.  None of these

3.  Rs 900

8. In a test, 52% students failed in Hindi, 40% failed in English and 27% failed in both. What percentage of students passed in both the subjects? 1.  25% 4.  35%

2.  48% 5.  None of these

3.  60%

9. The original price of an article is Rs 3000. The price is discounted by 20% and then raised by 10%. The new price of the article is 1.  Rs 2600 4.  Rs 2700

2.  Rs 2460 5.  None of these

3.  Rs 2640

10. A trader bought some books for Rs 8 each. The wholesaler gave 15% discount on each of the books. If the discount amount deducted on the bill was Rs 216, how many books did he buy? 1.  180 4.  190

2.  280 5.  None of these

3.  140

3. A reduction of 20% in the price of sugar enables a person to obtain 40 kg more for Rs 210. What is the reduced price per kg?

11. If the difference between the CI and SI earned at the end of second year on a sum of money at the rate of 10% pa is Rs 20, what was the sum?

1.  Re 1 4.  Rs 1.75

1.  Rs 3000 4.  Rs 3500

2.  Rs 1.10 3.  Rs 1.150 5.  None of these

4. The cost price of 21 articles is the same as the selling price of 15 articles. The profit percentage is 1.  28 __ ​ 47 ​  

4.  60%

2.  25%

3.  50%

5.  None of these

5. A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 875 g for the kg weight. Find his gain percentage. 1.  14 __ ​ 27 ​  

4.  12 __ ​ 23 ​  

2.  12 __ ​ 12 ​  

3.  14 __ ​ 37 ​ 

5.  None of these

6. Find the difference between the compound interest and the simple interest for the sum Rs 1200 at 15% per annum for 2 years 1.  Rs 22.50 4.  Rs 30.60

2.  Rs 23.70 5.  None of these

3.  Rs 27

7. A sum of Rs 1550 is lent out in two parts, one at 8% and other one at 6%. If the total annual interest is Rs 106, the money lent at 8% is

2.  Rs 2000 5.  None of these

3.  Rs 2500

12. The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by 1.  45% 4.  62%

2.  82% 5.  None of these

3.  42%

13. If four-fifths of one-third of 75% of a number is 27, what is two-thirds of it? 1.  28 4.  90

2.  135 5.  45

3.  100

14. The difference in CI and SI on a certain amount at the rate of 10% per annum at the end of 3rd year is Rs 620. What is the principal amount? 1.  Rs 2000 4.  Rs 5000

2.  Rs 20000 3.  Rs 10000 5.  None of these

15. The profit earned by selling a watch for Rs 820 is as much as loss incurred when it is sold for Rs 650. What is the cost price of the watch? 1.  Rs 735 4.  Rs 700

2.  Rs 835 5. Rs 690

3.  Rs 750

Percentage  Direction for questions 16 and 17:  There are two statements given. Choose the option that you feel is required to solve the question given. 16. The difference between the CI and SI earned on sum of money at the end of four years is Rs 256.40. Find the sum. I. The rate of interest per cent per annum

  1.53

21. The rate of simple interest on a sum of money is 6% pa for the first 3 years, 8% pa for the next 5 years and 10% pa for the period beyond 8 years If the simple interest accrued for a sum for a total period of 10 years is Rs 1560, what is the sum? 1.  2750 4.  2500

2.  2000 5.  None of these

3.  1800

1. Only I is required and question cannot be done by I alone

22. In a library, 20% books are on drawing, 50% of the remaining are in economics and the remaining 9000 are in various other languages. What is the total number of books?

2. Only II is required and question cannot be done by II alone

1.  4500 4.  2500

3. Both I and II are required and question cannot be done by either alone

23. Mohan bought 3 cows for Rs 21,200. He sells all the three cows for Rs 22,360. On the first cow, he makes a profit of Rs 560 at 10% on cost price. On the second, he makes a profit of Rs 1440 at 20% on cost price. Find the % profit of % loss made on the third cow.

II. Amount of simple interest accrued after four years

4.  Either I or II can solve the question 5.  Neither I nor II can solve the question 17. A shopkeeper sells some articles on profit of 20% of the cost price. Find the gain in Rs. I. Selling price of the articles.

1.  20% profit 4.  10% loss

2.  5000 5.  None of these

3.  3000

2.  20% loss 3.  10% profit 5.  Cannot be determined

24. At a profit of 20% the selling price of an article is Rs 180. If the profit is increased by Rs 30, what is the new percentage profit?

II. Cost price of the articles 1.  Neither I nor II can solve the question 2.  Either I or II can solve the question 3. Both I and II are required and question cannot be done by either alone

1.  30% 4.  40%

2.  35% 5.  None of these

3.  35%

4. Only II is required and question cannot be done by II alone

25. A person saves 15% of his income. If his income increase by 35% and he starts savings 20% of his income, by what percentage does his savings increase?

5. Only I is required and question cannot be done by II alone

1.  60% 4.  80%

18. An amount doubles itself in 5 years at SI. In how many years will its interest become its 250%?

26. A pen was sold at 14% loss. In order to get a profit of 12%, the selling price of the pen has to be increased by Rs 91. What is the cost price of the pen?

1.  10 years 4.  15 years

2.  7 __ ​ 12 ​  years

5.  None of these

3.  12 __ ​ 12 ​  years

1 ​  of 20% of __ 19. ​ __ ​ 13 ​  of 9 times of a number is 18. Find out 5 that number. 1.  150 4.  85

2.  250 5.  110

3.  75

20. Chamanlal purchased 20 dozen pencils at Rs 48 per dozen. He sold 8 dozen at 10% profit and remaining 12 dozen on 20% profit. What is the profit percentage in this transaction? 1.  15 4.  18

2.  16 5.  None of these

3.  17

1.  Rs 2275 4.  Rs 450

2.  70% 5.  None of these

2.  Rs 455 5.  None of these

3.  75%

3.  Rs 350

27. Narangi Lal loses 50%, by selling 12 bananas in a rupee. How many bananas in a rupee must he sell to gain 50%? 1.  2 4.  25

2.  4 5.  Not possible

3.  8

28. A sum of money was put at simple interest at a certain rate for 5 years Had it been put at 3.5% higher rate, it would have fetched Rs 700 more. What is the sum? 1.  Rs 5000 4.  Rs 7500

2.  Rs 4000 5.  None of these

3.  Rs 3000

1.54 

  Quantitative Aptitude and Data Interpretation

29. A shopkeeper sold a radio and got Rs 125 as profit. Find the profit percentage.

1.  Only A alone is sufficient

30. Rajeev got 675 marks in the examination. What is the maximum marks in the exam? A. His average percentage of marks in each paper is 75%. B.  He got 30 marks more in Maths than in English. C.  The maximum marks for each paper is 100.

2.  Only B alone is sufficient

1.  Only B and C together are sufficient

A.  Ratio of selling price and cost price is 5 : 4. B.  He gave 15% discount on the labelled price.

2.  A and B together are necessary

3.  Any one of A or B is sufficient

3.  Either A or C and B together are sufficient

4.  Both A and B together are necessary

4.  A alone is sufficient.

ANSWER KEYS

5.  Even both together are not sufficient

5.  B alone is sufficient.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

5

4.

5

5.

1

6.

3

7.

1

8.

4

9.

3

10.

1

11.

2

12.

2

13.

4

14.

2

15.

1

16.

4

17.

2

18.

3

19.

1

20.

2

21.

2

22.

1

23.

4

24.

4

25.

4

26.

3

27.

2

28.

2

29.

1

30.

4

HINTS AND EXPLANATIONS 1 ___ × 100 = 23 ​    ​ % 1. (2)  required percentage = ________ ​     ​  100 + 30 13

True weight – False weight _____________________ 5. (1)  % gain = ​         ​× 100 False weight

2. (2)  Suppose Sanjeev’s income = x

1000 – 875 100 2 _________ ___ __   = ​   ​    × 100 = ​   ​  = 14 ​   ​ % 7 7 875

30

3x ___   Reema’s income = ​   ​  4 9x ___   Anil’s income = ​   ​  20

(  )

(  )

15 2 r 2 ___ ___ 6. (3)  Difference = Sum ​ ​     ​   ​ = 1200 ​ ​    ​   ​ = Rs 27 100 100 7. (1)

9x 3x ___ ___   From (B) ⇒ ​   ​ + ​   ​ = 7200 ∴ x = 6000 4 20

8. (4) % passed students in both the subjects = 100 – (52 + 40 – 27) = 35%

3x ___   From (C) ⇒ ​   ​ = 1500 ∴ x = 6000 4

80 ___ 110 ___ 9. (3)  New price = 3000 × ​    ​ × ​   ​ = Rs 2640 100 100

3. (5) Owing to the fall in price, there is a saving of 20% on Rs 210 i.e., Rs 42.   So, for Rs 42, a person purchases 40 kg of sugar.   Hence, reduced price per kg = Rs 42 ÷ 40 = Rs 1.05 21 – 15 ______ 4. (5)  Profit per cent = ​   ​   × 100 = 40% 15

216 ___ 10. (1)  15% of Rs 8 = Rs 1.2 i.e., No. of books = ​   ​ = 180 1.2

(  )

2

(  )

2

100 100 ___ ___ 11. (2)  Sum = Difference ​ ​   ​   ​ = 20 ​ ​   ​   ​ = Rs 2000 10 R 40 × 30 _______ 12. (2)  Percentage change = 40 + 30 + ​   ​    = 82% 100 5 __ 100 __ 3 ___ 2 __ 13. (4)  Required number = 27 × ​    ​× ​   ​  × ​   ​ × ​    ​= 90 4 1 75 3

Percentage   ⇒ CP of third cow = 21,200 – (5600 + 7200) = Rs 8400

620 × 100 × 100 × 100 ___________________ 14. (2)  Principal = ​         ​= Rs 20000 100(300 + 10)

  Now, total profit = Rs (22,360 – 21,200) = Rs 1160

820 + 650 _________ 15. (1)  CP = ​   ​    = Rs 735 2

( 

 ⇒ Profit made on 3rd cow =1160–(560+1440)= – 840 = Rs 840 loss.

Prt r ___ ___ 16. (4)  From I, P ​ 1 + ​     ​   ​– P – ​    ​ = 256.40 100 100

840 ____   So, % loss = ​    ​ × 100 = 10% 8400

 Now, putting t = 4 and r from I, P can be easily calculated.

100 180 ________ ___ 24. (4)  Cost price = 180 ​ ​    ​    ​= ​   ​ × 100 = Rs 150 100 + 20 120

)

  From II,   SI =



( 

)

  Now profit = 20% of 150 + 30 = 30 = Rs 60

rt

( 

  1.55

60 ___   So New percentage profit = ​    ​ × 100 = 40% 150

r ___ 100 ​ 1 + ​     ​  ​– 1 100

)

25. (4)  Assume his initial income = Rs 100, so savings = 15

 From II and the given statement CI can be calculated. Now, putting t = 4, CI and SI, r can be calculated. Now it will be like statement I. 18. (3)  Amount doubles itself → 100% is added to the principal in five years → 20% is added to principal every year.

  So, Rate of interest = 20%



 For interest to become 250%, time required = 250/20 = 12.5 years

100 __ 3 __ 1 ___ 19. (1)  Required number = 5 × ​   ​ × ​   ​  × ​   ​  × 18 =150 20 1 9

  New income = 135 ⇒ new savings = 27   Percentage increase in savings = 80% 91 ___ 26. (3) (14 + 12 =) 26% of CP = Rs 91, So, CP = Rs ​   ​  × 100 26 = Rs 350 1 ___ 27. (2)  50% = Rs ​    ​  12 1 1 1 ___ ___ __   150% = ​    ​ × ​    ​ × 150 = Rs ​   ​  i.e., 4 in a rupee 12 50 4 28. (2) Total rate of interest accrued in five years = 5 × 3.5% = 17.5%

20. (2)  Profit = (8 × 52.80 + 12 × 57.60) – 20 × 48 = 153.6

  17.5% of Principal = 700 ⇒ Principal = 4000

153.6 _____   % profit = ​   ​ × 10 = 16% 960

29. (1)  Profit = Rs 125

1560 × 100 ___________________ 21. (2)  Principal = ​        ​= Rs 2000 6 × 3 + 8 × 5 + 10 × 2 22. (1)  20% = Drawing.

5_____ –4  (A) ⇒ Ratio of SP and CP is 5 : 4 ⇒ Profit % = ​   ​   × 100 4 = 25%

 50% of remaining 80% i.e., 40% = Economics = 9000

  (B) ⇒ We don’t know the labelled price.

  Hence 20% = 4500 and 100% = 22500



(  )

100 ___ 23. (4)  CP of first cow = 560 ​ ​   ​   ​= Rs 5600 10

( 

  So, only (A) alone is sufficient

30. (4) (A) ⇒ Since, average percentage marks in each paper is 75%, so maximum marks can be calculated (75% = 675)

)

100 ___   CP of second cow = 1440 ​ ​   ​   ​= Rs 7200 20

  So, A alone is sufficient.

  EXERCISE  2 1. A dishonest dealer professes to sell his goods at a profit of 20% and also uses weight 800 gm at the place of 1 kg. Find actual gain percentage. 1.  40%

2.  45%

4.  60%

5.  None of these

3.  50%

2. Sum of Cost Price of two watches is Rs 3360. One watch is sold at a profit of 12% and other at a loss of 12%. Due to this transaction, there is neither profit nor loss. Find the cost price of each watch. 1.  Rs 1680, Rs 1680 2.  Rs 1280, Rs 1280

1.56 

  Quantitative Aptitude and Data Interpretation

3.  Rs 1000, Rs 1000

1.  Rs 3600 4.  Rs 4000

4.  Rs 2100, Rs 1260 5.  None of these

2.  Rs 3200 5.  None of these

3.  Rs 3800

3. A bicycle seller give 25% discount at advertising price and gain 20% profit. If the cost price of cycle is Rs 1200. Find advertising price.

11. In a bulb factory there are 3 machines M1, M2 and M3 which produces 25%, 35% and 40% of the total bulbs respectively. If M1, M2 and M3 produces 2%, 4% and 5% defective bulbs respectively. What is the percentage non–defective bulbs?

1.  Rs 1920 4.  Rs 1840

1.  89% 4.  86.1%

2.  Rs 1900 5.  Rs 2120

3.  Rs 1800

2.  97.1% 3.  96.1% 5.  Cannot be determined

4. A seller fixes the market price 50% more than cost price and gives a discount of 15%, and so he gets a profit of Rs 165. Find the market price of that article.

12. The length and breadth of a rectangle are increased by 30% and 20% respectively. Which of the following can be the percentage increase in its perimeter?

1.  Rs 900 4.  Rs 1000

1.  20 4.  28

2.  Rs 800 5.  None of these

3.  Rs 700

2.  16 5.  18%

3.  15

5. Anish buys a table and a chair for Rs 2000. He sells table at the profit of 20% and chair at the profit of 30% and thus he gains 23% profit in whole transaction. Find the cost price of table(in Rs).

13. If the area of a square is increased by 100%, then the percentage increase in the length of its diagonal is

1.  1400 4.  600

14. My Alliance India phone bill for the month of May is Rs B. Moreover, there is a service tax of S% which is to be levied upon this value. But since they are overcharging their customers fraudulently, they offer a discount of D% on it. So, now I have two options to make the payment:

2.  1200 5.  1000

3.  1300

6. A seller buys 50 kg oranges for Rs 525 and gains a profit equal to the cost price of 10 kg of oranges. Find the selling price per kg of oranges (Rs/kg). 1.  12.60 4.  12

2.  11.60 5.  13.125

3.  10.20

7. A seller buys 50 kg oranges for Rs 525 and gains a profit equal to the selling price of 10 kg of oranges. Find the selling price per kg of oranges (Rs/kg). 1.  12.60 4.  12

2.  11.60 5.  13.125

3.  10.20

8. A seller gives a discount of 20% on a pen and sells it at Rs 960. Had he not given the discount, profit would have been 40%. If he wants to gains a profit of 54% on the cost price of watch, what should be selling price? 1.  Rs 1320 4.  Rs 1280

2.  Rs 1400 5.  None of these

3.  Rs 1200

9. A merchant purchases two watches for Rs 1950. He sells first watch at the profit of 20% and second watch at the loss of 25%. If the selling price of two watches is equal find the cost price of watches? 1.  750, 1200 4.  1100, 850

2.  1200, 700 3.  1250, 700 5.  None of these

10. A man sells three cows for Rs 8000, Rs 12000 and Rs 6000 respectively. If he sells the first cow at profit of 25%, the 2nd cow at a profit of 20% and, the 3rd cow at a profit of N%, overall profit obtained is 30%. Find the cost price of third cow.

1.  10% 4.  55.5%

2.  41.4% 5.  None of these

3.  50%

Rs B –→ S%↑ –→ D% ↓→ Final Bill ––––––Option 1 Rs B –→ D% ↓–→ S%↑→ Final Bill –––––––Option 2 Which option is beneficial for me if S > D? 1.  Option 1

2.  Option 2

3.  Option 1 = Option 2

4  cannot be determined

5.  None of these 15. A sum of money gets 10 times in 6 years at SI. In how many years will the same sum of money become 13 times of the original sum? 1.  8 years 4.  7 years

2.  7.8 years 5.  None of these

3.  9 years

Direction for questions 16 and 17:  Read the passage below and solve the questions based on it. Patna and Lucknow are the only cities of India which are having only adults. Female population in Patna grows by 50% to 60000, but maintaining the same male to female ratio as previous year. Population in Lucknow increased by 12.5% to 90000, but the ratio of male to female changed by 1:1 to 4:5. Male population in Patna was 10% more than male population in Lucknow in the previous year.

Percentage  16. What is the female population in Lucknow in the second year? 1.  55000 4.  50000

2.  45000 5.  None of these

3.  400000

17. What is the total population in Patna after the increase (i.e., in the second year)? 1.  80000 4.  126000

2.  100000 5.  None of these

3.  20000

Direction for questions 18 to 21: Read the passage below and solve the questions based on it. There are two statements given in each question: A and B, either of which can be true or false on the basis of the information given below. The following table gives us the detailed information regarding the admission process of a reputed B–School, IIM–Jehanabad for the year 2003 and 2004. Year Gender Number Number Number Number of appli- of canof canof cancants didates didates didate appeared called for selected for writ- an inter- for the ten test view course

2003 2004

Male

6100

5900

60

12

Female

1900

1500

15

5

Male

6300

6000

64

13

Female

4000

3500

30

6

Choose (1) if only A is true Choose (2) if only B is true. Choose (3) if both A and B are true. Choose (4) if neither A nor B is true. Choose (5) if nothing can be said. 18. Statement A

  1.57

Statement B The percentage of absentees in the written test in 2003 among females was larger than that among females in 2004. 20. Statement A The percentage of the female candidates selected in 2004 from the female applicants is more than the percentage of the male candidates selected for year 2004 out of the total male applicants of that year. Statement B In 2003, from among those called for an interview, the males had a greater success rate than the females. 21. Statement A

The difference in total number of male and female applicants is more than 50% of the total candidates who appeared for the written test in 2004. Statement B The total number of the candidates selected for the job for both the years is more than 70% of the total female candidates called for an interview in both the years. 22. If the difference between the CI and SI on a certain sum of money is Rs 72 at 12 per cent per annum for 2 years, find the amount. 1.  Rs 8000 4.  Rs 6500

2.  Rs 6000 5.  None of these

3.  Rs 5000

23. The population of Pune is 2,00,000 on 1st January 2007. If the annual birth rate and the annual death rate are 7% and 3% respectively. Its also known that o Birth rate and death rate calculations are done as per the population data on 1st January of the respective years o Birth rate and death rate are the only factors affecting the population.

The success rate of moving from written test to interview stage for females was worse than for males in 2003.

Calculate the population of Pune two years from this period.

Statement B

1.  210090 4.  216320

The success rate of moving for written test to interview stage for males was better in 2003 than in 2004. 19. Statement A The percentage of absentees in the written test among males decreased from 2003 to 2004.

2.  212090 5.  218900

3.  214500

24. According to a recent census, the birth rate of Russia is an increasing AP with first term = 5% and common difference = 5%. At the same time death rate is an increasing GP with first term as 1% and common ratio of 2. If population on 31 December, 2008 is 1 million, then in which year will Russia witness its first fall in population?

1.58 

  Quantitative Aptitude and Data Interpretation

1.  English 4.  Maths

[Birth rate and death rate have the same meaning as given in previous question. 1st term corresponds to the year 2009] 1.  2012 4.  2015

26. What is the lowest total marks that S. C. Mayank can have in this examination?

2.  2013 3.  2014 5.  Will Never happen

1.  166 4.  None of these

Direction for questions 25 and 28: Read the passage below and solve the questions based on it.

1.  76 4.  56

The following is the percentage marks obtained by him in different subjects: 10%

Biology

14%

Maths

22%

Chemistry

14%

Physics

18%

English

22%

2.  85 3.  62 5.  Cannot be determined

28. In which subject did S. C. Mayank get maximum marks? 1.  English 4.  Hindi

2.  Physics 3.  Chemistry 5.  cannot be determined

29. Two articles are sold at Rs 12,000 each. One is sold at a profit of 20% and another one at a loss of 20%. What is the net loss? 1.  Rs 100 4.  Rs 480

2.  Rs 1000 5.  Rs 960

3.  Rs 1200

30. A retailer keeps Reebok shoes, which are listed at a mark up of 10% above their factory price. However on Monday he realized the shortage of demand and hence decreased the list price by 10%. On the very next day, that is, Tuesday, he realized that he is making a loss so he increased the list price by 10% again. He continues this trend indefinitely. On which day he will suffer a loss of more than 10% per shoe for the first time?

For example, in Hindi he has obtained 10% of the total marks for Hindi. Sum of total marks in all the six papers = 600, although not each of the papers carry same marks. Marks obtained and total marks for any subject can take integral values only. 25. S C Mayank wants to obtain maximum total marks. Which subject should have maximum marks for this to happen?

ANSWER KEYS

2.  85 3.  80 5.  Cannot be determined

27. What is the average marks obtained by S C Mayank in this examination?

S C Mayank sits in an examination having 6 subjects— English, Physics, Chemistry, maths, Biology and Hindi.

Hindi

2.  Physics 3.  Chemistry 5.  Maths or English

1.  Monday 4.  Sunday

2.  Tuesday 5.  Friday

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

1

3.

1

4.

1

5.

1

6.

1

7.

5

8.

1

9.

1

10.

1

11.

3

12.

4

13.

2

14.

3

15.

1

16.

4

17.

4

18.

1

19.

2

20.

4

21.

2

22.

3

23.

4

24.

3

25.

5

26.

3

27.

5

28.

5

29.

2

30.

4

3.  Thursday

Percentage 

  1.59

HINTS AND EXPLANATIONS   3–4 Go through the options.

23. Effective growth in population = 4% per annum

5. Ratio of cost price of Table and Chair = 7 : 3 (Using alligation)

Now it can be approximated that a little higher than 8% (=16,000) should be the growth in population in two years. Go through the options now.



So cost price = (3/10)×2000 = Rs 1400

7. Assume that the selling price per kg = Rs X/kg

50 X – 525 = 10 X ⇒ 40 X = 525



So, X = Rs 13.125/kg

24. Consider the following table:

2009

2010

2011

2012

2013

2014

2015

Birth rate

5

10

15

20

25

30

35

Death rate

1

2

4

8

16

32

64

1200 ____ To gain a profit of 54%, SP should be = ​   ​ × 1.54 = Rs 1320 1.4

Resultant

4

8

11

12

9

–2

–29

9. Ratio of cost price =CP1 : CP2 = 100 ±profit/Loss % on 2nd item: 100 ±profit/ Loss % on 1st item = 100 – 25 : 100 + 20 = 75 : 120 (+ sign for profit, – sign for loss).

1st drop in population will come in 2014 (negative growth rate).

8. Mark up price = 960/0.8 = 1200

Had the SP been Rs 1200, profit percentage = 40%



CP = 1200/1.4



So the cost prices are Rs 750 and Rs 1200.

11. Answer is– [ 0.25 × 0.98 + 0.35 × 0.96 + 0.4 × 0.95] = 96.1% 12. It has to be in between 20% and 30% (the extremes). 13. Assume some values and solve the question.

Assume original area = 100 ⇒ Diagonal = 2√10



New area = 200 ⇒ Diagonal = 20



Percentage increase = 41.4%

14. Prima facie, it might appear that 1st one is better than the 2nd one or 2nd one is better than 1st one, but a close and deep inspection will reveal that final bill is same in both the cases.

It can be checked with the help of assuming values also.



B = Rs 100, S% = 20% and D% = 10%



Rs 100 – (20%↑) – Rs120→ (10%↓) – Rs 108 (Final Bill)



Rs 100 – (10%↓) – Rs 90→(20%↑) – Rs 108 (Final Bill)



So, both the values are same at the end.

15. A sum of money gets 10 times in 6 years at SI. In how many years will the same sum of money become 13 times of the original sum?

10 times in 6 years ⇒ Addition of 900% in the original sum in 6 years ⇒ 150%/year addition



To become 13 times of the original sum, 1200% is required to be added up in the original sum



⇒ Time taken = 1200/150 = 8 years

 

25. Since Maths and English are the highest contributors, maximum marks should be highest for these. 26. Marks obtained and total marks have to be integral. For minimum marks, maximum marks for Hindi should be maximum (S. C. Mayank’s minimum contribution comes from there only) Look at following table now:

 

Minimum possible total marks for that subject

Marks obtained

Hindi

10%

350

35

Biology

14%

50

7

Maths

22%

50

11

Chemistry

14%

50

7

Physics

18%

50

9

English

22%

50

11

Total marks obtained

80

Subjects

28. We don’t know the maximum marks for different subjects, so cannot be determined. 29. There is a loss of 4%. So, for every Rs 100 invested, Rs 96 is coming back and Rs 4 is lost. In our case, 96% = Rs 24,000; so, 4% = Rs 1000.

c h a p t e r

 4

Ratio, Proportion and Variation  LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   What is Ratio, Proportion and Variation?   Definitions and properties   Different application of the Ratio, Proportion and Variation   Kind of questions which are asked in the CAT   Method of solving questions

Ratio is a quantity which expresses the relationship between two similar quantities. It expresses a magnitude by which one quantity is a part of or a multiple of another quantity.

can be also seen that A : B = kA : kB, where k is any constant known as constant of proportionality, k ≠ 0. If antecedent is more than consequent (or, numerator is more than denominator), then this kind of ratio is known as improper ratio.

E.g.,

E.g.,

If monthly salary of A is Rs 5000 and of B is Rs 10, 000 then we say that ratio of salary of A and B is 1 : 2.

5/3, 55/19 etc. If antecedent is less than consequent (or, numerator is less than denominator), then this kind of ratio is known as proper ratio.

  RATIO

However, we should keep in our mind that we can compare two similar quantities only. Due to this reason, we cannot compare the profitability of one company with the turnover of other company. Ratio of two quantities A and B is written as A : B. Here A is known as antecedent and B is known as consequent. It

E.g., 3/7, 7/18 etc.

Ratio Proportion and Variation  Example  1 Example 

Example  4 Example 

1

  1.61

4

Salary of Amar and Akbar are in the ratio 2 : 7. If the salary of Amar is Rs 4000, what is the salary of Akbar?

Ratio of the age of A and B is 2 : 5 and ratio of age of B and C is 3 : 4. What is the ratio of age of A, B and C?

Solution Solution

Solution Solution

Let us assume that the salaries of Amar and Akbar are 2x and 7x respectively.

Since B is the common platform which associates A and C, so we will try to make B equal in both the cases.

Hence 2x = 4000, or, x = 2000. Hence 7x = Rs 14, 000.

Age of A : Age of B = 2 : 5 ] × 3 Age of B : Age of C = 3 : 4 ] × 5

Example  2 Example 

2

Or, Age of A : Age of B = 6 : 15 ………..(1)

Sum of ages of A and B is 60 years and ratio of their ages is 2 : 3. What are their individual ages?

Age of B : Age of C = 15 : 20………...(2) Since ratio of B is same in both the cases, hence age of A : age of B: age of C = 6 : 15 : 20.

Solution

Solution

Let us assume that the ages of A and B are 2x and 3x respectively. Hence sum of their ages = 2x + 3x = 5x According to the question, 5x = 60, hence x = 12 Hence 2x = Age of A = 24 years

3

On the eve of the foundation day party of due North inc., ratio of males to females was 5 : 3. However, when 10 males left the party, this ratio got changed to 1 : 1. How many people were there originally at the party? Solution Solution

Let us assume that the number of males = x and number of females = y. So, x/y = 5/3

Example  5

If A : B = 1 : 4, B:C=5:6 C : D = 10 : 11 What is the ratio of A : D?

3x = Age of B = 36 years

Example  3 Example 

Example  5

……………………..(1)

When 10 males had left the party, then number of males = x – 10 Hence, (x – 10)/y = 1 : 1 ⇒ x – 10 = y ……………..(2) Solving (1) and (2) we get, total number of persons at the party = 40

Solution Solution

A = 1 × 5 × 10 and D = 4 × 6 × 11. So, ratio = 50 : 264 Alternatively, (A/B) × (B/C) × (C/D) = (1/4) × (5/6) × (10/11) = (1 × 5 × 10)/(4 × 6 × 11) = 50 : 264

Example  6

Example  6

1  ​ A, B, C and D purchase a gift worth Rs 60. A pays ​ __ 2 of what others are paying, B pays __ ​ 13  ​of what others are 1 paying and C pays ​ __ 4 ​  of what others are paying. What is the amount paid by D?

(CAT 2001)

1.62 

  Quantitative Aptitude and Data Interpretation

Solution Solution

Example  8 Example 

1  ​of what others are paying, so A is Since A is paying ​ __ 2 1 __ paying ​ 3 ​  of total amount. (To understand this, let us assume that B, C, D are paying Rs 2x. So A is paying Rs x. So, total amount being paid by A, B, C and D = 3x = Rs 60, hence amount paid by A = x/3x = __ ​ 31 ​  of total.)

A train approaches a tunnel AB. Inside the tunnel a cat located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat exactly at the exit. What is the ratio of speed of train and speed of cat? (CAT 2001)

So, amount paid by A = 60/3 = Rs 20 Similarly, B is paying ¼ th of total and C is paying 1/5th of total. Hence, amount paid by B and C are Rs 15 and Rs 12 respectively.

8

Solution Solution Train

So, amount paid by D = Rs 13

B

A

3/8

Application of Ratio in different contexts Since there lies the multiplying relationship between the quantities in several contexts like that of time and work, or time speed and distance etc., there is a possibility of usage of concepts of ratio in those contexts. Let us understand this with the help of examples: Example  7

Example  7 10 persons can cut 8 trees in 12 days. How many days will 8 persons take to cut 6 trees?

Solution Solution

Let us see this question in a bit changed perspective: Suppose if the question is – 10 persons can cut 8 trees in 12 days. How many days will 10 persons take to cut 4 trees? Answer to this question is – Since amount of work is getting halved, so number of days will also get halved. Now, there are three factors namely number of men, number of days and number of trees, which are responsible for the final answer. Let us see how these factors are affecting the final result: Since number of men is less now in the final situation, so more days will be required. Hence multiplier = 10/8 (Had there been 12 persons, multiplier would have been 10/12.) Number of trees is less now in the final situation, so less days will be required. So, multiplier = 6/8 Hence total number of days = 12 × 10/8 × 6/8 = 90/8 = 11.25 days.

CAT

Initially, this is the position of train and cat. Now, let us assume that cat is moving towards exit B. The moment cat covers 3/8 AB distance in the direction of exit B, train will be at the entrance A. B

A Train

6/8

CAT

Now, if the cat moves in the direction of exit B, the train is catching up with the cat at the exit B. So, in the time cat covers 2/8 distance, train is covering whole distance from A to B. So, ratio of the distance covered by train and the distance covered by cat = 4 : 1 So, ratio of speed = 4 : 1.

  PROPORTION Proportion expresses the relation between two ratios. C A ​  = ​ __ ​ __ B D  ​  When A, B, C and D are in proportion, then A and D are known as ‘Extremes’ and B and C are known as ‘Means’. So, now we can say that, Product of Extremes = Product of Means or A × D = B × C

Ratio Proportion and Variation  Example  9 Example 

8

What is the value of x in the following expression: 5 ___ x? ​ __ 8  ​= ​ 12 ​  Solution Solution

5 ___ x ​ __ 8 ​  = ​ 12  ​  60 ​ 8 ​ = 7.5 ⇒ x = ___ (It can be calculated with the help of percentages also. In the question, percentage increase in denominator is 50 per cent, so numerator will also increase by 50 per cent.)

  1.63

c a+c a  ​= __ 7.  If ​ __ ​    ​= _____ ​     ​  b d b+d c e a  ​= __ In general, if ​ __ ​    ​= __ ​   ​  =………...…..= K b d f c e a+c+e+… Then, __ ​ a  ​= __ ​    ​= __ ​   ​  =………..= K =​ _____________    ​ b d f b + d + f +… = (any combination of numerator/combination of corresponding denominator) [ Provided Sum of numerators ] Example

Example ½ = 3/6 = 4/8 = ………. = (1+3+4)/(2+6+8) = (3+4)/(6+8)

8.  If we multiply the numerator and denominator of a ratio by any number N(N≠0), then the ratio remains same. A/B = NA/NB

Standard results/definitions on ratios/ proportions

9.  If we divide the numerator and the denominator of a ratio by any number N(N≠0), then the ratio remains same. A / B = (A/N) / (B/N)

1.  Continued proportion b a  ​= __ a, b and c are said to be in continued proportion if ​ __ ​   ​  b c So, b2 = ac. Here, b is known as the mean proportion. Similarly if a, b, c and d are in continued proportion, then b we get __ ​ a ​= __ ​   ​ = ​ __c ​ b

c

d

2.  Componendo c a  ​= __ If ​ __ ​    ​, then b d

10.  If a/b, c/d, e/f …etc., are all unequal ratios, then the value of (a + c + e + …..)/(b + d + f +….) lies in between minimum and maximum of all these ratios. Example  10

Example  10

b c a   ​ =​ _____    ​ = _____ ​     ​ then each fraction is equal to If ​ _____ b+c c+a a+b i.  –1

ii.  ½

iii.  1

1.  i and ii only

2.  ii and iii only

a + b _____ c+d _____ ​   ​   = ​   ​    d b

3.  i, ii and iii only

4.  None of these (CAT 2004)​

3.  Dividendo

Solution Solution

a – b _____ c–d c a  ​= __ If ​ __ ​    ​, then _____ ​   ​   = ​   ​    d b d b

b c a+b+c _____ ​     ​ = _________ ​  a   ​ =​ _____    ​ = _____ ​     ​  b + c c + a a + b 2(a + b +c) a+b+c  ​  = 1/2 Now if (a + b + c) ≠ 0, then ​ _________ 2(a + b +c) 

4.  Componendo and Dividendo a +b _____ c+d c a  ​= __ If ​ __ ​    ​, then _____ ​     ​= ​   ​  b d a–b c–d

if (a + b + c) = 0, then a = – (b+c) ⇒ a / (b+c) = –1 Hence, option 1 is the answer.

5.  Invertendo b d c a  ​= __ If ​ __ ​    ​, then __ ​ a ​  = __ ​ c ​  b d

6.  Alterando b c a  ​= __ If ​ __ ​    ​, then __ ​ ca  ​= __ ​   ​  d b d

  VARIATION Two quantities A and B are said to be varying with each other if there exists some relationship between A and B such that the change in A and B are uniform and guided by some rule.

1.64 

  Quantitative Aptitude and Data Interpretation

It can be observed here that partnership is a typical case of direct variation.

Example Example

Area (A) of a circle = π R 2 , where R is the radius of the circle. Area of a circle depends upon the value of Radius of circle, OR, in other words we can say that area of circle varies as the square of radius of circle.

Direct Variation and Inverse Variation Two quantities are said to be varying directly if the multiplying factor or percentage change in one quantity brings exactly the same multiplying factor or percentage change in the second quantity. For example, if the price of tea gets doubled and that doubles the expenses (consumption and any other factor being constant), then it will be said that expenses is directly proportional to the price. Two quantities are said to be varying inversely if the multiplying factor in one quantity brings exactly the reciprocal multiplying factor change in the second quantity. For example:

Example  11

Example  11

A and B invest Rs 12,000 and Rs 16,000 respectively in a business. At the year-end, they share the profit in the ratio 3 : 1. If A has invested his capital for whole year, for how many months B has invested his capital? 1.  4 months 3.  6 months 5.  10 months

2.  3 months 4.  8 months

Solution

Solution

Investment by A = Rs 12,000 and time period = 12 months Investment by B = Rs 16,000 and time period = ? (assume x months) So the profit at the end of the year should be distributed in the ratio = A’s investment × Time period for A : B’s investment × Time period for B

If distance is constant, then Speed α(1/time.)

Application of variation in different contexts

⇒ 12,000 × 12 : 16,000 × x = 9 : x

Partnership If two or more than two persons are investing their money in a joint venture, then the profit or loss incurred is distributed among everybody in the ratio of the (Time period × Sum of money) invested by each of them.

Given that the profit is shared in the ratio 3 : 1. 9 7 ⇒ __ ​ x ​  = __ ​ 1  ​,so, x = 3 months

  EXERCISE 1 1. For two consecutive years, my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5. If my income in the second year is Rs 42000 and my expenses in the first year in Rs 21000, my total savings for the two year is 1.  Rs 5,000 4.  Rs 15,000

2.  Rs 10,000 3.  Rs 12,000 5.  None of these

2. Two-third of the boys and three–fourth of the girls of a school participate in a function. If the number of participating students is 550, out of which 150 are girls, what is the total number of students in the school? 1.  500 4.  750

2.  550 5.  800

3.  600

3. Rupesh was thrice as old as Ravi 6 years back. He will be 5/3 times as old as Ravi 6 years hence. How old is Ravi today? 1.  24 year 2.  18 years 3.  12 years 4.  Cannot be determined 5.  None of these 4. 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24 days. If 8 more cows and 9 more buffaloes are brought in, how long will the fodder last? 1.  20 days 4.  21 days

2.  18 days 5.  None of these

3.  16 days

  1.65

Ratio Proportion and Variation  5. Ajay opened a shop investing Rs 30000. Anju joined him 2 months later, investing Rs 45000. They earned a profit of Rs 54000 after completion of one year. What will be Anju’s share of profit?

1.  Chen spends Rs 2000.

1.  28000 4.  30500

1.  Only 1 and 2 together are sufficient 2.  Only 2 and 3 together are sufficient 3.  1, 2 and 3 together are necessary 4.  Either 1 and 2 together or 3 alone sufficient 5. Either 1 and 2 together or 2 and 3 together are sufficient

2.  20000 5.  None of these

3.  31000

6. On sports day, if 30 children were made to stand in a column, 16 columns could be formed. If 24 children were made to stand in a column, how many columns could be formed? 1.  20 4.  18

2.  21 5.  None of these

3.  22

7. A 85 cm long wire is to be cut into two pieces such that one piece will be two third as long as the other. What will the length of the shorter piece (in centimetres)? 1.  32 4.  34

2.  18 5.  None of these

3.  27

8. On a test consisting of 30 questions. Number of wrong answers is 50 per cent less than number of right answers Each answer was either right or wrong. What is the ratio of right answers to wrong answers? 1.  3 : 2 4.  2 : 1

2.  4 : 1 5.  None of these

3.  5 : 1

2.  Brawn saves Rs 700. 3.  Brawn spends Rs 5000.

14. A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the dog to that of the cat? 1.  11 : 15 4.  15:16

2.  15 : 11 5.  None of these

3.  16 : 15

15. The students in three sections of IIM L are in the ratio 2 : 3 : 5. If 20 students are increased in each section, the ratio changes to 4 : 5 : 7. The total number of students in the three sections before the increase are 1.  75 4.  150

2.  90 5.  None of these

3.  100

9. If 30 oxen can plough 1/7th of a field in 4 hours, in how many hours 18 oxen will do the remaining work?

16. In a fort there is sufficient food for 200 soldiers for 31 days. After 27 days, 120 soldiers leave the fort. For how many extra days will the rest of the food last for remaining soldiers?

1.  30 h 4.  40 h

1.  4 days 4.  8 days

2.  20 h 5.  60 h

3.  15 h

10. Four numbers in the ratio 1 : 3 : 4 : 7 add up to give a sum of 75. Find the value of the biggest number. 1.  42 4.  63

2.  35 5.  42

3.  49

2.  6 days 5.  None of these

3.  12 days

17. Manish and Satish were in partnership business for several years At the end of 1997, a profit of Rs 35000 was made by the two. To find out the share of Manish which of the following statements is/are sufficient?

11. In the above question, what is the difference between the biggest and the smallest number?

A. Manish invested Rs 35000 at the beginning of the year 1997.

1.  42 4.  63

B. Satish withdrew his capital at the end of the month of July.

2.  30 5.  40

3.  49

12. A and B invested the same capital in a business. At the year-end they share the profit in the ratio 3 : 2. If A has invested his capital for whole year, for how many months B has invested his capital? 1.  6 months 4.  5 months

2.  8 months 3.  9 months 5.  None of these

13. Anshu and Brawn have incomes in the ratio 5 : 3. The expenses of Anshu, Brawn and Chen are in the ratio 8 : 5 : 3. To find the income of Anshu, which of the following information(s) is/are sufficient?

C.  Satish gets 1/5 of his investment as share in profits. 1.  A and B together are sufficient 2.  B and C together are sufficient 3.  A and C together are sufficient 4.  All the three even together are not sufficient 5.  All the three together are necessary 18. Sunny and Kapil used a field for grazing their cows for one year at a total cost of Rs 300. Sunny used the field for 8 months for his 15 cows. How many cows

1.66 

  Quantitative Aptitude and Data Interpretation

1.  1 : 2 4.  4 : 1

can Kapil graze in the field for the remaining period of time if he pays 100 rupees less then Sunny? 1.  30 4.  15

2.  25 5.  None of these

3.  20

A. Hari and Vijay invested Rs 20,000 and Rs 30,000 respectively in a business. These are the only investors in business.

1.  2/5 4.  3/8

B. They decided 75% of their profit should be divided equally.

1.  5 : 8 4.  8 : 5

1.  A alone is sufficient 2.  A and B together are sufficient 3.  A and C together are sufficient 4.  All are necessary 5.  All the three even together are not sufficient

3.  1/5

2.  9 : 10

3. 15 : 24

24. A bag contains Rs 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of 2 : 3 : 4. The number of 50 paise coins is 1.  96 4.  141

20. D, K and A can do a work in 5, 15 and 35 days respectively. They get an amount of Rs 1054 for finishing the work working together. What is the share of K in that amount?

2.  144

3.  114

25. At the start of seminar, the ratio of the number of male participants to the number of female participants was 3 : 1. During the tea break, 16 participants left and 6 more female participants registered. The ratio of the male to the female participants became 2 : 1. What was the total number of participants at the start of the seminar?

3.  Rs 238

21. The ratio of the rate of flow of water in pipes varies inversely as the square of the radius of the pipes. What is the ratio of the rates of flow in two pipes of diameters 2 cm and 4 cm?

ANSWER KEYS

2.  5/12 5.  2/7

23. Given that 24 carat gold is pure gold; 18 carat gold is 3/4 gold and 20 carat gold is 5/6 gold, the ratio of the pure gold in 18 carat gold to the pure gold in 20 carat gold is

C. The remaining profit is divided in the ratio of investment.

2.  Rs 324 5.  None of these

3.  1 : 8

22. Half the girls and one-third of the boys of a college reside in the hostel. What fractional part of the student body is hostelries if the total number of girls in the college in 100 and is 1/4 of the total strength?

19. What is the total profit made in the business?

1.  Rs 242 4.  Rs 245

2.  2 : 1 5.  None of these

1.  64 4.  72

2.  48 5.  76

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

5

3.

3

4.

2

5.

5

6.

1

7.

4

8.

4

9.

4

10.

2

11.

2

12.

2

13.

5

14.

3

15.

3

16.

2

17.

4

18.

4

19.

5

20.

3

21.

4

22.

4

23.

2

24.

2

25.

4

3.  54

Ratio Proportion and Variation 

  1.67

HINTS AND EXPLANATIONS 4 __ 1. (2)  Income in first year = ​   ​  × 42000 = Rs 24000 7 5 __   Expenses in second year = ​   ​  × 21000 = Rs 35000 3   Total savings = Total income – Total expenses   = (42000 + 24000) – (21,000 + 35000)   = 66,000 – 56,000 = Rs 10,000 2. (5) Let total number of boys be x and total number of girls be y. 3y 2x ___ __  ​   ​ = 400 ⇒ x = 600 and ​   ​ = 150 ⇒ y = 200 3 4   Now, x + y = 800.



 Now cat takes 5 leaps for every 4 leaps of a dog → in the same time, cat covers 15 m while dog covers 16m. So ratio of speed of dog : cat = 16 : 15

15. (3) Go through the options. Since the sum of ratios = 10, so total number of students should be multiple of 10. Now check the options one by one. 16. (2) Ratio of the new number of persons in the fort : original number of persons in fort = 80 : 200 = 2 : 5

 Hence the food will last for 5/2 days of the original (4 days = 31 days – 27 days) = 5/2 × 4 = 10

  So extra days = 6 days.

3. (3)  Rupesh – 6 = 3 (Ravi – 6) ....(i)

17. (4) No information is provided about the capital of Satish. So using all the statements together is not sufficient to get the answer.

5 __   and Rupesh + 6 = ​   ​  (Ravi + 6) ......(ii) 3

18. (4)  Sunny pays 2000 and Kapil pays Rs 100.

  Solving both the equations we get,



  Ravi = 12 years

4x __ 1 ___   4x : 8 × 15 = 100 : 200 or, ​    ​ = ​   ​  120 2

4. (2)  2 oxen = 3 buffaloes = 4 cows

120 ___   ⇒ x = ​   ​  = 15 cows. 8

  8 oxen = 16 cows and 15 buffaloes = 20 cows   16 cows + 20 cows + 24 cows = 60 cows   Since fodder is available for 60 cows for 24 days

19. (5) Statements nowhere mention the profit generated (in Rs). 20. (3)  D share : K share : A share

  = K time × A time : D time × A time : D time × K time



  = 15 × 35 : 5 ×35 : 5 × 15 = 21 : 7 : 3

  So fodder will be available for (60 + 8 + 12) = 80 cows 24 × 60 _______   for ​   ​   = 18 days 80 30 ×12 __ 4 _______ 5. (5) ​     ​  = ​   ​ . So Anju’s share = [5/9] × 54000 45 × 10 5 16 × 30 _______ 6. (1)  Required number = ​   ​   = 20 24 7. (4)  Ratio = 2 : 3 2 __   So, Shorter piece = ​   ​  × 85 = 34 cm 3 Solution 10 and 11.  Assume the numbers are x, 3x, 4x and 7x.

1054 ____   So, K’s share = ​   ​   × 7 = Rs 238 31 21. (4)

Radii of the two pipes are 1 cm and 2 cm.



Hence, Rates of flow of the two pipes are in the ratio

1 __ = 1 : ​   ​  , i.e., 4 : 1. 4 22. (4)

Number of girls = 100



Number of boys = 300



Number of hostel dwellers = 50 + 100 = 150



3 __ ⇒ Required ratio = 150 : 400 = 3 : 8 = ​   ​ . 8

  15x = 75 → x = 5 10. (2)  Largest number = 7x = 35 11. (2) Difference between largest and smallest number = 7x – x = 6x = 30

  Now, if Kapil grazes x cows for 4 months then

14. (3) 3 leaps of the dog are equal to 4 leaps of the cat = 12 m (assume)

23. (2)

  So, 1 leap of dog = 4 m and 1 leap of cat = 3 m

24. (2)

1.68 

  Quantitative Aptitude and Data Interpretation

Solution Let number of one-rupee coins = 2K

25. (4)

Number of 50-paise coins = 3K

Let the incomes of the two persons be 4I and 5I respectively.

Number of 25-paise coins = 4K

Let the expenditure of the two persons be 7E and 9E respectively.

2 K + 0.50 × 5 3 K + 0.25 × 4K = 216

  41 – 7E = 50 and 51 – 9E = 50 ⇒20l – 35E = 250 ∴



⇒ 2 K + 1.5K + K = 216



⇒ K = 48. Hence, Number of 50-paise coins = 3K = 144.



Alternatively this question can be done by options too.

  20l – 36E = 200 ⇒ E = 50 and I = 100 So, monthly incomes are Rs 400 and Rs 500 respectively.

  EXERCISE 2 1. The monthly income of two persons are in the ratio of 4 : 5 and their month expenditure are in the ratio of 7 : 9. If each saves Rs 50 a month, then what are their monthly incomes? 1.  Rs 100, Rs 125

2.  Rs 200, Rs 250

3.  Rs 300, Rs 375 4.  Rs 400, Rs 500 5.  None of these 2. If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then 3 (B + G) is 1.  Equal to 3

2.  Less than 3 3.  More than 3

4.  Less than __ ​ 13 ​  

5.  None of these

2.  5 : 4 : 3 5.  3:2:1

3.  3 : 4 : 5

P+Q P 4. What is value of ______ ​ P – Q ​ if ​ __   ​ = 7? Q

4 ​   1. ​ __ 3

7 ​   4. ​ __ 8

2 ​   2. ​ __ 3

2 ​  3. ​ __ 6

5.  4/7

5a + 3b ___ 5. If ​ _______ = ​ 23 5 ​ then the value of a : b is 2a – 3b ​  1.  2 : 1 4.  4 : 1

2.  1 : 4 5.  3:2

2.  1 5.  3

3.  2

7. The intensity of illumination on a surface from a source of light varies inversely as the square of the distance of the surface from the source. The effect of moving a piece of paper 3 times as far from the source is to 1.  Divide the intensity by 3 2.  Multiply the intensity by 3 3.  Divide the intensity by 9 4.  Multiply the intensity by 9 5.  None of these 8. The ratio of the age of a man and his wife is 4 : 3. After 4 years, this ratio will be 9 : 7. If at the time of the marriage, the ratio was 5 : 3, then how many years ago they were married?

1  ​A= __ 3. If ​ __ ​ 14  ​B = __ ​ 15 ​  C. Then A : B : C is 3 1.  4 : 3 : 5 4.  2 : 5 : 1

1.  0 4.  7

1.  12 years 4.  15 years

6. What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the numbers left are proportional?

3.  10 years

9. For each 200 rupees spent by the R&D, sales department spends 20 rupees. For every 400 rupees spend by the sales department, the advertising department spends 150 rupees. What is the ratio of the money spent by the R&D to the money spent by the sales department to the money spent by the advertising department? 1.  40 : 8 : 3 4.  2 : 1 : 5

3.  1 : 2

2.  8 years 5.  9 years

2.  80 : 8 : 3 5.  None of these

3.  20 : 4 : 1

10. x² varies directly as y³ and when x = 6 and y = 3. Which of the following equations correctly represents the relationship between x and y? 1.  6x² = 3y³ 4.  3x2 = 4y³

2.  3y² = 6x³ 3.  3x² = 2y³ 5.  None of these

Ratio Proportion and Variation  11. Two numbers are in the ratio of 1 : 2. If 7 be added to both, their ratio changes to 3 : 5. What is the greater number? 1.  20 4.  32

2.  24 5.  30

3.  28

12. Two numbers A and B are such that the sum of 5% of A and 4% of B is 2/3 of the sum of 6% of A and 8% of 2. Find the ratio of A : 2. 1.  4/3 4.  2/3

2.  3/4 5.  None of these

3.  1

13. Eight people are planning to share equally, the cost of a rental bus. If one person withdraws from the arrangement and the others share equally the entire rent of the bus, then the share of each of the remaining persons increased by 1.  1/9 4.  7/8

2.  1/8 5.  2/7

3.  1/7

14. Determine the ratio of the number of people having characteristic X to the number of people having characteristic Y in a population of 100 subjects from the following table: Having X and Y

10

Having X but not Y

30

Having Y but not X

20

Having neither X nor y

40

1.  4/3 4.  5/3

2.  3/4 5.  None of these

3.  1/3

15. The speed of a railway engine is 42 kmph when no compartment is attached, and the reduction in speed is directly proportional to the square root of the number of compartments attached. If the speed of the rain carried by this engine is 24 kmph when 9 compartments are attached, the maximum number of compartments that can be carried by the engine is 1.  49 4.  47

2.  48 5.  50

3.  46

16. Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders The average expense per boarder is Rs 700 when there are 25 boarders and Rs 600 when there are 50 boarders What is the average expense per boarder when there are 100 boarders? 1.  550 4.  570

2.  580 5.  450

3.  540

17. A student took five subjects in an examination, where the full marks were the same for each subject. His marks in these subjects were in the proportion of 6 : 7 : 8 : 9 : 10.

  1.69

In all subjects together, the candidate obtained 60 per cent of the total marks. Then the number of subjects in which he got more than 50 per cent marks is 1.  2 4.  5

2.  3 5.  None of these

3.  4

18. There are two containers A and B filled with different variant of petrol having different prices. Volume of petrol in container A is 140 litres and in container B is 60 litres. Equal quantities of petrol are being drawn from each of the containers and poured in the other container [from container A to container B and vice versa]. Due to this, the price per litre of petrol becomes same in both the containers. What is the quantity of petrol drawn from each of the containers A and B (in litres)? 1.  20 4.  50

2.  36 5.  None of these

3.  42

19. There are two alloys made up of copper and gold. In the 1st alloy, copper is half of the gold and in the second alloy copper is thrice as much as gold. How many times the second alloy must be mixed with first alloy to get the new alloy in which copper is twice as that of gold? 1.  3 4.  6

2.  4 5.  None of these

3.  5

20. A and B are two alloys. Alloy A consists of elements P, Q, R and alloy B consists of elements P and Q. A mixture of alloys A and B is prepared in which the final percentage composition of elements P, Q and R is 26%, 68% and 6% respectively. Ratio of elements P, Q and R in alloy A is 2 : 7 : 1. Find the percentage composition of elements P and Q in alloy B. 1.  33.33%, 66.66% 2.  35%, 65% 3.  27%, 63% 4.  70%, 30% 5.  25%, 75% 21. Two alloys of chromium have different percentage of chromium in them. First one weighs 6 kg and second one weighs 12 kg. One piece each of equal weight was cut off from both the alloys and the first piece was alloyed with the second alloy and the second piece alloyed with the first one. As a result, the percentage of chromium became the same in the resulting two new alloys. What was the weight of each piece cut-off ? 1.  4 kg 4.  1kg

2.  2 kg 5.  None of these

3.  3 kg

22. The cost C of manufacturing a brick can be estimated by the formula C = 0.03 ABt2, where A and B are the amounts in Rs of the two major ingredients sand and clay and t is the production time in hours If A is increased by 50%, B is increased by 20% and t is decreased by 30% by what percentage will the estimated cost of manufacturing the brick change?

1.70 

  Quantitative Aptitude and Data Interpretation

1.  12.4% 4.  18.2%

2.  11.8% 5.  13.2%

3.  14.6%

other and receives a pension greater by Rs 250. If the length of service of the first had exceeded that of the second by 4 __ ​ 14 ​  years their pensions would have been in the ratio of 9 : 8. How long had they served respectively?

23. During the Bank Wiring experiment to understand the impact of pattern of informal relationship among employees in any organization, it is found that the quantity of work done by a man in an hour is directly proportional to his pay per hour and inversely as the square root of the number of hours he works per day. He can finish a piece of work in six days when he works 9 hours a day at Re 1 per hour. How many days will he take to finish the same work when working 16 hours a day at the rate of Rs 1.50 per hour? 1.  10 days 4.  4 days

2.  3 days 5.  6 days

1.  16 years and 25 years 2.  9 years and 16 years 3.  9 years and 25 years 4.  9 years and 36 years 5.  None of these 25. Given is 2x = 4y = 8z and xyz = 288. What is the value 1 __ 1 __ 1 of ​ ___ 2x  ​ + ​ 4y  ​ + ​ 8z  ​ ?

3.  8 days

ANSWER KEYS

24. According to the personnel administration prevalent in India, people are awarded pensions in proportion to the square root of the number of years they have served. One has served 9 years longer than the

18 1. ​ ___ 74 ​  

18 ​   2. ​ ___ 96

11 4. ​ ___ 96 ​  

5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

3

3.

1

4.

4

5.

3

6.

3

7.

4

8.

1

9.

2

10.

4

11.

3

12.

1

13.

3

14.

1

15.

2

16.

1

17.

3

18.

3

19.

2

20.

2

21.

1

22.

2

23.

2

24.

1

25.

4

11 ​  3. ​ ___ 74

HINTS AND EXPLANATIONS 1. (3)

3. (1)

x x __ __ ∴ ​ y ​  = B and ​ y ​  = G

P __ ​    ​ + 1 Q P + Q _____ 8 __ 7 + 1 __ 4 ______ _____ ​   ​  = ​   ​  = ​   ​ =​   ​  = ​    ​ 7–1 6 3 P – Q __ P ​    ​ – 1 Q

3(x2 + y2) x __y __ ________ ∴ 3(B + G) = 3 ​ y ​  +​ x ​  = ​  xy ​    > 3.

Alternatively, assume any value of P and Q such that ratio = 7. For example, P = 7 and Q = 1

2. (3)

4. (4)

C A __ B __ __ ​   ​ = ​   ​  = ​   ​  = C 3 4 5

5a + 3b _______ ​   ​  = 23/4 ⇒ 25a + b = a – b ⇒ 21a = 84b 2a – 3b

⇒ A = 3K, B = 4K, c = 5K

4 _a __ ⇒ a = 4b ⇒ ​   ​  = ​   ​  b 1

A : B : C = 3 K : 4K : 5 K = 3 : 4 : 5

Best way of solving these questions is — Go through the options.

Let number of boys = x and number of girls = y

Ratio Proportion and Variation 

  1.71

5. (3)

14. (1)

34 – x 14 – x ______ ______ A = ​   ​  = ​   ​  ⇒ x = 2. 17 – x 42 – x

Number of people having characteristic X = 10 + 30 = 40 Number of people having characteristic Y = 10 + 20 = 30

6. (3)

Required ratio = 40 : 30 = 4 : 3.

7. (4) 1 __ Let y ∝ p + q, where p ∝ x and q ∝ ​ x  ​ So, Y = K (p + q),

( 

)

N N __ __ p = Mx, q = ​ x ​ ⇒ y = K​ Mx + ​ x ​   ​

( 

)

N 10 ___ __ y = ​   ​ , when x = 3 ⇒ K​ 3M + ​   ​   ​ 3 3

15. Here x = number of compartments __ ​ __ 9 ​  √ 18 ___ ___ ​   ​ = ​    ​ ​ x ​  42 √

So, MK = 2 and NK = – 8

Simplifying, x = 49, but this is with reference to maximum speed. Hence number of compartments would be one less in order to run i.e., 48.

–8 8 2x ___ ___ __ ∴ P = ​   ​ , P = ​    ​.  So y = 2x – ​ x  ​ K Kx

16. Let x be the fixed cost and y the variable cost

8. (1)

17500 = x + 25y

…(i)

Husband’s age = 4k and wife’s age = 3k

30000 = x + 50y

…(ii)

4k – x __ 9 ______ ​     ​  = ​   ​  ⇒ k = 8 3k + 4 7

Solving the equation (i) and (ii), we get

So, husband’s age = 32 years and wife’s age = 24 years Suppose they were married x years ago. 5 32 – x __ ______ ∴ ​   ​  = ​   ​  ⇒ x = 12 24 – x 3

X = 5000, y = 50 Now if the average expense of 100 boarders be ‘A’ Then 100× A = 5000 + 500 × 100 ⇒ A = 550.

9. (2)

17. Let the marks in five subjects be 6x, 7x, 8x, 9x and 10x (on a scale of 1).

10. (4)

Average score = 60%

x² ∝ y³ ⇒ x² = Ky³ 4 __ Or, x = 6, y = 3 ⇒ K = ​   ​ . So, 3x² = 4y³. 3 11. (3) x+7 x __ 1 _____ __ ​ y ​  = ​   ​  , ​   ​ = ⇒ x = 14, y = 28. 2 y+7 12. (1)

6x + 7x + 8x + 9x + 10x ___ 60 _____________________ ​   ​       = ​    ​ ⇒ 8x = 0.6 100 5 x = 0.075 So the marks are 0.45, 0.525, 0.675 and 0.75. Number of times the marks exceed 50% is 4. 18. Ratio of quantities = 140 : 60 = 7 : 3

2 __ 5% of A + 4% of B = ​   ​  [6% of A + 8% of B] 3

140 × 3 + 60 × 7 ______________ So the quantity to be exchanged = ​      ​  = 42 litres 2(7 + 3)

16B 12A ____ ____ ⇒ 5A + 4B = ​   ​   + ​   ​   3 3

19. Copper in 1st alloy = 1/3

4 A __ __ ⇒ 3A = 4B ⇒ ​   ​ = ​    ​. B 3

Copper in 2nd alloy = 3/4

13. (3) Initially, number of persons = 8, so share of each

Now it can be solved by using alligation:

1 __ person is ​   ​  of the total cost. 8

Copper in combined = 2/3

1/3 2/3

Now there are seven persons. 1 __ 1 ___ 1 1 1 __ __ __ Share of each person = ​   ​  – ​   ​  = ​    ​ , i.e., ​   ​  of ​   ​  , 7 8 56 7 8 1 __ i.e., ​   ​ of the original share of each person. 7

3/4

1/12 So final ratio = 1 : 4

1/3

1.72 

  Quantitative Aptitude and Data Interpretation

20. Let us look at the initial condition vis a vis the final condition:  

Initially

 

P

Q

R

Alloy A

20%

70%

10%

Alloy B

x%

y%

0%

26%

68%

6%

Finally

So, Alloy B and alloy A are mixed in 2 : 3. Using this, we can find out the percentage composition of elements in alloy B. 20%

x% 26%

It can be observed that 6 per cent of R in final mixture is coming from alloy A. Using this, we can find out the ratio in which alloy A and alloy B has been mixed using alligation. 0%

10% 6%

10% - 6% = 4% 2

3

:       

x – 26 __ 3 ______ So, ​     ​  = ​   ​  ⇒ x = 35%, so y = 65% 26 – 20 2 6% - 0% = 6%

:    



3

24. Go through the options.

2

c h a p t e r

 5

Time and Work

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Time and Work Equivalence   Relationship between Time and Efficiency   Different types of Work   Kind of questions which are asked at CAT   Method of solving questions

  TIME AND WORK Under this topic, we study the happening of a work with relation to the time and the number of persons/agents doing that work.

Time-Work Equivalence

completed, then the other factor i.e., number of persons will change accordingly and vice versa, so that product of the factors becomes equal to 200 man-days. For example, if the number of persons = 5, then the number of days required to finish the job = 200/5 = 40 days. Similarly, if the number of days in which work is to be ___ finished = 2 days, then number of persons required = ​ 200 2    ​ = 100 persons.

Number of days × Number of men = Work done W=M×D This gives us a very important concept of man-days. To understand the above relation better, if there are 10 persons working for 20 days to complete a job, then the total work done is equal to 200 man-days. Now if we change the number of days in which work is to be

Example  1 Example 

1

A contractor undertakes to do a work in 50 days by 50 labourers. After 40 days, he realizes that only 50 per cent work is done. How many more labourers should be employed so that work is complete on time?

1.74 

  Quantitative Aptitude and Data Interpretation

Solution Solution

Example  3 Example 

W = M × D 50% 50 40 ------(i) Rest 50% (50 + M) 10 -------- -----(ii) Since work is constant in both the cases, so, change in the number of labourers and number of days will be reciprocal to each other. As no. of days left in (ii) is ¼ of (i)initial period, so, number of persons will become 4 times of the initial number of persons. Hence, no. of persons = 50 × 4 = 200. So, M = 150 men

12 persons can plough 10 hectares in 16 days. In how many days can 8 persons plough 12 hectares?

Example  2

Five persons can cut ten trees in 12 days. In how many days can 9 persons cut 15 trees? Solution

Total number of man-days required to cut 10 trees = 5 × 12 = 60 man-days Total number of man-days required to cut 1 tree = 6 mandays Total number of man-days required to cut 15 trees = 15 × 6 = 90 man-days Hence number of days taken = 90/9 = 10 days.

Important Derivation W1/W2 = (M1/M2) × (D1/D2) In other words: M1 × D1 × W2 = M2 × D2 × W1 Where W1 = Work done in the 1st case, W2 = Work done in the 2nd case M1 = No. of persons in the 1st case, M2 = No. of persons in the 2nd case D1 = No. of days in the 1st case, D2 = No. of days in the 2nd case Extension of the above result: If daily working hours are also given, then the above result will get transformed into: M1 × D1 × T1 × W2 = M2 × D2 × T2 × W1 If efficiency of the workers is also given, then the above result will get transformed into: M1 × D1 × T1 × E1 × W2 = M2 × D2 × T2 × E2 × W1

3

Solution Solution

Here W1 = 10 W2 = 12 M2 = 8 M1 = 12 D2 = ? D1 = 16 Putting the values in the equation W1/W2 = (M1/M 2) × (D1/D2) 10 12 16 We get = × Hence,D2 = 28.8 days 12 8 D2

Individual Work/Individual Efficiency If A can do a work in 20 days, then A will be doing 1/20th of the whole work in one day. Similarly, A will be doing 2/20th of the whole work in two days. In n days, A will be doing n/20th of the whole work. Example  4

Example  4

A can do some work in 10 days and B can do the same work in 20 days. In how many days will both of them finish the work is they work together? Solution Solution

Assume total work = 1 unit Work done by A in one day = 1/10 unit Work done by B in one day = 1/20 unit Work done by both of them in one day working together = (1/10) + (1/20) = 3/20 units Hence they will be doing the whole work in 20/3 days = 6.66 days

LCM Method of Solving Time and   Work Questions Let us take the above example once again: Assume total work to be equal to the LCM of the days taken by A and B (i.e., of 10 and 20) = 20 units Work done by A in one day = 2 units and Work done by B in one day = 1 unit Work done by both of them in one day working together = 3 units

Time and Work 

So, no. of days taken by both of them working together = 20/3 = 6.66 days Example  5 Example 

5

Amit, Bidhan and Charu can do a work individually in 8 days, 10 days and 15 days respectively. In how many days will all of them complete the work working together?

  1.75

Solution Solution

Let us assume work = LCM of (12, 10, 8) = 120 units So, A and B are doing 10 units in one day, B and C are doing 12 units in a day and A and C are doing 15 units in a day. Adding all these, 2(A +B +C) are doing 37 units in a day. ⇒ (A +B +C) are doing __ ​ 37 2  ​= 18.5 units in a day.

120 ​ days = 6.48 So, Time taken to complete the work = ​ ___ 18.5    days

Solution Solution Let us assume that the total work = LCM (8, 10, 15) = 120 units Work done by Amit in one day = 15 units Work done by Bidhan in one day = 12 units Work done by Charu in one day = 8 units Work done by all of them in one day = 35 units

Individual Efficiency

Hence number of days taken to do the whole work by all of them = 120/35 = 3.42 days

Efficiency is known as Work-Rate also.

Example  6 Example 

So, more the efficiency, less will the number of days and less the efficiency, more will be number of days. We have observed Individual Efficiency in case of Percentage also (Product Stability ratio).

6

In the above question, they worked together only for 1 day and after that Amit stopped working. After how many days the remaining work will be finished by Bidhan and Charu working together? Solution Solution

Let us assume that the total work = LCM (8, 10, 15) = 120 units Work done by Amit in one day = 15 units Work done by Bidhan in one day = 12 units Work done by Charu in one day = 8 units Work done by all of them in one day = 35 units At this point of time, Amit stops working. Hence remaining work = 120 – 35 = 85 units Work done by Bidhan and Charu in one day = 20 units Hence no. of days taken to do the remaining work = 85/20 = 4.25 days

Example  7 Example 

7

A and B together can do a work in 12 days, B and C together can do the same work in 10 days and A and C together can do the same work in 8 days. In how many days will the work be complete if A, B and C are working together?

The moment we say that A is taking less no. of days with respect to B to complete the same work, what we mean to say is that efficiency of A is more than efficiency of B.

Now, assume A takes 20 days to complete a work and B takes 25 days to complete the same work. So, efficiency of A is 25 per cent more than efficiency of B.

General Expression correlating Time taken and Efficiency If efficiency of A is x% more than efficiency of B and B takes ‘B’ days to complete the work, then A will take ( work.

B × 100) days to complete the same 100 – x

If efficiency of A is x% less than efficiency of B and B takes ‘B’ days to complete the work, then A will take ( B × 100) days to complete the same work. 100 – x So, if A is 20 per cent more efficient than B and B takes ‘B’ days to complete the work, then A will take B days to 1.2 do the same work. With this, it can also be observed that if work is constant then time taken is inversely proportional to the efficiency.

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  Quantitative Aptitude and Data Interpretation

Example  8 Example 

8

John is thrice as efficient as Abraham and hence completes a work in 60 days less than the number of days taken by Abraham. What will be the number of days taken by both of them working together? Solution Solution

Since John is thrice as efficient as Abraham, so number of days taken by him will be 1/3rd the number of days taken by Abraham. So. if John is taking x days, then Abraham will take 3x days to complete the same work. Now, 3x – x = 2x = 60 days So, x = 30 days and 3x = 90 days Let us assume that total work = 90 units (LCM of 30 and 90) So, total work done by both of them in one day = 3 + 1 = 4 units of work. So, total no. of days = 90 days = 22.5 days 4

Example  9

Effective time to produce  1500 bolts = 30 min Effective time to produce  9000 bolts = 30 × 6 – 10 = 170 min … (2) From (1) and (2) Minimum time = 170 minutes

Concept of Collective Work/ Collective Efficiency When people of different efficiencies start working together, then we cannot simply use Time-Work equivalence to find out the time or the amount of work done. In those cases, we will be required to relate time with the efficiency of group. As for example, if 5 men and 8 women can do a work in 10 days, then we can not find out that in how many days a man or a woman can do the work working individually, since right now we are not aware of their individual efficiencies. However, if we get a similar equation like x men and y women can do the same work in ‘p’ days, then we can correlate these two equations to find the number of days taken by one man and one woman to do the work.

Example  9

In a Nuts and Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to cleaned for10 minutes after production of every 1500 bolts. If both the machines start the production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts? 1.  130 minutes 3.  170 minutes

2.  135 minutes 4.  80 minutes

Solution

Solution Machine I: Number of nuts produced in one minute = 100 To produce 1000 nuts time required = 10 min Cleaning time for nuts = 5 min Over all time to produce 1000 nuts  = 15 min. Over all time to produce 9000 = 135 min – 5 min = 130 min … (1) Machine II: To produce 75 bolts time required  = 1 min To produce 1500 bolts time required = 20 min Cleaning time for bolts = 10 min.

Example  10

Example  10

12 men and 40 women can do a work in 10 days. Same work can be done by 8 men and 12 women in 30 days. In how many days the same work can be done by 1 man and 1 woman? Solution Solution

12 men and 40 women can do the work in 10 days ⇒ 10 × (12 men and 40 women) can do the same work in 1 day. Similarly, 8 men and 12 women can do same work in 30 days ⇒ 30 × (8 men and 12 women) can do the same work in 1 day. So, efficiency of 10 × (12 men and 40 women) = Efficiency of 30 × (8 men and 12 women) Or, 120 men + 400 women = 240 men + 360 women Or, 120 men = 40 women ⇒ 3 men = 1 woman So, total work = 10 × (12 men and 40 women) = 10 × (4 + 40) women = 10 × 44 = 440 units (woman-days) Total no. of persons supplied = 1 man + 1 woman = 1.333 women So, Time taken = 440/1.33 = 330.8 days

Time and Work 

Extension of Concept of Time and Work Pipes and Cisterns

Example  12 Example 

12

Pipe A can fill a tank in 3 hours. But there is a leakage also, due to which it takes 3.5 hours for the tank to be filled. How much time will the leakage take in emptying the tank if the tank is filled initially?

Pipes and Cisterns is just another application of the concepts of Time and Work. While we see only +ve work being done in normal cases of Time and Work, in case of Pipes and Cisterns, –ve work is also possible. Let us understand this with the help of an example:

Solution Solution

Example  11

Assume total units of work = 10.5 units

Example  11

A and B are two taps which can fill a tank individually in 10 min and 20 min respectively. However there is a leakage at the bottom which can empty a filled tank in 40 min. If the tank is empty initially, how much time will both the taps will take to fill the tank (leakage is still there)?

  1.77

Work done by Pipe A/hour = 3.5 units/hour (Positive work) Work done by leakage + Pipe A = 3 units/hour

Solution

So, Net work done by leakage/hour = 0.5 units/hour

Let us assume the units of work = LCM of (10, 20, 40) = 40 units

So, Time taken = 10.5 = 21 hour 0.5

Work done by Tap A/min = 4 units/min (Positive work)

   Alternatively, due to the leakage, pipe is required to work for half an hour extra. So, the quantity filled by pipe in half an hour is being emptied by the leakage in 3.5 hours. Hence, the quantity filled by pipe in 3 h will be emptied by the leakage in 21 hours.

Solution

Work done by Tap B/min = 2 units/min (Positive work) Work done by leakage/min = 1 unit/min (Negative work) Net work done/min = 4 + 2 – 1 = 5 units/min Hence Time taken = 8 mins

  EXERCISE  1 1. 24 men working 8 h a day can do a work in 21 days. In how many days will 32 men working 7 h a day do the same work? 1.  12 4.  24

2.  16 5.  26

3.  18

2. If A, B and C together can finish a piece of work in 4 days, A alone can do it in 12 days and B in 18 days then in how many days C alone can do it? 1.  21 days 4.  16 days

2.  9 days 5.  None of these

3.  14 days

3. Bucket A has four times the capacity as bucket B. It takes 40 turns for bucket A to fill an empty drum. How many turns will it take for both the buckets A and B, having each turn together to fill the empty drum?

1.  28 4.  42

2.  32 5.  None of these

3.  36

4. 24 labours working 8 hours a day finish a work in 18 days. If the number of labourers and the working hours are increased by 12 and 4 respectively, the work will be finished in how many days? 1.  12 4.  16

2.  8 5.  None of these

3.  18

5. Nitu and Nitika plan to finish a work in 10 days. They start working together. But after 7 days they found that only half of the work was done. So they took help of Naveen who is as efficient as Nitika. In how many days will they finish the work if Neetu is 1.5 times as efficient as Nitika?

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  Quantitative Aptitude and Data Interpretation

1.  8 days 4.  9 days

2.  10 days 5.  None of these

3.  12 days

6. A group of men decided to do a work in 13 days, but six of them became absent. If the rest of the group did the work in 16 days, find the original number of men. 1.  26 4.  32

2.  28 5.  None of these

3.  30

7. A can do a 2/3rd of a work in 10 days, B can do ¾ work in 12 days and C can do 2/3rd work in 6 days. If all work together, how many day will it take to complete the whole work? 1.  10 days 4.  11 days

2.  12 days 5.  None of these

3.  13 days

8. A’s efficiency is 50% of efficiency of B and C together and efficiency of A and C is 19/8 times the efficiency of B. Ratio of efficiency of B and C is 4 : 5. If all of 1 them working together complete the work in 13 – days, 3 In how many days can B do the work, working alone? 1.  45 days 4.  50 days

2.  50 days 5.  None of these

3.  30 days

9. In the above question, in how many days C will complete the work, working alone? 1.  36 days 4.  60 days

2.  25 days 5.  None of these

3.  20 days

10. 36 men can do a piece of work in 30 days if they work 6 h/day. In how many days 20 men working 10 h/day will complete three times of this work? 2.  32 2 3.  20 –2 1.  40 3 5 5 5 7 4.  20 5. None of these 8 11. 5 men and 7 boys can do a piece of work in 10 days. Find in how many days 10 men and 6 boys do the same work. 1 1 2.  3 3.  5 1 1.  2 2 2 2 1 4.  3 5.  Cannot be determined 2 12. 25 men can do a work in 10 days and 20 children can do the same work in 50 days. 5 men start doing that work. After 10 days how many children should join the 5 men, so that remaining work is finished in 20 days? 1.  30 children 4.  28 children

2.  20 children 3.  36 children 5.  None of these

13. Two taps can fill a cistern in 18 minutes and 24 minutes respectively. Both the taps are opened simultaneously and after some time A is closed. It is found that the cistern is full in 16 min. After how many minutes tap A was closed?

1.  3 min 4.  9 min

2.  6 min 5.  None of these

3.  7 min

14. An engineer undertook a project to build a road hav-

ing a length of 15 km long in 300 days and employs 45 men for this purpose. After 100 days he finds that only 2.5 km of the road has been completed. Find (approx) the number of extra men required so that the job is finished on time.

1.  52 4.  68

2.  67 5.  None of these

3.  65

15. A can do a work in 12 days and B does the same work in 18 days. Efficiency of C is 3/2 times the efficiency of A. In how many days, all of them working together will do the job? 1.  25 4.  40

2.  30 5.  None of these

3.  35

16. Efficiency of A and B are in ratio 6:11. If A takes 35 days more than B find the number of days taken by B to finish the work working alone. 1.  42 days 4.  25 days

2.  46 days 5.  None of these

3.  50 days

17. Amit is thrice as good as Vinit and takes 60 days less to complete a work. What is the time taken to finish the work both working together? 1.  22.5 days 4.  20.5 days

2.  25 days 5.  None of these

3.  24 days

18. A work is given to a group of men to do it in 20 days. But 12 men did not turn up for the job and remaining men did the job in 32 days. What is the original number of men in the group? 1.  26 4.  40

2.  32 5.  None of these

3.  36

19. A is 40% more efficient than B, and B is 20% less efficient than C. If A can do a work in 50 days. In how many days all of them together can do the whole work? 1.  8 days 4.  27 days

2.  6 days 5.  None of these

3.  12 days

20. Efficiency of A and B are in the ratio 4 : 5, efficiency of B and C in the ratio 2 : 3, efficiency of C and D in the ratio 4 : 5. If C takes 20 days more than D to complete the work then in how many days will A, B, C and D together complete the work? 1.  12 2 2.  12 7 3.  13 2 3 8 3 4.  14 1 2

5.  None of these

Time and Work  21. 8 men and 12 boys can do a piece of work in 10 days. 6 men and 12 boys can do the same work in 12 days. Find in how many days 6 men and 2 boys can do the same work. 1.  16 days 4.  12 days

2.  20 days 5.  None of these

  1.79

23. A + B can do a job in 20 days, B + C can do the same job in 30 days and C + A can do the job in 40 days. In how many days A + B + C can do the same job? 1.  20 days 4.  10 days

3.  18 days

2.  15 days 3.  12.33 days 5.  None of these

22. A, B and C together can do a piece of work in 10 days whereas B and C can do the same work in 20 days. In how many days A can do the work, working alone?

24. Efficiency of A, B and C are in the ratio 4 : 3 : 6. C finishes the same work working alone in 12 days. Find in how many days A and B will do the whole work together.

1.  30 days 4.  15 days

1.  10 days 4.  40 days

ANSWER KEYS

2.  20 days 5.  None of these

3.  40 days

2.  20 days 5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

2

3.

2

4.

2

5.

3

6.

4

7.

5

8.

1

9.

1

10.

5

11.

5

12.

2

13.

2

14.

2

15.

5

16.

1

17.

1

18.

2

19.

5

20.

5

21.

3

22.

3

23.

5

24.

5

3.  30 days

  Quantitative Aptitude and Data Interpretation

1.80 

HINTS AND EXPLANATIONS 1. (3)  Since the work is same in both the cases

Similarly you can easily calculate the value of A and C by considering above equations.

M1 D1 T1 = M2 D2 T2 M1D1T1

10. (2)  Use formula

24 × 21 × 8 32 × 7 M2T2 2. (2)  C alone in 1 day does D2 =

=

1 1 4 1 [ – ( + )] work = 12 18 36 4

× days.

1 = work 9

M1D1T1 W1

=

M 2D2T2 W1

13. (2)  Assume total units of work = 500 units

So, he does 1 work in 9 days.

Proportion of work done by 5 men in 10 days = 1/5 = 100 units

3. (2)  the ratio of the capacity of A and B = 4 : 1

If the work is to be finished in another 20 days, everyday 400/20 = 20 units of work should be done.

  ⇒ Ratio of time = 1 : 4

5 men are doing total 10 units of job daily ⇒ 10 Units of job to be done by children daily

  In 1 turn A and B together can fill =

1 child does 500/(20 × 50) unit = 0.5 unit in 1 day ⇒ For 10 units, children required = 10/0.5 = 20

x 5x x x   40 + = = drum 160 160 32

1 15. (5)  A in one day = 12

  So, to fill a drum it will take = 32 turn. 4. (2)  Required no. of days = 18 ×

24 8 × days 36 12

1 B in one day = 18

5. (3)

3 C’s efficiency = 2

6. (4)  Assume there are X men initially

3 1 1 C in one day = 2 × = 12 8

  So, we have 13 X = 16 (X – 6) → X = 32 men 3 work in = 10 days ⇒ 4 days

7. (5) 

1 work in =

10 × 3 = 15 2

3 work in = 12 days ⇒ 1 work in = 16 days 4 2 work in = 6 days ⇒ 1 work in= 9 days 3 Using LCM Method =

+

LCM 16

+

LCM 9

It will give total work done in days. 1 (B + C) ------- (1) 2 19 Efficiency of A + C = Efficiency of B -------(2) 8 Efficiency of B : Efficiency of C = 4 : 5 --- ------(3) 8. (1)  Efficiency of A = Efficiency of

3 A + B + C = 40 ------(4) Put the value of A+C in equation ---4

19 8

3 B + B = 40

B = 45 days

Hence, C will take = 8 days to do the work. You can easily find out the number of days that A, B and C will take by LCM method. 17. (1)  Let us assume that Amit takes x days to finish a work ⇒ Vinit will take 3x days From the question, (3x – x) = 2x = 60 days ⇒ x = 30

LCM of (15, 16, 9) LCM 15

A

Assume work = 90 units Amit does 1 unit/day and Vinit does 3 units per day. Total work done by both of them = 4 units/day Time taken to finish the work (90 units) = 90/4 = 22.5 days 19. (5)  A does the work in 50 days and A is 40% more efficient than B ⇒ B will take 70 days to finish the same work B takes 70 days to finish the work and B is 20% less efficient than C ⇒ C is 25% more efficient than B ⇒ C will take 70/1.25 = 56 days to finish the work. Let us assume the LCM of 70, 50 and 56 = 1400 units of work to be done.

Time and Work  1400

Work done by A/day = ____ ​  50    ​ 28 units

  1.81

Work done/day by (A + B) = 6 units per day Work done/day by (B + C) = 4 units per day

1400

Work done by B/day = ____ ​  70    ​  20 units

Work done/day by (A + C) = 3 units per day

Work done by C/day = 25 units

Work done/day by 2(A + B + C) = 13 units per day

Work done by all of them together/day = 73 units

Work done/day by (A + B + C) = 6.5 units per day

Time required to finish the work = 1400/73 = 19.17 days 22. (3)  Let us assume that the total work = 20 units (LCM of 10 and 20)

Time required by (A + B + C) to finish the work =

120 6.5

24. (5)  B will finish the whole work in 6 days [Twice more efficient than C. So number of days = (3/6) × 12 = 6 days]

Work done/day by (A + B + C) = 1 unit per day Work done/day by (B + C) = 0.5 unit per day

A will finish the whole work in 8 days [Number of days = (4/6) × 12 = 8 days]

So work done/day by A = 0.5 unit per day Hence time required by A to finish the job = 20/0.5 = 40 days 23. (1)  Assume total work = 120 units (LCM of 20, 30 and 40)

Time required to finish the work = 24/5 days [Assuming the work = 24 units = LCM of 6 and 8]

  EXERCISE  2 Direction for questions 1 to 5:  Read the passage below and solve the questions based on it.

1.  30 4.  36

Modern Boutique received a large order for stitching uniforms from A R Academy and T M High School. He has two cutters who will cut the fabric, five tailors who will do the stitching, and two assistants to stitch the buttons and button-holes. Each of these 9 persons will work for exactly 10 hours a day. Each of the A R Academy uniform requires 20 minutes for cutting the fabric, 1 hour for doing the stitching and 15 minutes for stitching the buttons and the button holes. The T M High School uniform requires 30 minutes, 1 hour and 30 minutes respectively for the same activities.

4. If Modern Boutique hires one more assistant, what is the maximum number of A R Academy uniforms that can be completed in a day?

1. Find the maximum number of T M High School uniform that Modern Boutique can complete in a day. 1.  30 4.  36

2.  35 5.  42

3.  40

2. On a particular day, Modern Boutique decided to complete 20 T M High School uniforms. How many A R Academy uniforms can it complete on that day? 1.  30 4.  36

2.  35 5.  42

3.  40

3. If Modern Boutique decided to complete 30 T M High School uniforms only and no other uniform on a particular day, how many total man-hours will go idle?

1.  60 4.  50

2.  60 5.  50

2.  48 5.  45

3.  45

3.  120

5. Modern Boutique has the option to hire one more employee of any category. Whom should it hire to get maximum increase in production capacity, assuming that it needs to stitch only A R Academy uniform on that day? 1.  One cutter 2.  One tailor 3.  One assistant 4.  Either of the tailor or cutter 5.  None of these Direction for questions 6 and 7: Answer the questions based on the following information. There are three bottles of water—A, B, C, whose capacities are 5 L, 3 L and 2 L respectively. For transferring water from one bottle to another and to drain out the bottles, there exists a piping system. The flow through these pipes is computer-controlled. The computer that controls the flow through these pipes can be fed with three types of instructions, as explained below:

1.82 

  Quantitative Aptitude and Data Interpretation

Instruction type

Explanation of the instruction

Fill (X,Y)

Fill bottle labelled X from the water in bottle labelled Y, where the remaining capacity of X is less than or equal to the amount of water in Y.

Empty (X,Y)

Empty out the water in bottle labelled X into bottle labelled Y, where the amount of water in X is less than or equal to remaining capacity of Y.

Drain (x)

Drain out all the water contained in bottle labelled X.

Initially, A is full with water, and B and C are empty. 6. After executing a sequence of three instructions, bottle A contains one litre of water. The first and the third of these instructions are shown below: First instruction: FILL (C,A)

Then which of the following statements about the instructions is true? 1.  The second instruction is FILL (B, A) 2.  The second instruction is Empty (C, B) 3.  The second instruction transfers water from B to C. 4. The second instruction involves using the water in bottle 1. 5.  None of these



7. Consider the same sequence of three instructions and the same initial state mentioned above. Three more instructions are added at the end of the above sequence to have A contain 4L of water. In this total sequence of six instructions, the fourth one is DRAIN (A). This is the only DRAIN instruction in the entire sequence. At the end of the execution of the above sequence, how much water is contained in C? 2.  2 L 5.  None of these

3.  0 L

8. A can complete a piece of work in 4 days. B takes double the time taken by A, C takes double that of B, and D takes double that of C to complete the same task. They are paired in groups of two each. One pair takes two-thirds the time needed by the second pair to complete the work. Which is the first pair? 1.  A and B 4.  A and D

2.  A and C 5.  C and D

There are infinite pipes attached to a very big tank. Pipes are numbered like P1, P2 , P3 …………..and so on. Its also known that efficiency of every subsequent pipe is half the efficiency of earlier pipe i.e., efficiency of P2 pipe is half the efficiency of P1 pipe and so on. However, in case of P1 pipe, this rule is not true since there is no earlier pipe. When all the pipes are working together, the tank gets filled in 2 hours. 9. How much time will P4 take to fill the tank working alone? 1.  8 h 4.  4 h

3.  B and C

2.  16 h 3.  32 h 5.  Cannot be determined

10. What is the difference in the time taken by P5 and P6? 1.  32 h 4.  16 h

2.  64 h 3.  128 h 5.  Cannot be determined

11. How many pipes can fill the tank within 100 hours working alone? 1.  4 4.  7

Third Instruction: FILL (C,A)

1.  1 L 4.  1.5 L

Direction for questions 9 to 13:  Read the passage below solve the questions based on it.

2.  5 5.  Infinite

3.  6

12. Due to some technical problem, only four pipes P1, P2, P3 and P4 are in working condition. These pipes are now paired up to obtain two pairs of pipes. Now it is found that one pair of pipe is taking 2/3rd of the time taken by the other pair to fill the tank independently. Which of the following is one of the two pairs? 1.  P1, P2 4.  P2, P4

2.  P1, P3 3.  P1, P4 5.  cannot be determined

13. How much time will P2 take to fill the tank working alone? 1.  4 4.  32

2.  8 5.  12

3.  16

14. Ram finishes a work in 7 days. Rahim finishes the same job in 8 days and Robert in 6 days. They take turns to finish the work. Ram worked on the first day, Rahim on the second day and Robert on the third and then again Ram and so on. Who was working on the last day when work got finished? 1.  Ram 2.  Rahim 4.  Rahim and Robert 5. Cannot be determined

3.  Robert

15. Construction of a road was entrusted to a civil engineer. He has to finish the work in 124 days for which he employed 120 workers. Two-third of the work was completed in 64 days. How many workers can be

Time and Work  reduced now without affecting the completion of the work on time? 1.  56 4.  24

2.  64 5.  None of these

3.  80

16. Two workers earned Rs 225 first worked for 10 days and the second for 9 days. How much did each of them get daily if the first worker got Rs 15 more for working 5 days than the second worker got for working 3 days? 1.  Rs 11.70; Rs 12.00 3.  Rs 11.25; Rs 12.50 5.  None of these

2.  Rs 10.80; Rs 13.00 4.  Rs 12.60; Rs 11.00

17. Two pipes A and B can fill a tank in 20 and 30 h respectively. Both the pipes are opened to fill the tank but when the tank is 1/3 full, a leak develops in the tank. Due to this leakage one-third of the water supplied by pipes A and B goes waste. What is the total time to fill the tank if the leak if not closed? 1.  12 h 4.  20 h

2.  16 h 5.  None of these

3.  18 h

18. In how many days will 10 men finish the job? To answer the question which of the following information(s) is/are sufficient (assume equal efficiency of work)? A.  20 men can finish the same job in 20 days. B.  40 men can finish the job in 1 time of what 10 4 men take. C.  50 men can finish double the job in 16 days.

1.  Only (A) alone is sufficient. 2.  Only (C) alone is sufficient. 3.  Any one of (A), (B), (C) alone is sufficient 4.  (A) and (B) together or (C) alone is sufficient. 5.  (A) or (C) alone is sufficient

19. In how much time can a tank be filled by two pipes A and B? A.  Pipe A can fill the tank in 4 hours. B.  Pipe B can fill the same tank in 6 hours. C. They were opened on alternate hours and pipe B was opened first.

1.  Only A and B together are sufficient 2.  Only B and C are together sufficient 3.  Only A and C together are sufficient 4.  A, B and C all together are necessary 5.  All the three even together are not sufficient.

20. In how many days will 22 men finish the work? A.  6 women and 8 men can finish a work in 10 days. B.  6 women work as much as 3 men in the same time.

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C. Each woman takes twice more time taken by a man to finish the work.

1. A alone is sufficient 2.  A and B together are only sufficient 3.  A and either B or C together are sufficient 4.  All A, B and C together are necessary 5.  All even together are not sufficient

21. Amit can do a job in 9 days. To find the number of days in which Gagan can do the same job, which of the following information(s) is/are necessary/sufficient? P.  Gagan is 50% more efficient than Amit. 3 Q. Amit and Gagan together can do the job in 3 5 days. 1 R.  Amit is 33 % less efficient than Gagan.

3

1.  Only P alone is sufficient 2.  Only Q alone is sufficient 3.  Only either P or Q is sufficient 4.  Any one of the three statements is sufficient 5.  All the three statements are necessary

Direction for questions 22 and 23:  Read the passage below and solve the questions based on it. Tank at a water supply station is filled with water by several pumps. At first, three pumps of the same capacity are turned on; 2.5 h later, two more pumps (both the same) of a different capacity are set into operation. After 1 h, the additional pumps were set into operation; the tank was almost filled to its capacity (15 m3 were still lacking); in another hour the tank was full. One of the two additional pumps could have filled the tank in 40 h. 22. What is the volume of the tank? 1.  60 m3 4.  90 m3

2.  80 m3 5.  None of these

3.  75 m3

23. How much water does one of the first three pumps emit in an hour? 1.  5 m3 4.  2 m3

2.  4 m3 5.  None of these

3.  3 m3

24. A man makes 60 articles in the 1st hour. His efficiency decreases by 25% in the 2nd hour, increases by 40% in the 3rd hour, decreases by 33% in the 4th hour and increases by 50% in the 5th hour. If he has to work for more than 1 hour, then in which hour, the average number of articles produced per hour till then would be minimum? 1.  2nd hour 3.  2nd and 4th 5.  None of these

2.  After 5th hour 4.  1st and 3rd

  Quantitative Aptitude and Data Interpretation

1.84 

ANSWER KEYS

25. A worm climbs a vertical bamboo stick 32 cm tall. The worm climbs 3 cm in the day and slips 2 cm during the night each time. However, there are cavities in the stick at 2 cm, 4 cm,16 cm from the bottom that would not let the worm slip further. If the worm climbs only

during the daytime and slips only during the night, on which day from the start will it reach the top? 1.  29 days 4.  26 days

2.  28 days 5.  25 days

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

1

3.

1

4.

4

5.

2

6.

2

7.

3

8.

4

9.

3

10.

2

11.

5

12.

3

13.

2

14.

1

15.

1

16.

2

17.

2

18.

5

19.

4

20.

3

21.

4

22.

5

23.

3

24.

3

25.

4

3.  27 days

HINTS AND EXPLANATIONS 6. At the end of first operation, A = 3, B = 0, C = 2. At the end of the second operation, the possible set can be, all the liquid of C is emptied into B or drained of, such that now once again the liquid of A can be transferred to 3. Thus, A should have in all once litre. Best method is to use choices.

15. (1)

7. At the end of the above stated three steps, and three more steps, if A has in all 4 L, then the only possible thing is that B and C have emptied their contents into 1. Thus, C shall have 0 litre.

Also 1 rd of the work is to be completed in 60 days by (120 – x) 3 workers, where x is the number of men reduced in order to finish the work on schedule.

8. Work done in one day by A,B,C and are

So, (120 – x) × 60 = 120 ⇒ x = 56

1 1 1 1 , , and respectively 4 8 16 32

3 Using answer choices we note that the pair of B and C does of 16 work in one day; the pair of A and D does 1 9 1 4 + = 32 of work in one day . 32 32 Hence, A and D take days. 9 16 32 B and C take = days. 3 6 Hence, the first pair must comprise of A and D. Alternatively, assume that the total work = 32 units. Now find individual work done by each of them and solve. 14. (1) Three day’s work = Six day’s work =

73 84

1 7

+

1 8

+

2 rd of the work was completed in 64 days by 120 workers. 3 1 rd of the work was completed in 32 days by 120 workers. 3

1 6

=

73 168

1 Seventh day work = , done by Ram 7 85 73 1 Since + = > 1, therefore, Ram was 84 84 7 working on the last day.

M received 5% of Rs 7400 extra for being the working member, i.e., Rs 370. 16. (2) Let A got Rs x per day and B got Rs y per day. So, 10x + 9y = 225 and 5x = 3y + 15 ⇒ x = 10.80, y = 13. 17. Let us assume total work = 180 (we are not assuming it to be LCM of 20 and 30 = 60 because in that case 1/3rd of A + B will be fractional) Time taken to fill 1/3rd of the tank = 180/(9 + 6) = 4 h Due to leakage, net inflow = 2/3 (9 + 6) = 10 units Time taken to fill remaining 120 units = 12 h So total time taken = 12 + 4 = 16 h 18. (4) (A) alone: (Use M1 D1 = M2 D2) 10 × N = 20 × 20 ⇒ N = 40 days. (C) alone: (Use M1 D1 W2 = M2 D2 W1)

Time and Work  10 × N × 2 = 50 × 16 × 1 ⇒ N = 50 × 16 = 40 days 20 Statement B provides the same information as given in the question. 19. (4)  We need all the information. 20. (3)  2 women = 1 man (6 women + 8 men) = (3 + 8) men = 11 men ⇒ 11 × 10 = 12 days 12 21. (4)  From statement P

From statement Q: 18 × 9 5 18 × 9 Gagan will do the job in = = 18 45 – 18 9– 5 From statement R: Gagan will do the job in ​(  ​ 

( 100100+ 50 ) = 9 23 = 6 days

100

18 × 9 6 days 27

) ( ) = 6 days

100 – ​ ___    ​ 200 3 _______     ​  ​= 9 100 300

22. The first three pumps are on for 4.5 hours and two additional pumps for 2 hours. Let any one of the 1st three pumps take x hours to fill the tank and it is given that any one of the two additional pumps take 40 hours to fill the tank. So according to the question:

Since Gagan is 50% more efficient than Amit, he will do the job in 9

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4.5 + 4.5 + 4.5 + 2 + 2 + = 1 x x x 40 40

Now find x.

c h a p t e r

 6

Time, Speed and Distance  LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Basic relationship among time, speed and distance   Different Situations viz., Motion in a straight line.   Concepts attached to the these motions   Kind of questions which are asked in the CAT   Method of solving questions

  INTRODUCTION The concept of time speed and distance is used very extensively in different situations to generate questions pertaining to different areas in the CAT and other exams. Some of these areas are given below:

1.  Motion in a straight line 2.  Boats and streams/Escalators 3.  Races 4.  Circular Motion 5.  Trains 6.  Clocks

To get a good command over this topic, students should try to understand the inter-relationship between the factors time, speed and distance.

Relationship between Time, Speed and Distance Distance = Speed × Time It means that if a person is running at a speed of 30 kmph and he runs for 3 h, he will be covering a total distance of 90 km. Distance = 30 × 3 = 90 km

Unit of Distance Usually we take kilometer (km) and metre (m) as the unit of distance. Some other units of distance are mile or feet etc.

Time, Speed and Distance 

Unit of Time Hour and second are mostly taken as the unit of Time. However, day or minute etc. are also used as the unit of time.

Unit of Speed Though we commonly take km/hour and metre/sec as the units of speed. Yet any unit of distance upon any unit of time can be taken as a unit of speed. For example- mile/hour, feet/ sec, mile/sec, feet/hour etc. are units of speed.

Conversion from m/s to km/h and viceversa If speed is given in m/s and we are required to convert it into km/h, we multiply it by 18 and when speed is given in km/h 5 ​ 5  ​  and we have to convert it into m/s, we multiply it by __ 18 . 36 km/h = 36 × 5 = 10 m/s 18 20 m/s = 20 ×

18 = 72 km/h 5

It is one of the primary areas of application of Time, speed and Distance. Using the basic relationship between time, speed and distance; we can observe that three different cases are possible:

Case  1 When S (Distance) is constant Vα

We’ll see that T constant is a situation specific to meeting point cases.

Case  3 When V (Speed) is constant S αT So, S1/S2 = T1/T2 In layman terms, if a person is running with a speed of 20 kmph, then the ratio of distance covered in one hour to the distance covered in two hours will be 1:2. Example  1 Example 

1 . T

1

A man cycles with a speed of 10 kmph and reaches his office at 1 pm. However, when he cycles with a speed of 15 kmph, he reaches his office at 11 am. At what speed should he cycle so that he reaches his office at 12 noon? (CAT 2004) Solution Solution 

1.  Motion in a Straight Line

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1

Using product stability ratio, Speed is being increased by 50%, so time taken will reduce by 33.33%. So, 33.33 % of Time = 2 h Hence, Total time = 6 h So, distance = 10 × 6 = 60 km This distance is to be covered in 5 h(6 – 1)h. So, speed = 60/ 5 =12 kmph Example  2 Example 

2

It can be understood in terms of the reciprocal-ratio-multiplication relationship between V and T.

A boy goes to his school at a speed of 30 kmph and comes back to his home at a speed of 20 kmph. He takes a total of 5 hours in all. What is the distance between his home to school?

Suppose distance = 1000 km and Speed = 100 kmph

Solution Solution 

Speed = 100 kmph

Time = 10 h

Speed = 100 × 2

Time = ½ × 10

Ratio of Speed = 3 : 2, hence ratio of time = 2 : 3 So, time taken from home to school = 3 hours Hence distance = 20 × 3 = 60 km

So, V1/V2 = T2/T1

Case  2

Inverse relation between speed and time

When T (Time) is constant S  α  V So, S1/S2 = V1/V2 The higher the speed is, the more will be the distance covered and the slower the speed, the lesser will be the distance covered.

2

Example  3 Example 

3

Distance between two points AB = 110 km. Manoj starts running from A at a speed of 60 kmph and Ravi starts running from B at a speed of 40 kmph at the same time. They meet at a point X, somewhere on the line AB. What is ratio of AX to BX? A  X  B

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  Quantitative Aptitude and Data Interpretation

Solution Solution  3

Example  4 Example 

Since both Manoj and Ravi are running for the same time, T is constant. Hence, ratio of distance covered by them will be same as ratio of their speed.

Speed of boat in still water is 6 km/h and the speed of river is 1.2 km/h. It takes a total of 20 h. to go to a place and come back. What is the total distance covered in the whole process?

So, AX/BX = Speed of Manoj/Speed of Ravi = 60/40 =3:2

2.  Boats and Streams/Escalator Boats and streams should be ideally seen as just a logical extension of Motion in a Straight Line, with distance being constant. As we know, if distance is constant then V α 1/T.

Basic Terminology

Solution Solution 

4

6

Let us assume D is the distance. Upstream Speed = 4.8 km/h Downstream speed = 7.2 km/h According to the question, D/4.8 + D/7.2 = 20 So, D = 57.6 km and total distance = 57.6 × 2 = 115.2 km Alternatively, Ratio of downstream speed: upstream speed = 3 : 2 Ratio of downstream time: upstream time = 2 : 3

Downstream Movement When the direction of the movement of river and a boat is same, their collective movement is known as Downstream Movement. And the distance covered by boat is known as Downstream Distance. If speed of River = R and speed of boat = B, then Downstream Speed = B + R

Upstream Movement When direction of movement of river and boat is opposite, they are said to be in Upstream Movement. Distance covered in this case is known as Upstream Distance. If speed of River = R and speed of boat = B, then Upstream Speed = B – R (Conventionally, we take speed of boat more than speed of river and if this would not have been the case, boat would not be able to go back.) Now, Speed of boat = ½ (Downstream Speed + Upstream Speed) = ½ (B + R + B – R) = B And speed of river = ½ (Downstream Speed – Upstream speed) = ½ (B + R - B + R) = R Hence, if Downstream speed and upstream speed are given as 20 kmph and 10 kmph, then speed of boat = 15 km/h and speed of river = 5 km/h. In most of the cases of boats and streams, distances covered downstream and upstream are same. In those cases, ratio of time taken becomes inversely of the ratio of the speeds. Time taken Downstream: Time taken Upstream = Upstream speed: Downstream speed

So, time taken in downstream movement = 8 h and time taken in upstream movement = 12 h. (out of total 20 h.) So, distance covered = 8 × 7.2 = 12 × 4.8 =57.6 km And hence total distance = 115.2 km In case of escalators, moving staircase works like an external agent much in the same fashion as river works in boats and streams. Let us see the case of staircase going up and person walking up with it, it can be realized here that since direction of movement of escalator and person (or, body) is same, then speed of escalator and person will be added. Now if the direction of the movement of escalator and person are opposite, then resultant speed ( or, relative speed) will be equal to (Speed of person – Speed of escalator).

3.  Races Basic statements 1. A gives a start of 10 m to B → When B has already run 10 m, then A starts running. B

A 10 m Example  5 Example 

90 m

5

In a race of 100 m, A gives a start of 10 m to B. Despite this, A wins the race by 20 m. What is the ratio of speed of A and B?

Time, Speed and Distance  Solution Solution  8

Obviously, time taken by A to cover 70 m = Time taken by B to cover 100 m Since distance is constant, ratio of speed of A and B = 10 : 7 2. A gives a start of 10 secs to B → B has already run for 10 secs, now A starts running. B A 10 v Where v m/s is the speed of B. Example  6 Example 

6

In a 100 m race, Tom runs at a speed of 1.66 m/s. If Tom gives a start of 4 m to Jerry and still beats him by 12 seconds, what is the speed of Jerry? Solution Solution 

9

Time taken by Tom to cover 100 m = 60 sec Now, since Tom beats Jerry by 12 seconds, time taken by Jerry = 72 seconds. And distance covered by Jerry = 96 m So, speed = 96/72 = 1.33 m/s Example  7 Example 

7

Karan and Arjun run a 100-meter race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with thesecond race? (CAT 2004) 1. Karan and Arjun reach the finishing line simultaneously 2.  Arjun beats Karan by 1 metre 3.  Arjun beats Karan by 11 metres. 4.  Karan beats Arjun by 1 metre Solution Solution  10

Situation (I):  In whatever time Karan covers a distance of 100 m, Arjun covers 90 m in the same time. Situation (II):  Now Karan is 10 m behind the starting point. Once again to cover 100 m from this new point Karan will be taking the same time as before. In this time Arjun will be covering 90 metres only. This means that now both of them will be at the same point, which will be 10 meters away from the finish point. Since both of them are required to cover the same distance of 10 m now and Karan has a higher speed, he will beat Arjun. No need for calculations as option (4) is the only such option.

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4.  Circular Motion In the case of races and motions in straight line, we have observed that if two bodies or persons are moving with different speeds in a straight line in one direction, they will never meet. It is all due to the fact that with the passage of time, distance between them is constantly increasing. Now, circular motion should be seen as a logical extension of races where runners are running on a circular track. And since it an enclosed track (by virtue of it being circular), runners are bound to meet at some point or the other. Now there is a possibility of so many different situations. Let us see some of those situations:

Case 1  When two or more than two persons are running around a circular track in same direction. Example  8 Example 

8

When will they meet for the first time anywhere on the track? A/B

A/B

B B

Starting Fig. 1

A

After 25 secs Fig. 2

A

After 75 secs After 100 secs Fig. 3

Fig. 4

To understand the situation completely, let us assume that there are two persons A and B. Speed of A = 20 m/s, speed of B = 10 m/s, length of track is 1000m and they are running in same direction. It can be seen in fig.1 that initially both of them are at the same point i.e., the starting point. They will be meeting for the first time only if the faster runner A has taken one more round of the track than the slower runner B. This can be interpreted as— A will have to cover 1000 m more than B. It can be understood with the help of the figures given above that the distance will keep on increasing between them with the passage of time. And the moment distance between them becomes equal to 1000 m, they will be at the same point i.e. they will meet (refer fig.4). 1000 = 100 secs. 10 Or, this can be done by using Unitary method also: So, Time taken = Distance/Relative speed = Distance of 10 m is created in 1 sec. So, distance of 1000 m will be created in 100 sec. Now, let us assume that there are three persons A, B and C running with following speeds in the same direction:

1.90 

  Quantitative Aptitude and Data Interpretation

Speed of A = 30 m/s

Example  10 Example 

Speed of B = 20 m/s

Anup and Shishir start running from same point of a circular track at the same time. After how much time will Anup and Shishir, who are running with a speed of 35 m/s and 40 m/s, respectively, meet at diametrically opposite point?

Speed of C = 10 m/s To calculate when will they meet for the first time, we are required to find out the time taken by fastest runner to take one round over the other runners.

Solution Solution

Time taken by A to take one round over B = t A-B = 1000/10 = 100 seconds

Simplest ratio of speed of Anup and Shishir = 7 : 8 So, if they are running in same direction, they will be meeting at 1 point and if they are running in opposite direction, they will be meeting at 15 different points. Now, for them to meet at diametrically opposite point, there should be atleast two meeting points or number of meeting points should be a multiple of 2. Since, they would meet either at 1 point or at 15 points,depending on the direction of their movement, they will, therefore, not meet at diametrically opposite point.

Time taken by A to take one round over C = t A-c =1000/20 = 50 seconds Now, LCM of these two values t A-B and t A-c will give us the time after which all of them will be meeting at the same place. LCM = (100, 50) = 100 seconds It can also be seen that they will be meeting after every 100 seconds. Example  9 Example 

9

When will they meet for the first time at the starting point? Solution Solution

10

5.  Trains We know that when the direction of movement of boat and river is same, relative speed is obtained by adding the speeds of both, the boat and river. But if two trains are moving in same direction, then what is the relative speed? Let us see some cases:

To calculate this, we will use the concept of LCM.

1. When two trains of length L1 and L2 and speed V1 m/s and V2 m/s respectively are crossing each other:

Find the time taken by each individual to take one round and then calculate LCM of these values.

i.  Direction of movement of both the trains are same:

Assume there are three persons A, B and C with a respective speed of 30 m/s, 20 m/s and 10 m/s running in same direction. Length of circular track is 1000 m.



Time taken by A to take one round = t1 = 1000/30 = 33.33 seconds

Relative speed = | V1 - V2 |

Time taken by B to take one round = t2 = 1000/20 = 50 seconds

L1 /V1

     

Number of distinct meeting points when two persons are running and their simple ratio of speed =V1 : V2 i. When they are in the same direction, No. of meeting points = V1 – V2 ii. When they are in the opposite direction. No. of meeting points = V1 + V2

→→→

Total distance covered = L1 + L2 ­ ii.  Direction of movement of both the trains are opposite:

Time taken by C to take one round = t3 =1000/10 = 100 seconds LCM of (t1, t2, t3 ) = 100 seconds.

→→→ L2 /V2

L1 /V1





→→→

L2 /V2



←←←

Relative speed = | V1 + V2 | Total distance covered = L1 + L2 ­ 2. When a train is crossing a stationary object: i.  W  hen the train is crossing a pole or a stationary human being: A(Fig 1) A (Fig 2)

Time, Speed and Distance  Let us assume that A is a pole. In fig.1, the front of train is about to cross the pole and in fig. 2, tail of train has just crossed the pole. It can be well understood here that train has crossed its whole length with respect to the pole. So, when the train is crossing any stationary object of negligible width, the total distance covered is its own length. Relative speed = V1 + V2 , since V2 = 0, so, Relative speed = V2 Total distance covered = L1 ­+ L2, since L2 (width of pole) is negligible with respect to L2 (Length of train), so we don’t consider it while calculating the quantities. So, distance = L1 However one thing should be kept clear in mind that this is mathematically not correct and all the solutions are bearing an assumption that width of pole is zero, which is obviously not true. ii.  W  hen the train is crossing a platform or a standing train:   Relative speed = V1 + V2,  Where V1 is the speed of moving train and V2 is the speed of standing train or platform.   Since V2 = 0, So. Relative speed = V1   Total distance covered = L1 + L2 ­  Where L1 is the length of moving train and L2 is the length of standing train or platform. Example  11 Example 

11

A train takes 10 seconds to cross a pole and 20 seconds to cross a platform of length 200 m. What is the length of train? Solution Solution 

18

Train takes 10 secs to cross its own length and 20 seconds to cross its own length and length of platform. So, it infers that train takes 10 seconds to cross platform and 10 secs to cross its own length. Since time taken to cross platform = time taken to cross its own length So, length of platform = length of train = 200 m Example  12 Example 

12

Speed of a train is 36 kmph. It takes 25 secs to cross a pole. What is the length of this train? Solution Solution

Speed of train = 10 m/s (36 × 5 ) 18 Distance covered = 10 × 25 = 250 m So, length of train = 250 m

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Important results in Time, Speed and Distance 1. When two persons cover the same distance with different speeds (in kmph)and difference in time taken to cover this distance is given:

Distance =

Multiplication of Speed Differnce ofspeed

× Difference intime to cover the distance (in h) 2. If two persons X and Y start in opposite direction from two point at the same time and after passing each other, they complete the journey (to their respective points) in T1 and T2 h, respectively, then  

___

Speed of X  ​ √  T2 ​  = ___ Speed of Y  ​  √  T1 ​  3. If a person goes to a place with V1 speed (kmph) and returns with V2 speed (kmph), and the total time taken in the whole journey = T hour, then Distance (in one direction) covered = Multiplication of two speeds × Total time Sum of speeds 4. Two persons A and B travel for T1 and T2 time towards each other from opposite ends on a linear track and then they meet After this meeting both of them reach at their respective destinations ( the opposite end of their starting ______ pt.) at the same time. then T = ​  √  T1 . T2 ​  (T = Time taken by each of them to reach their respective destination after meeting each other). For example, A and B start at 1 PM and 4 PM respectivdy from opposite ends P and Q, A has to go to Q and B has to go to P ( their respective opposite ends). They meet at 5 PM, and they reach at their respechive destinations at the   __________ same time after time T. So T = ​√ (​ 5-1 )​(​ 5-4 )​ ​   = 2 h. So, they are reaching their respective destinations at 7 PM.

1.92 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  1 1. How much time the train will take to cross a pole along the railway track if length of the train is 180 m and it is running at the speed of 54 km/h? 1.  10 sec 4.  24 sec

2.  12 sec 5.  None of these

3.  15 sec

2. The lengths of a train and a platform are 120 m and 180 m respectively. Train takes 9 seconds to cross the platform. Find the speed of train. 1.  100 km/h 4.  24 km/h

2.  102 km/h 3.  120 km/h 5.  None of these

3. Length of a goods train is 287 m and it passes a bridge in 38 sec running at the speed of 90 km/h. What is the length of the bridge? 1.  665 m 4.  580 m

2.  663 m 5.  None of these

3.  680 m

4. Length of two trains are 125 m and 275 m respectively. Speed of 1st train = 43 km/h and speed of 2nd train = 29km/h. If both the trains are running in opposite direction, what time will they take to cross each other? 1.  25 sec 4.  30 sec

2.  20 sec 5.  None of these

3.  40 sec

5. Length of 2nd train is 25% more than the 1st train. Speed of 1st train = 86 km/h, speed of 2nd train = 50 km/h. They are running in the same direction. If faster train passes the slow train in 36 sec, then find the lengths of the trains.

1.  250 m, 200 m 2.  220 m, 180 m 3.  200 m, 180 m 4.  200 m, 160 m 5.  None of these

3.  6 km

9. In a metric perfect world, a full metric day would have 10 metric hours, one metric hour would have 10 metric minutes, one metric minute would have 10 metric seconds and one metric second would have 10 metric miniseconds. If your team has been told to report to the Principal’s office at four metric hours, five metric minutes, six metric seconds and seven metric miniseconds, what time (approx.) would that be in the 24 hour system? 1.  8 : 32 4.  17 : 57

2.  10 : 57 5.  23 : 12

3.  13 : 32

10. Two trains of 80 m and 100 m lengths are moving in opposite directions on parallel tracks. It is found that they cross each other in 36 seconds. How much time will they take to pass each other if they move in the same direction? To find the solution which of the following statements is sufficient? A.  First train passes a pole in 60 seconds. B.  Second train passes a bridge of 60 m length in 48 sec. 1.  Only statement (A) is sufficient 2.  Only statement (B) is sufficient 3.  Either of the two statements is sufficient 4.  Both the statements together are necessary 5.  Both the statements together are not sufficient.

1.  9 km/h 4.  5 km/h

2.  120 5.  None of these

3.  150

7. A boat travels downstream to cover a distance of 80 km in 5 hrs and upstream to cover a distance of 48 km in 8 h. Find the speed of boat in still water. 1.  11 km/h 4.  16 km/h

2.  8 km 5.  None of these

11. ‘A’ goes upstream and downstream at 6 km/h and 12 km/h respectively. His speed in still water in km/h is

6. Walking at 6/7 times his usual speed, a man is 25 min late to his destination. What is his usual time to cover the same destination (in mins)? 1.  100 4.  200

1.  4.5 km 4.  10 km

2.  12 km/h 3.  14 km/h 5.  None of these

8. Parthasarathy Hariprasad walks from his house at 3 km/h and reaches the school 10 minutes late. If his speed had been 4 km/h, he would have reached the school 15 minutes earlier. How far is the school from his house?

2.  8 km/h 3.  10 km/h 5.  None of these

12. A train covers the distance between station P and Q in 48 minutes. If the speed is increased by 5km/h, it will cover the same distance in 45 minutes. What is the original speed of the train in km/h? 1.  65 4.  105

2.  90 5.  None of these

3.  75

13. A train 250 m in length running at a speed of 45 km/h crosses a man coming from opposite direction in 18 seconds. What is the speed of the man (in km/h)? 1.  5 4.  8

2.  6 5.  None of these

3.  7

14. A leaves hostel at 15 minutes to eight in the morning and reaches R’s house in 35 minutes. They take their breakfast in another 10 mins and leave for university

Time, Speed and Distance  1.  28 km/h 4.  25 km/h

which takes 45 minutes. At what time do they leave R’s house for university? 2.  8.30 am 3.  8.10 am 1.  8.40 am 4.  8.50 am 5.  None of these 15. A journey of 192 km between two cities takes 2 hrs less by a fast train than by a slow train. If the average speed of slow train is 16 km/h less than the fast train, find the speed of the fast train. 2.  64 km/h 3.  32 km/h 1.  36 km/h 4.  48 km/h 5.  64 km/h

2.  20 km/h 3.  32 km/h 5.  None of these

20. Two trains are running towards each other on a parallel railway track with a speed of 50 km/h and 60 km/h respectively. At 2 pm, the distance between them is 88 km. At what time both the trains meet each other? 1.  2.48 pm 4.  5.48 pm

2.  3.48 pm 5.  None of these

3.  4.48 pm

21. A train 300 m long overtook a man walking in the same direction at the speed of 4km/h and passed him in 30 sec. The train reached station in 15 minutes after it had passed the man. In what time will that man reach the station?

16. How much time will a train take to cross an electric pole (assume uniform speed)? A.  The train crosses a platform at a speed of 54 kmph. B. It crosses a 110 m long train running in opposite direction in 15 sec. C.  The train takes 40 seconds to cross the plaftform. 1.  A and B together are sufficient 2.  A and C together are sufficient 3.  A alone is sufficient 4.  All the three together are necessary 5.  All three together are not sufficient

1.  2.5h 4.  5.5h

2.  3.5h 5.  None of these

3.  4.5h

22. A train of 24 carriages, each of 60 meters in length with an engine of 60m length is moving at a speed of 60 km/h. In what time the will the train pass the bridge having a length of 1.5 km (neglect any other length)? 1.  47 sec 4.  58 sec

17. Ms Sreerekha arrives her office 30 minutes earlier if she walks at 7 kmph. However, if she walks at 5 kmph she arrives 18 minutes earlier. What is the distance she walks to reach the office? 2.  7 km 3.  14 km 1.  3.5 km 4.  5 km 5.  None of these 18. A bus covers the certain distance with constant speed X kmph. Had the speed of the bus been (X + 7) km/h, it would have taken 1 h less to cover the distance. Again, had the speed been (X - 5) km/h, it would have taken 1 h more to cover the distance. Find distance and speed of the train.

2.  43 sec 5.  None of these

3.  46 sec

23. Two men together start on the same journey. They travel 9 km and 15 km respectively daily. After traveling for 6 days the man traveling at 9 km/day doubled his speed and both of them finish the journey at the same time. Find the time taken by them to finish the journey. 1.  12 days 4.  20 days

2.  18 days 5.  Noneof these

3.  16 days

24. A train overtakes two persons walking at 2 and 4 km per hour respectively and passes them completely in 9 sec and 10 sec. What is the length of the train?

1.  52 km, 7 km/h 2.  58 km, 8 km/h 3.  60 km, 10 km/h 4.  45 km, 9 km/h 5.  None of these 19. Speed of a car is 56 km/h. During a journey between Patna and Lucknow, car driver spots a bus 120 m ahead and after 30 sec the same bus is 80m behind the car. If speed of car is 56 kmph, what is the speed of the bus?

ANSWER KEYS

  1.93

1.  150 m 4.  400 m

2.  275 m 5.  None of these

3.  300 m

25. Walking at 7/9 times the actual speed, a person covers 200 m less than the actual distance covered in the same time. Find the actual distance covered in the same time. 1.  800 m 4.  1000 m

2.  900 m 5.  700 m

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

5

3.

2

4.

5

5.

4

6.

3

7.

1

8.

5

9.

2

10.

3

11.

1

12.

3

13.

1

14.

2

15.

4

16.

5

17.

1

18.

5

19.

3

20.

1

21.

1

22.

5

23.

3

24.

5

25.

2

3.  300 m

1.94 

  Quantitative Aptitude and Data Interpretation

HINTS AND EXPLANATIONS 180 × 18 Distance = = 12 seconds 1. (2)  Time = Speed 54 × 5 2. (5)  Speed =

Distance

=

Time

3. Total distance covered =

120 × 180 9

90 ×

=

300 9

.

5 × 38 = 950m 18

10. (3) Both the statements independently enable us to find the speeds of both the trains and hence we can find the solution with the help of either of the statements. 11. (1)  Speed in still water =

45 2 = 48 – 45 60 5×

(125 + 275) (43 + 29) × –5– 18



5. A : B = 100 : 125 = 4 : 5

2

= 9 km/h

12. (3)  Required original speed

So, length of Bridge = 950 – 287 = 663

4. Time =

6 + 12

5 × 45 = 75 km/h 5

=

14. (2) A leaves hostel at 7.45. He reached R’s house at (7.45 + 35 min=) 8.20. They leave for university at (8.20 + 10 min=) 8.30.



Distance = Speed x Time



(86 – 50) × 5 = 18



Ratio of length of A and B are given you can easily calculate the length of each train.

× 36 =

36 × 5 18

× 36 = 360m

6. If speed becomes 6/7 of its original, then time will become 7/6 of its original.

So increase in time = 7t/6 – t = t/6 = 25 mins



So, t = 150 mins

7. Downstream speed = 80/5 = 16 kmph = Speed of boat in still water + speed of current

15. Go through options. 17. (1) 18. Go through the options. 19. In 30 sec, relative distance covered by car = (120 m + 80 m) = 200 m 18 200 = 24 kmph × 5 30



So, relative speed =



Let speed of bus is x km/h ⇒ 56 – x = 24⇒ x = 56–24 = 32 km/h



Upstream speed = 48/8 = 6 kmph = Speed of boat in still water - speed of current

21. Relative Speed = x–4 (Assume speed of train = x kmph)



So, speed of boat in still water = (Downstream speed + Upstream speed)/2 = 11 kmph

Distance x – 4 = Speed

=

300 9

= 10m/s = 36 kmph

8. (5)  Required distance =



So, x = 40 km/h

Product of two speeds



Distance traveled by train in 15 min =



Time taken by man to reach the station Time



=



    Diff. of speed 3×4



3–4

×

10 + 15 60

× Diff. between arrival time

=

12 × 25 1 × 60

= 5 km

Distance Speed

=

10 4

40 × 15 60

= 10 km

= 2.5 h

9. (2) 4mh 5mm 6ms 7mms = 4.567 = 10.9608 or about 10:57

  EXERCISE  2 1. Train A traveling at 60 km/h leaves Patna for Delhi at 6 pm. Train B travelling at 90 km/h also leaves Patna for Delhi at 9 pm same day. Train C leaves Delhi for Patna at 9 pm same day. If all three trains meet at the same time between Patna and Delhi, what is the speed of Train C if the distance between Delhi and Patna is 1260 km?

1.  60 kmph 4.  80 kmph

2.  120 kmph 3.  90 kmph 5.  None of these

2. Consider the following data: 1st train length = 318m and its speed = 41 km/h. 2nd train length = 277 m.

Time, Speed and Distance  Both the trains are running in the opposite direction. If they pass each other in 34 sec, find the speed of 2nd train. 1.  20 km/h 4.  36 km/h

2.  26 km/h 3.  32 km/h 5.  None of these

3. A train passes a platform of length 125m in 26 sec. The same train passes the other platform of length 275m in 38 sec. Find the length of train. 1.  200 m 4.  220 m

2.  300 m 5.  None of these

3.  260 m

Direction for questions 4 to 6:  Answer the questions based on the following information. Use the table about the speed of a train over a 3-hour period. The time count does not begin from starting of train Time (Minutes)

Speed at given time (in km/ hour)

0

40

30

45

45

47.5

60

50

90

55

120

60

150

65

180

70

2.  6t 5.  None of these

3.  50 kmph

Nitika reaches city B from city A in 4 hours, driving at speed of 35 kmph for the first two hour and at 45 kmph for the next two hours. Amit follows same route, but drives at three different speeds: 30, 40 and 50 kmph, covering an equal distance in each speed segment. The two cars are similar with petrol consumption characteristics (miles per litre) shown in the figure below.

3.  75% 24

6. At time t, measured in minutes after the beginning of the time period, which of the following gives the speed of the train in accordance with the table? 1.  t/6 4.  40 + t/6

8. What is the average speed of Y? 2.  49.5 kmph 1.  47.5 kmph 4.  52 kmph 5.  55 kmph

Direction for questions 11 and 12:  Answer the question based on the following information.

2.  55 km/h 3.  60 km/h 5.  None of these

2.  100% 5.  None of these

A road network (shown alongside) B C connects cities A, B, C and D . all road segments are straight lines. D is the mid-point on the road connecting A and C . Roads AB and BC are D at right angles to each other with BC shorter than AB. The segment AB is A 100 km long. Mr X and Mr Y leave A at 8.00 a.m., take different routes to city C and reach at the same time. X takes the highway from A to B to C and travels at an average speed of 61. 875 kmph. Y takes the direct route AC and travels at 45 kmph on segment AD. Y’ s speed on segment DC is 55 kmph.

10. What is the length of the road segment BD? 2.  52.5 km 3.  55 km 1.  50 km 4.  75 km 5.  Cannot be determined

5. During the three-hour period shown in the table, the speed of the train increased by: 1.  25% 4.  125%

Direction for questions 8 to 10:  Answer the questions based on the following information.

9. The total distance traveled by Y during the journey is approximately. 2.  150 km 3.  55 km 1.  105 km 4.  72 km 5.  Cannot be determined

4. How fast was the train travelling 2½ hours after the beginning of the time period? 1.  50 km/h 4.  65 km/h

  1.95

Mileage km per litre 16

16

3.  40 + t

30

40

50

7. A truck traveling at 70 km/h uses 30% more diesel to travel a certain distance than it does when it travels at a speed of 50 km/h. If the truck can travel 19.5 km/l of diesel at 50 km/h, how far can the truck travel on 10 l of diesel at a speed of 70 km/h?

11. The quantity of petrol consumed by Amit for the journey is

1.  130 km 4.  175 km

1.  8.31 4.  9.21

2.  140 km 5.  160 km

3.  150 km

Speed km per hour

2.  8.61 5.  9.82

3.  8.91

1.96 

  Quantitative Aptitude and Data Interpretation

12. Nitika would like to drive Amit’s car over the same route from A to B and minimize the petrol consumption for the trip. What is the quantity of petrol required by her? 1.  6.67 4.  6.0

2.  7 5.  7.2

3.  6.33

13. Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6.30 am and travels at 50 kmph towards Baroda situated 100 km away. At 7.00 am HowrahAhmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7.30 am Mr Shah, the traffic controller at Baroda realizes that both the trains are running on the same track. How much time does he have to avert a head-on collision between the two trains? 1.  15 min 4.  30 min

2.  20 min 5.  35 min

3.  25 min

14. At his usual rowing rate, Rahul can travel 12 miles downstream in a certain river in 6 h less than it takes him to travel the same distance upstream. But if he could double his usual rowing rate for this 24 miles round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles. What is the speed of the current in miles per hour? 7 4 ​   2. ​ __ 3 .  1.  3 3 5 3 8 4.  5.  None of these 3 15. Shyama and Vyom walk up an escalator (moving stairway). The escalator moves at a constant speed. Shyama takes three steps for every two of Vyom’s steps. Shyama gets to the top of the escalator after having taken 25 steps, while Vyom (because his slower pace lets the escalator do a little more of the work) takes only 20 steps to reach the top. If the escalator were turned off, how many steps would they have to take to walk up? 1.  40 4.  80

2.  50 5.  45

3.  60

16. Train X departs from station A at 11 a.m. for station B, which is 180 km far. Train Y departs from station B at 11 a.m. for station A. Train X travels at an average speed of 70 km/h and does not stop anywhere until it arrives at station B. Train Y travels at an average speed of 50 km/h, but has to stop for 15 min at station C, which is 60 km away from station B enroute. Ignoring the lengths of the trains, what is the distance, to the nearest kilometre, from station A to the point where the trains cross each other? 1.  112 km 4.  56 km

2.  118 km 5.  None of these

3.  120 km

17. Three runners A, B and C run a race, with runner A finishing 12 m ahead of runner B and 18 m ahead of runner

C, while runner B finishes 8 m ahead of runner 3. Each runner travels the entire distance at a constant speed. What is the length of the race? 1.  36 m 4.  72 m

2.  48 m 5.  84m

3.  60 m

18. The minutes and the hour hand of a watch meet every 65 minutes. How much does the watch lose or gain time?

1.  25 seconds 2.  27 seconds 3.  27.16 seconds 4.  30 seconds 5.  None of these

19. A watch gains uniformly, and is 5 minutes slow at 8 o’clock in the morning on Sunday, and is 5 minutes 48 seconds fast at 8 pm on the following Sunday. When was it correct?

1.  7 . 20 pm on Tuesday 2.  9 . 20 pm on Wednesday 3.  7 . 20 pm on Wednesday 4.  9 . 20 pm on Tuesday 5.  None of these

20. At what time between 8 and 9 O’clock will be hands of a clock be in straight line but not together? 10 10 1.  8 min past 4 2.  10 min past 8 11 11 3.  12

10 min past 6 11

4.  9 10 min past 6 11

5.  None of these 21. In a 1 km race, A wins over B by 80 m or 20 seconds. B can give a start of 100m to C in 1 km race. Find the ratio of speeds of A and C. 1.  10 : 9 4.  9 : 10

2.  100 : 92 3.  1000 : 828 5.  None of these

Direction for questions 22 and 23: Read the passage below and solve the questions based on it. A train started at 9.00 am at station X with a speed of 72 kmph. After two hours, another train started at station Y towards X with a speed of 90 kmph. The two trains are expected to cross each other at 1.30 pm. Owing to a signal problem arising at 12 noon, the speed of each of them was reduced by the same quantity and they crossed each other at 4.30 pm. 22. What is the new speed of the train that started from station X? 1.  18 kmph 4.  54 kmph

2.  36 kmph 5.  42 kmph

3.  45 kmph

Time, Speed and Distance 

  1.97

23. If the signal problem had occurred at 1:00 p.m. instead of 12 noon, at what time would the two trains have crossed each other? 1.  3.30 pm 4.  2.30 pm

2.  3.00 pm 5.  2.45 pm

3.  2.00 pm

o P

Direction for questions 24 and 25:  Read the passage below and solve the questions based on it.

Q

Three persons A, B and C start running simultaneously on three different concentric circular tracks from three collinear points P, Q and R respectively which are collinear with the centre O and are on the same side of the centre as shown. The speeds of A, B and C are 5 m/s, 9 m/s and 8 m/s respectively. The lengths of the tracks on which A, B and C are running are 400 m, 600 m and 800 m respectively.

R

25. If A runs in the clockwise direction and C in the anticlockwise direction, after how much time will the positions of A and C be collinear with the centre, (and on the same side), for the fourth time after they start? 1.  177 7 seconds 9 2.  160 seconds

24. If A and B run in clockwise direction and C in anti-clock wise direction, after how much time will the positions of time A, B and C be collinear with the centre (and on the same side of the centre), for the first time they start?

4.  1

2.  400 seconds 3.  600 seconds 5.  None of these

ANSWER KEYS

1.  200 seconds 4.  800 seconds

3.  145

5 seconds 11

5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

5

3.

1

4.

4

5.

3

6.

4

7.

3

8.

2

9.

5

10.

2

11.

3

12.

1

13.

2

14.

4

15.

2

16.

1

17.

2

18.

1

19.

3

20.

2

21.

3

22.

1

23.

4

24.

2

25.

1

HINTS AND EXPLANATIONS 1. (2) Let the three trains meet x hours after train A left Patna.

So when trains A and B meet, both would have travelled the same distance.



60 x = 90 (x – 3) ⇒ x = 9



Distance covered by A in 9 hours = 540 km.



For meeting at the same point, C will cover 1260 – 540 = 720 kms



If speed of train C is V kmph then V × 6 = 720 ⇒ V = 120 kmph.

4. (4)  It is clearly given in the table.

5. (3)  Required percentage =

30 70 – 40 = 75% = 40 40

6. (4)  Go through the options 7. (3) The vehicle travels 19.5 km/l at the rate of 50 km/h. So it should travel

19.5 km/l at the rate of 70 km/h 1.3



= 15 km/l. the distance covered at 70 km/h with 10l



= 10 × 15 = 150 km

8. (2) Since AD= DC, the distance travelled is same for the two stretches. Hence, the average speed is given by

  Quantitative Aptitude and Data Interpretation

1.98 



2ab = (a + b)

(2 × 45 × 55) = 49.5 kmph. 45 + 55

9. Now, since X and Y reach C at the same time, 100 + BC 61.875

=

=



If AC = 105, BC2 = AC2 – AB2 = 1052 – 1002 = 1025 or BC = 32



So,

100 + BC AC

For 20 steps, he takes



Difference between their time = 1.66 min. Escalator takes 5 stps in 1.66 min and difference in number of steps covered=5. Speed of escalator is 1 step for 0.33 min, i.e., 3 steps per minute. If escalator is moving, then Shyam takes 25 steps and escalator also takes 25 steps. Hence, total number of steps = 50.

AC Let us take help from options now 49.5



132 = 52.5 km 105

=

16. Total time taken by B to cover 60 km = 105 = 52.5km 2

10. (2)  In this triangle, AD = DC = BD =

11. (3) Distance between A and B = (35 × 2) + (45 × 2) = 160 km. 160 Distance covered by Amit in each = 3

Hence, total petrol consumed



160 1 160 1 160 1 + × × × + = 8.91 16 3 24 3 3 16

160 = 6.67. 24 13. (2) At 7.30 a.m, Navjivan Express at 50 km from A at the same time, howrah-Ahmedabad Express is at 20 km from B. petrol consumption =



Hence, distance between the trains at 7.30 am. is 30 k.m.



Relative speed = 50 + 40 = 90 kmph



Hence, time left =

30 1 = h = 20 min. 90 3





y=

x 2– y 2 4

When Rahul doubles his rowing rate, then we have 2y 12 12 1 = =1⇒ 2 2 12 2x + y 4x – y 2x – y 4x 2 – y 2



... (ii) y= 24 Hence, from (i) and (ii), have 2x2 = 5y2 3 2 y 2

8 5 2 , so y = y in (i), we get y= Putting x2 = 3 2 4 1 15. If Shyam takes 1 min for every 3 steps, then he takes min for every 3 step. 25 min, i.e., 8.33 min. 3



For 25 steps, he takes



1 So Vyom takes min for every step. 2

1 h . 4



Now in



This means they do not cross each other by the time train Y finishes its stop at station C. Let they meet after t h.



Then 70t + 50 (t –



192.5 Distance from A will be ( 70 × 120 approximately.

29 6 1 = 105.5 km + h train X travels 70 × 20 1 4

192.5 1 ) = 180 t= 120 h 4

h ) km = 112 km

19. (3) 

From 8 A.M. on Sunday to 8 P.M. on the following Sunday, the watch will be 648 seconds fast.



There will be difference of 648 seconds in the duration of 180 hours.



Difference of 300 seconds (5 minutes), so that the watch shows 180 250 hours, i.e., hours, i.e., the correct time will be there after 648 3 1 83 hours, i.e., 7.20 pm on Wednesday. 3

... (i)



6 h 5

It stops at station C for

14. (4) Let x be rate of Rahul, and y be the rate of current in mph. 12 12 24 y − =6⇒ 2 =6 x− y x+ y x − y2

60 h= 50



12. (1) For minimum petrol consumption, she should drive at 40 kmph,



20 min, i.e. 10 min. 3



20. (2) For hands to be in straight line (and not together), angle between them should be 180o.

At 8’O clock, angle between hands = 240o



Relative angle covered (over hour hand) by minute hand/minute = 5.5o



Angle to be covered = 240o – 180o = 60o







Time = 10

Hence time taken = 60o/5.5 minutes = 10 10 11

10 11

mins

mins past 8

21. (3)  Ratio of speed of A and B = 1000 : 920 = 100 : 92

Ratio of speed of B and C = 10 : 9



So, ratio of speed of A, B and C = 1000 : 920 : 828

r e v i e w

t e s t

 2

Arithmetic This review test

based on the following chapters

  Average   Percentage   Ratio, Proportion and Variation   Time and Work   Time Speed and Distance

  INSTRUCTIONS 1. This test contains 20 questions. You have forty-five minutes to complete the test 2. All questions carry four marks each. Each wrong answer will attract a penalty of one mark. 3. Do your rough work only on the Test Booklet and not on the Answer Sheet. 1. Forty per cent of the employees of a certain company are men, and 75% of the men earn more than Rs 25,000 per year. If 45% of the company’s employees earn more than Rs 25,000 per year, what fraction of the women employed by the company earn less than or equal to Rs 25,000 per year? 2 1 ​  1 ​  1. ​ ___ 2. ​ __ 3. ​ __ 11  ​   4 3 3 1 __ __ 4. ​ 4 ​  5. ​ 2 ​ 

2. In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked, favoured proposal I, 30% favoured proposal II and 20% favoured proposal III. If 5% of those asked, favoured all three of the proposals, what percentage of those asked, favoured more than one of the three proposals? 1.  10 4.  22

2.  12 5.  14

3.  17

Direction for questions 3 and 4: Answer the question based on the following information. There are blue vessels with known volumes V1, V2…, Vm, arranged in ascending order of volume, V1 > 0.5 litre, and Vm < 1 litre. Each of these is full of water initially. The water from each of these is emptied into a minimum number of empty white vessels, each having volume 1 litre. The water

1.100 

  Quantitative Aptitude and Data Interpretation

from a blue vessel is not emptied into a white vessel unless the white vessel has enough empty volume to hold all the water of the blue vessel. The number of white vessels required to empty all the blue vessels according to the above rules was n. 3. Among the four values given below, which is the least upper bound on e, where is the total empty volume in the white vessels at the end of the above process? 1.  m∙Vm 4.  m(1–v1)

2.  m(1–Vm) 5.  1–V1

3.  mV1

4. Let the number of white vessels needed be n1 for the emptying process described above, if the volume of each white vessel is 2 litres, among the following values, which is the least upper bound on n1? 1.  __ ​ m 4 ​  2.  Smallest integer greater than or equal to ​ __n ​  2 3.  n n 4.  Greatest integer than or equal to ​ __ 2  ​ 5.  None of these 5. Consider the following data for a snacks shop “Santushti” located at Mukherjee Nagar, Delhi: 2009

2010

CP/Unit

A

B

SP/Unit

C

D

It is given that B – A = D – C [All the values A, B, C and D are in natural numbers and Rs] Which of the following is definitely true? 1. Profit percentage per unit in 2010 is more than profit percentage per unit in 2009. 2. Profit percentage per unit in 2009 is more than profit percentage per unit in 2010. 3. Profit percentage per unit in 2010 is equal to the profit percentage per unit in 2009. 4. CP/unit in 2010 is more than CP/unit in 2009. 5. Cannot be determined Direction for questions 6 and 7:  Read the passage given below and solve the questions based on it. A pedestrian having traveled from A to B found that if his rate had been one kmph quicker, he would have performed his journey in 1​ 1 __ 2 ​ hours less and if it had been one kmph slower, he would have taken 2​ 1 __ 2 ​ hours more to perform it.

6. The distance from A to B is 1.  12 km 4.  30 km

2.  20 km 5.  None of these

3.  26 km

7. The rate at which, the pedestrian covered the distance is 1.  2 kmph 4.  6 kmph

2.  3 kmph 5.  7.5 kmph

3.  4 kmph

8. There were 500 seats in PVR placed in similar rows. After the reconstruction of the hall the total number of seats became 450. The number of rows was reduced by 5 but each row contained 5 seats more than earlier. What is the total number of rows and total numbers of seats in a row initially in the hall respectively? 1.  30 and 15 4.  50 and 10

2.  25 and 20 3.  20 and 25 5.  None of these

9. Krishna owns several cows, some black and some white. He finds that 4 black cows and 3 white cows provide the same amount of milk in 5 days as 3 black cows and 5 white cows provide in 4 days. What is the ratio of milk provided by a black cow in a day to that by a white cow in a day? 1.  8 : 5 4.  5 : 3

2.  5 : 8 5.  1 : 2

3.  3 : 5

10. Two friends Karan and Arjun start running around a circular track in the same direction. Karan and Arjun take one full round in 7 mins and 4 mins respectively. After how much time will they meet at diametrically opposite point of their starting point?

1.  120 s 2.  240 s 3.  They will never meet 4.  60 s 5.  None of these

11. While the analysis of the recently held CBSE exams were done, it was found that Chennai zone, Delhi zone and Ajmer zone has performed best. The average marks of Ajmer zone and Delhi zone put together is 71%. The average marks of Chennai zone and Delhi zone put together is 76% and average marks of Ajmer zone and Chennai zone put together is 79%. What is the range of the average marks of all the three zones (Assume N) put together?

1.  71% < N < 78% 2.  70.5% < N < 77.5% 3.  73.5% < N < 77.5% 4.  73% < N < 79% 5.  71% < N < 73.5%

Review Test 2 

2.  10 min 5.  None of these

3.  15 min

14. Water is filled in a container in such a manner that its volume doubles after every five minutes. If it takes 30 minutes for the container to be full, in how much time will it be one-fourth full? 1.  7 mins 4.  25 Mins

2.  10 Mins 5.  None of these

3.  20 mins

15. Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps the weight measure in the left pan while buying goods but keeps it in the right pan while selling his goods. He uses only 1 kg weight measure. If he sells his goods at cost price, what is his gain percentage? 200 100 1000 1. ​ ___ 2. ​ ___ 3. ​ ____  % 11 ​ % 11 ​ % 9 ​  200 4. ​ ___   5.  None of these 9 ​ % 16. There are fifty successive percentage discounts given in a series of 2%, 4%, 6%, 8%……………and so on. What is the net discount? 1.  98% 4.  2006%

2.  2550% 5.  None of these

19. There is a certain number of apples, guavas and oranges in a basket. The number of each variety is more than one. The ratio of the number of apples to the number of guavas is equal to the ratio of the number of guavas to the number of oranges. If the total number of fruits is 61, then find the number of guavas.

20. Neo is going to NDLS from PNBE by his car at a speed of 40 kmph. While coming back, he returns with a speed of x kmph. What should be the value of x so that his average speed during the whole journey is 80 kmph? 1.  160 kmph 4.  160 kmph

3.  100%

17. The packing process in a garment factory involves processing by 3 machines. The first machine, A, inserts the garment in a packet, after which the second machine, B, seals the packet and finally the third machine, C, attaches a price tag to the packet. Machine A takes at

2.  20 3.  25 5.  cannot be determined

1.  16 4.  1

Section Test   3

2.  40 kmph 3.  120 kmph 5.  It is not possible

RoI/minute

1.  5 min 4.  12 min

18. A contractor needs to complete a given work in 24 days. For every day that he finishes ahead of time, he gets an incentive I and for every day that he finishes behind time, he needs to pay a penalty P. He has a choice of 2 workers who work as follows: A completes the work in 24 days for 75% of the time and in 30 days for 25% of the time. B completes the work in 20 days for 60% of the time and in 30 days for 40% of the time. At what ratio of P to I will the contractor be indifferent of using A or B? 8 ​  7 ​  1. ​ __ 2.  2 3. ​ __ 3 3 3 7 __ __ 4. ​ 4 ​  5. ​ 8 ​ 

% Accuracy

13. In a 4000 m race around a circular stadium having a circumference of 1000 m, the fastest runner and the slowest runner reach the same point at the end of the 5th minute, for the first time after the start of the race. All the runners have the same starting point and each runner maintains a uniform speed throughout the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?

3.  300

Marks

3.  p > q

2.  240 5.  600

Wrong

2.  p < q 5.  None of these

1.  360 4.  900

Right

1.  p = q 4.  p = q/2

least 10 seconds per unit. Machine B takes at least 15 seconds per unit. Machine C takes at least 12 seconds per unit. The factory starts at 8 AM and runs non-stop, till 6 PM, What is the maximum number of packets that can be processed in a one hour period?

Attempts

12. At the end of year 1998, shepherd bought nine dozen goats. Henceforth, every year he added p% of the goats at the beginning of the year and sold q% of the goats at the end of the year, where p > 0 and q > 0. If shepherd had nine dozen goats at the end of year 2002, after making the sales for that year, which of the following is true?

  1.101

  Quantitative Aptitude and Data Interpretation

ANSWER KEYS

1.102 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

2

3.

4

4.

2

5.

5

6.

4

7.

3

8.

2

9.

2

10.

3

11.

3

12.

3

13.

2

14.

3

15.

4

16.

3

17.

2

18.

1

19.

2

20.

5

HINTS AND EXPLANATIONS 1. Men



Women

5. Profit percentage = Profit/CP



40%



60%



Out of 40% men, 75% earn more than Rs 25,000. Hence, 30% of the company (men) earn more than Rs 25, 000. But in all 45% of the employees earn more than Rs 25, 000. Hence among women 15% earn more than Rs 25, 000 and the remaining (60–15)% earn less than or equal to Rs 25, 000. 45 __ 3 ___ Therefore, the fraction of women = ​   ​  = ​    ​ 60 4

It can be seen that the profit amount remains the same the change in CP/unit = change in SP/unit. However, we don’t know that A > B or B > A, so we do not have the information, that if the base has increased or decreased. Hence cannot be determined. 15. Assume cp/1000 gm = Rs 1000

He gets 1100 g for Rs 1000 and

2. 78 = 100 – x – 2(5)



Sells 900 g for Rs 1000.





So, cp/gram

3. Let m = 1. so, option (a) will give the answer as Vm and option (c) will give the answer as Vm both of these cannot be the answers as Vm are the amount of volume filled.



Sp/gram =





So, profit % =





Therefore, x = 12.

Let m=2. So, option (b will give the answer as 2 (1–V2) and option (d) will give the answer as 2(1–V1) Now consider option (b).

Actual empty volume > 2(1–V2). Therefore, for this situation m (1–V1) is the only possible answer. 1 __ 4. Let m = 1 and n= 1. Option (a) gives the answer as ​    ​ and option 4 1 __ (d) gives the answer as greatest integer less than or equal to ​    ​ 2 So, both of these cannot be the answer. Option (b) gives the 1 __ answer as smallest integer greater than or equal to ​    ​, and option 2 (c) gives the answer as 1. But the actual answer can be greater than 1 as the volume of the vessel is 21. Hence, (b) is the answer.



1000 = Rs 0.90/g 1100 1000 = Rs 1.11/g 900

1.11 − 0.90 × 100 0.9 Hence option (4) is the answer.

16. 50th (Last one) discount = 100%. Hence Net discount = 100% 17. Constraint is on Machine B. This works slowest of all.

Hence No. of units processed/hour =

3600 secs = 240 units 15

19. No. of Apples, Gvavas and Oranges are in Geometic Progression.

(Guavas)2 = Apples × Oranges. Now Go through options.

c h a p t e r

 7

Geometry and Mensuration  LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Different Structures viz., Polygons, Circles, Triangles etc.   Relationship between 2–D and 3–D figures   Different Theorems and their applications   Process of generating volume, total surface area etc.   Similarity and Congruency   Kind of questions asked in the CAT   Methods of solving questions

  GEOMETRY In Geometry, we will be discussing:

1.  Properties of lines 2.  Polygons and their properties 3.  Triangles and their properties 4.  Quadrilaterals and their properties 5.  Circles and their properties

Types of Angles

Property

Diagram

A

Acute Angle 0˚ 0, then f(x) = x2 + 7x + 12 = 0 Or, x2 + 7x + 12 = (x + 3) (x + 4) = 0, So, x = –3 and x = –4 But we have taken x > 0, so negative values of x are not admissible. Now, If x < 0, then f(x) = x2 – 7x + 12 = 0 Or, x2 – 7x + 12 = (x – 3) (x – 4) = 0, So, x = 3 and x = 4 But we have taken x < 0, so positive values of x are not admissible. And x = 0 is not possible. So, no real value of x can be obtained.

Alternatively, it is worth observing that all the terms of f(x), viz., x2 and 7|x| and 12, are positive. So, sum of these three terms cannot be equal to zero for any real value. Hence, no real value of x can be obtained.

Properties of Roots

Roots of a Quadratic Equation and Their Nature

i. A polynomial equation of degree n will have n roots, real or imaginary.

Given is the quadratic equation ax2 + bx + c = 0, where a ≠ 0. Assuming that α and β are the roots of this equation.

Equations 

  1.159

2 2 Then α = – b + b – 4ac and β = – b – b – 4ac 2a 2a

Example  6 Example 

It can be seen that nature of both of these two roots depends upon the value of b2 – 4ac. (b2 – 4ac) is also known as Discriminant (D) of the quadratic equation ax 2 + bx + c = 0.

Given is the quadratic equation ax 2 + bx + 1 = 0, where a, b ε (1, 2, 3, 4). For how many set of values of (a, b), quadratic equation ax2 + bx + 1 = 0 will have real roots? (CAT 2003)

•  Roots are real D = 0 •  Roots are equal •  Roots are real D > 0 •  Roots are unequal •  Roots are not real D 0, hence this equation will have two real roots. Case 2: (x2 + 15x) = p = – 54, hence (x2 + 15x) + 54 = 0 Since D > 0, hence this equation will have two real roots. Hence, there are four real roots of the equation.

6

Solution Solution

For roots to be real, D ≥ 0. D = b2 – 4a ≥ 0. Forming the table for the above written condition: b a 1 Not possible 2 1 3 1 3 2 4 1 4 2 4 3 4 4 So, there are seven set of values for (a, b).

  ALGEBRAIC CALCULATIONS ON ROOTS f(x) = axn + bxn–1 + cxn–2 + ………………………+K Sum of roots taking one at a time = (Coefficient of n–1 x /Coefficient of xn )× (–1)n, where n is the number of roots taken at a time. Sum of roots taking two at a time = (Coefficient of xn–2/Coefficient of xn)× (–1)n, where n is the number of roots taken at a time. Sum of roots taking three at a time = (Coefficient of n–3 x /Coefficient of xn)× (–1)n, where n is the number of roots taken at a time. ……. …...... ..........…. …......... ..........… Product of roots, taken all at a time = (Constant term/Coefficient of xn ) × (–1)n, where n is the total number of roots.

Quadratic Equation f(x) = ax2 + bx + c = 0 Assume that the roots are α and β. α + β = (Coefficient of xn–1/Coefficient of xn) × (–1)n = b a (–1)1 = – b a α β = (Constant term/Coefficient of xn ) × (–1)n = c (–1)2 a = c a

1.160 

  Quantitative Aptitude and Data Interpretation

Cubic Equation

Example  8 Example 

f(x) = ax3 + bx2 + cx + d = 0 Assume that the roots are α, β and γ.

8

Find the value of K in the quadratic equations Kx 2 – 3x + 2 = 0, such that one root is double the other.

α + β + γ = (Coefficient of xn–1/Coefficient of xn) × (–1)n

= b (–1)1 = – b a a α β + γ α + β γ = (Coefficient of xn–2/Coefficient of xn ) × (–1)n = c (–1)2 = c a a α β γ = (Constant term/Coefficient of xn) × (–1)n = d (–1)3 a =– d a

Solution Solution

Bi-quadratic Equation

And α β = 2β2 = 2/k ⇒ β2 = 1/k ……………………..(2)

f(x) = ax4 + bx3 + cx2 + dx + e = 0 Assume that the roots are α, β, γ and δ.

Solving (1) and (2), we get k = 1.

Let us assume that the roots of the equation = α and β From the given equation, sum of the roots α + β = 3/k and product of the roots α β = 2/k It is given that α = 2β Hence α + β = 3β = 3/k ⇒ β = 1/k ---------------------(1)

α + β + γ + δ = (Coefficient of xn–1/Coefficient of xn) × (–1)n =

b (–1)1 = – b a a

Example  9 Example 

α β + γ δ + α δ + β γ + α γ + δ β = (Coefficient of x /Coefn–2

ficient of xn) × (–1)n = c (–1)2 = c

a

a

α β γ + δ α β + γ δ α + β γ δ = (Coefficient of xn–3/Coefficient of

xn) × (–1)n = d (–1)3 = – d

a

a

α β γ δ = (Constant term/Coefficient of x n) × (–1)n = e (–1)4

a

= e a

Example  7 Example 

7

If the roots of the equation x 2 + px + q = 0 differ from the roots of the equation x 2 + qx + p = 0 by the same quantity, then what is the value of (p + q)? Solution Solution

Let x1, x2 be the roots of the equation x2 + px + q = 0 and x3, x4 be the roots of the equation x 2 + qx + p = 0. Hence, x1 + x2 = -p, x1 × x2 = q, x3 + x4 = -q, x3 × x4 = p ------------------------(1) According to the question, x1 – x2 = x3 – x4 Or, (x1 – x2)2 = (x3 – x4)2 , or, (x1 + x2)2 – 4 x1 × x2 = (x3 + x4)2 – 4 x3 × x4 --------(2)

9

What will be the quadratic equation having the roots opposite in sign as that of the quadratic equation x2 + 7x + 10 = 0? Solution Solution

Putting (–x) at the place of x will give us the solution. Desired equation is (–x)2 + 7(–x) + 10 = 0 So, equation is x2 – 7x + 10 = 0 Alternatively, roots of the quadratic equation x 2 + 7x + 10 = 0 are –2 and –5. So, roots of the desired equation should be 2 and 5. So, the quadratic equation is (x – 2) (x – 5) = 0, or, x 2 – 7x + 10 = 0

Example  10 Example 

10

What values of x will satisfy the quadratic inequation f(x) = – x2 + 3x + 4 > 0?

Putting the values from (1) in (2), we obtain (p – q) (p + q + 4) = 0

Solution Solution

Hence, either p = q (not possible otherwise both the equations will become same) or

f(x) = – x2 + 3x + 4 > 0, or, x2 – 3x – 4 < 0

p + q = –4

So values of x satisfying f(x) = –1 < x < 4.

or, (x + 1) ( x – 4 ) < 0

Equations 

Worked Out Problems

Example  12 Example 

Example  11 Example 

Let x = 4 + 4 – 4 +

11

For which value of k does the following pair of equations yield a unique solution of x such that the solution is positive? (CAT 2005) 2 2 X –y=0

(x – k)2 + y2 = 1



1.  2

2.  0

1.  3 3.  ( 13 + 1) 2

4 – to infinity. Then x equals 2.  ( 13 – 1) 2 4.  3 (CAT 2005)

Solution

Solution Solution



12

Solution

4.  – 2

3.  2

  1.161

x= 4+

4 – x ⇒ x2 – 4 + 4 – x

(x2 – 4) = 4 – x

y2 = x2 (2x 2)2 – 2kx + k 2 – 1 = 0, For unique Soln : D = 0 (2x) => b2 – 4ac = 0 → 4k 2 = 8k 2 – 8 → 4k 2 = 8 →k= 2



Now put the values from options.



  Only 3rd option satisfies the condition.  Alternatively, value of x will be more than 2, which is given there in only option 1 and option 3. Since it is only slightly more than 3, option 2 will be the answer.

  EXERCISE  1 1.  a = 1, b = 0 3.  a ≠ 0, b ≠ 0 5.  None of these

1. If x + y + z = 0, then x3+y3 + z3 is equal to 1.  0 xy + yz + zx 3.  xyz 5.  None of these 2. If x – x1 1.  4 4.  34

(

1 3. If x + x 1.  927 4.  322

2.  3 xyz 4.  xyz (xy + yz + zx)

= 2, then the value of x4 + 14 is x 2.  8 5.  None of these

)

6. Find the numerical value of ‘c’, if the expression xy 3x + 5y + c can be factorized. 1.  9 4.  –9 3.  12

1 = 3, then the value of x + 6 is x 2.  414 3.  364 5.  414 6

4. Let f(x) = x2 -27x+196. If (x) = x, then what is the value of x? 1.  ±28 4.  4

2.  14 5.  28

2.  a = 0, b = 1 4.  a = 1, b = 1

3.  7

5. Consider the following statement: The equations ax + by = 1 and ax - by = 1 have a unique solution for

2.  –15 5.  –4

3.  15

7. If x is less than 2, then which of the following statements is always true? 1.  x is negative 2.  2x is greater than or equal to x 3.  x2 is greater than or equal to x 4.  x is positive 5.  None of these 8. If x – y = 8, then which of the following must be true? I Both x and y are positive. II If x is positive, y must be negative. III If x is negative, y must be negative. 1.  I only 4.  III only

2.  II only 5.  None of these

3.  I and II

1.162 

  Quantitative Aptitude and Data Interpretation

9. Five tables and eight chairs cost Rs 7,350. Three tables and five chairs cost Rs 4,475. What is the price of one table?

18. What is the value of a, if (x – a) is a factor of (x3 – a2x + x + 2)?

1.  Rs 950 4.  Rs 350

1.  2 4.  1

2.  Rs 325 5.  None of these

3.  Rs 925

10. The cost of 3 apples and 2 guavas is Rs 23 and that of one apple and four guavas of the same type is Rs 21. What is the cost of 5 guavas? 1.  Rs 4 4.  Rs 25

2.  Rs 20 5.  Rs 24

3.  Rs 12

3.  0

19. Find the value of (a + b) if the polynomial x3 – ax2 – 13x + b has (x – 1) and (x + 3) as factors. 1.  12 4.  9

2.  15 5.  None of these

3.  18

20. What is the value of p, if x + 3 is a factor of 3x2 + px + 6?

11. If the two digits of the age of Mr Manoj Sagar are reversed then the new age so obtained is the age of his wife. 1 of the sum of their ages is equal to the 11 difference between their ages. If Mr Manoj Sagar is elder than his wife then find the difference between their ages.

1.  9 4.  –11

1.  9 years 4.  12 years

1.  0 4.  2

2.  10 years 3.  8 years 5.  Cannot be determined

2.  –2 5.  –1

2.  –9 5.  None of these

3.  11

21. Sum of all the real roots of the equation |x – 2|2 + |x – 2|–2 = 0 is ….. 2.  –4 5.  None of these

3.  4

12. Find the remainder when the polynomial f(x) = 2x4 – 6x3 + 2x2 – x + 2 is divided by x + 2.

22. The condition that both the roots of quadratic equation ax2 + bx + c = 0 are positive is

1.  102 4.  –92

1.  a and c have opposite sign that of b. 2.  b and c have opposite sign that of a. 3.  a and b have opposite sign that of c. 4.  Sign of a is opposite to the sign of c. 5.  None of these

2.  –102 5.  None of these

3.  92

13. Find the remainder when f(x) = 4x3 – 12x2 + 14x – 3 is divided by g(x) = x – 1 . 2 1.  2/3 2.  –2/3 3.  3/2 4.  –3/2 5.  None of these

23. How many real roots will be there of the equation: x2 + 7 |x| + 12 = 0

14. Find the remainder when f(x) = x3 – 6x2 + 2x – 4 is divided by g(x) = 3x – 1.

1.  0 4.  1

1.  107/27 4.  4

24. If x2 – kx + 5 = 0 has 3 as a root, then the value of K is

2.  –107/27 5.  None of these

3.  –4

15. Find the remainder when f(x) = x3 – 6x2 + 2x – 4 is divided by g(x) =1 – 3x. 1.  107/27 4.  4

2.  –107/27 5.  None of these

3.  –4

1.  17/5 4.  16/5

2.  2 5.  None of these

2.  13/2 5.  None of these

3.  4

3.  14/3

25. If x, y and z are distinct positive numbers, then (x + y) (y + z) (x + z) is

16. If the polynomials ax3 + 4x2 + 3x – 4 and x3 – 4x + a leave the same remainder when divided by (x – 3), find the value of a.

1.  Less than 4     3.  Greater than 8xyz 5.  None of these

1.  1

26. What should be the value of ‘p’ so that the roots of the equation 9x2 + 2px + 4 = 0 are equal?

4.  101

2.  0 5.  None of these

3.  –1

17. The polynomials ax3 + 3x2 – 13 and 2x3 – 5x + a are divided by x + 2. If the remainder in each case is the same, find the value of a. 1.  5/9 4.  – 2/7

2.  – 5/9 5.  1/3

3.  2/7

1.  6

4.  –4

2.  Less than 4xyz 4.  greater than (xyz)3

2.  –6 5.  Option 1 and 2

27. Given are three quadratic equations: x2 + px + qr = 0 x2 + qx + pr = 0 x2 + rx + pq = 0

3.  4

Equations  Now each of the pair of equations given above has a common root. Which of the following could be equal to the sum of these common roots? 1.  p + q + r 4. –pqr

2.  2(p + q + r) 5.  – (p + q + r)

3.  pqr

28. If the roots of the equation ax2 + bx + c = 0, a > 0, be

greater than unity than: 2.  a + b + c > 0 1. a + b + c = 0 3.  a + b + c < 0 4.  a + b = c 5.  None of these

29. If α and β are the roots of the equation px2 + qx + r = 0 (p, q, r > 0), then which of the following is describes α and β most comprehensively? 1.  non-real numbers 2.  real and negative 3.  real and positive 4.  rational numbers 5.  None of these 30. If α, β are roots of x² + x + 1 = 0 and γ, δ are the root of x² + 3x + 1 = 0, then what is the value of (α – γ) (β + δ) (α + δ) (β – γ)? 1.  2 4.  8

2.  4 5.  10

3.  6

31. What is the value of y if |y – 1| = |y – 2|? 1.  0.5 4.  –1

2.  1.5 5.  Not possible

3.  1

32. What is the value of 2x in 26x + 23x + 5 = 11?

1.  2/3 4.  2

2.  3 5.  8/3

3.  1

33. If 3z+1 – 3z–1 = 24, then what is the value of (2z)z?



1.  2 4.  512

2.  16 5.  None of these

3.  216

34. What is the value of

1 1 + 1+ 2+ 3 1– 2+ 3

+

+

1 1+ 2– 3

1 ? 1– 2– 3

1.  2 4.  2 – 3

2.  –2 3.  2 + 3 5.  None of these

35. Find the set of values of p for which both the roots of the equation x2 – px + 1 = 0 are greater than unity. 1.  p < 2 3.  –2 < p < 2 5.  None of these

2.  p > 2 4.  No such value exist

  1.163

3.  a/b, b/e, c/f are in HP 4.  a/b, b/e, c/f are in AP or GP 5.  None of these Direction for questions 37 and 38:  Read the passage below and solve the questions based on it. One of the +ve roots of a quadratic equation ax2 + m x + c = 0, where a = 1, is twice that of the other. The sum of the coefficient of x and constant term is 2. 37. What is the value of m in the equation? 1.  –4 4.  6

2.  4 5.  2

3.  –6

38. If x1 and x2 are the roots of this equation, then find the value of | x1 – x2 |. 1.  2 4.  0

2.  4 5.  None of these

3.  6

39. The two roots of the quadratic equation ax2 + bx + c = 0 are both two-digit integers with the same units digit, but D/a2 (where D is the discriminant given as b2 – 4ac) is not a multiple of 100. Which of the following is a possible value of the units digit of b/2a? 1.  4 4.  7

2.  5 5.  2

3.  6

40. The polynomial (ax 2 + bx + c) (ax 2 – bx – c), ac ≠ 0, has

1.  four real zeroes 2.  at least two real zeroes 3.  at most two real zeroes 4.  no real zeroes 5.  None of these

41. Find the maximum and the minimum values of the 2 function x 2 – x + 1 for real values of x. x  + x + 1 1 1.  3 and –3 2.  and – 1 3 3 1 3.  3 and 5.  – 1 and 1 3 5.  None of these 42. If the roots of ax2 + bx + b = 0 be in the ratio p : q, q p then q + + ab = p 1.  1 2.  –1 3.  2 4.  0 5.  None of these

36. If a, b and c are in GP, and equations ax2 + 2bx + c = 0 and dx2 + 2ex + f = 0 have a common root then

43. If the roots of the equation x2 – 2ax + a2 + a – 3 = 0 are less than 3 then

1.  a/b, b/e, c/f are in AP

1.  a < 2 4.  a > 4

2. a/b, b/e, c/f are in GP

2.  2 ≤ a ≤ 3 3.  3 < a ≤ 4 5.  None of these

1.164 

  Quantitative Aptitude and Data Interpretation

44. The number of values of k for which (x2 – (k – 2)x + k2) (x2 + kx + (2k – 1)) is a perfect square is 1.  1 4.  3

2.  2 5.  none of these

49. Which of the following equations has real roots?

3.  0

45. If x2 + ax + b = 0 and x2 + bx + a = 0, a ≠ b, have a common root α then which of the following is true?

50. Which of the following is a quadratic equation?

1.  a + b = 1 2.  α + 1 = 0 3.  α = 0 4.  a + b + 1 = 0 5.  None of these 46. Rajat planned to drive a distance of x km. After driving 120 km, Rajat stopped for petrol. What fractional part of trip had Rajat covered when he stopped? 1.  x/120 4.  120/x

1.  x1/2 + 2x + 3 = 0 2.  (x – 1) (x + 4) = x² + 1 3.  x4 – 3x + 5 = 0 4. (2x + 1) (3x – 4) = 2x² + 3 5.  None of these

2.  x/(x + 120) 3.  1/(x + 120) 5.  None of these

51. If α and β are the two roots of the equations 2x² – 7x – 3 = 0, then find the value of (α + 2) (β + 2).

4 7. The system of linear inequations x + y < 0 x > 0, y > 0 has

1.  9 4.  6

1.  Three solutions 2.  Exactly 1 solution 3.  No solution 4.  An infinite number of solutions 5.  None of these

1.  1 4.  – 2

3.  9.5

2.  – 1 5.  None of these

3.  2

53. If equation ax2 + bx + 6 = 0 doesn’t have two distinct roots, what is the least value of (3a + b)?

1.  x² + 2x + 8 = 0 2.  x² – 4x + 8 = 0 3.  x² – 24x + 128 = 0 4.  2x² + 8x + 9 = 0 5.  None of these

ANSWER KEYS

2.  – 9.5 5.  4.5

52. One of the roots of the equation x² – x + 3m = 0 is double of one of the roots of the equation x² – x + m = 0. If m ≠ 0, then find its value.

48. If a, b are the two roots of a quadratic equation such that a + b = 24 and a – b = 8, then the quadratic equation having a and b as its roots is,

1.  3x² + 4x + 5 = 0 2.  x² + x + 4 = 0 3.  (x – 1) (2x – 5) = 0 4.  2x² – 3x + 4 = 0 5.  None of these

1.  2 4.  –6

2.  –2 5.  3

3.  0

54. How many quadratic equations are there which remain unchanged even if its roots are squared? 1.  2

2.  4

3.  0

4.  6

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

4

3.

4

4.

2

5.

4

6.

2

7.

5

8.

4

9.

1

10.

2

11.

1

12.

3

13.

3

14.

2

15.

2

16.

3

17.

1

18.

2

19.

3

20.

3

21.

3

22.

1

23.

1

24.

3

25.

3

26.

5

27.

1

28.

2

29.

2

30.

4

31.

2

32.

1

33.

2

34.

2

35.

4

36.

3

37.

3

38.

5

39.

2

40.

2

41.

3

42.

4

43.

1

44.

1

45.

4

46.

4

47.

3

48.

3

49.

3

50.

4

51.

3

52.

4

53.

2

54.

2

5.  3

Equations 

  1.165

HINTS AND EXPLANATIONS 1. (2)  x + y = –z ⇒ (x + y)3 = (–z)3

f(1/3) =



Hence, required remainder =

⇒ x3 + y3 + 3xy (x + y) + z3 = 0. So, x3 + y3 + z3 = 3xyz 2. (4)  x –

1 = 2 ⇒ [x – 1 ]2 = 4 ⇒ x2 + 1/x2 = 6 x x

Or, [x + 1/x ] = 36 2

Hence x4 +

2 2

1 = 34 x4

1 2 2 – 107 – + –4= 3 3 27 27



– 107 27

16. (3)  Let f(x) = ax3 + 4x2 + 3x – 4 and g(x) = x3– 4x + a be the given polynomials. The remainders when f(x) and g(x) are divided by (x – 3) are f(3) and g(3) respectively.

According to the question, f(3) = g(3)

4. (2)  f(x) = x2 –27x + 196 = x, or, x2 –28x + 196 = 0 ⇒ (x – 14)(x – 14) = 0



⇒ 27a + 36 + 9 – 4 = 27 – 12 + a



⇒ 26a + 26 = 0 ⇒ a = – 1

So, x = 14

17. (1)  Let f(x)= ax3 + 3x2 – 13 and g(x) = 2x3 – 5x + a be the given polynomials. The remainder when p(x) and q(x) are divided by (x + 2) are f(–2) and g(–2) respectively.

7. (5)  Statement 1 is obviously not always true. Statement 2 is not true for negative values of x. Statement 3 is not true for 0 < x < 1. 10. (2)  Assume that price of an apple = Rs X and price of a guava = Rs Y



Given that f(–2) = g(–2)



⇒ a(–2)3 + 3(–2)2 – 13 = 2 (–2)3 – 5(–2) + a



⇒ –8a + 12 – 13 = –16 + 10 + a ⇒ –8a – 1 = a – 6 5 9

Given is 3X + 2Y = 23 and X + 4Y = 21

⇒ a =

Solving we get Y = 4, Hence cost of 5 guavas = Rs 20

18. (2)  Let f(x) = x3 – a2 x + x + 2 be the given polynomial. By factor theorem, (x – a) is a factor of f(x) if f(a) = 0.

12. (3)  We have, x + 2 = x-(–2). So, by remainder theorem, when f(x) is divided by {x – (–2)} the remainder is equal to f(–2).



Now, f(a) = 0 ⇒ a3 – a2 × a + a + 2 = 0



Now, f(x) = 2x4 –6x3 + 2x2 – x + 2



⇒ a + 2 = 0 ⇒ a = –2.



⇒f(–2) = 2(–2)4 –6(–2)3 + 2(–2)2 – (–2) + 2



Hence, (x – a) is a factor of the given polynomial, if a = –2



⇒ f(–2) = 2 × 16 – 6 × –8 + 2 × 4 + 2 + 2



⇒ f(–2) = 32 + 48 + 8 + 2 + 2 = 92

19. (3)  Let f(x) = x3 – ax2 – 13x + b be the given polynomial. If (x – 1) and (x – 3) are factors of f(x), then

Hence, required remainder = 92. 13. (3)  Using remainder theorem, we know that f(x) when divided by g(x) 1 1 = (x – ) gives a remainder equal to f . 2 2 Now, f(x) = 4x3 – 12x2 +14x – 3

3 1 ⇒ f( ) = 2 2

1 3 Hence, required remainder = f( ) = 2 2 1 14. (2)  We have, g(x) = 3x – 1 = 3 (x – 3 ). Therefore, by remainder 1 theorem, when f(x) is divided by g(x) = 3 (x – 3 ), the remainder 1 is equal to f( ). 3 Now, f(x) = x3 – 6x2 – 2x – 4



1 1 3 1 2 1 ⇒ f( ) = ( ) – 6( ) + 2( ) – 4 3 3 3 3







1 1 1 – + – 4 = –107/27 27 27 27 107 Remainder = – 27

15. (2)  Using remainder theorem, when f(x) is divided by g(x) = 1 – 3x, the remainder is equal to f(1/3).

Now, f(x) = x3 – 6x2 + 2x – 4



f(1) = 0 and f(–3) = 0



⇒ 13 – a × 12 – 13 × 1 + b = 0 and (–3)3 – a(–3)2 – 13 × (–3) + b =0



⇒ 1 – a – 13 + b = 0 and –27 – 9a + 39 + b = 0



⇒ – 12 – a + b = 0 and – 9a + b + 12 = 0



⇒ a – b = –12



Solving the equations, we get ⇒ a = 3



Putting a = 3 in a – b = –12, we get b = 15



Hence, a = 3 and b = 15

20. (3)  f(–3) = 0

⇒ 3(–3)2 + p(–3) + 6 = 0



⇒ 27 – 3p + 6 = 0 ⇒ p = 11

21. (3)  Taking (x – 2) > 0 we get x = 0, 3. So, x = 3

Taking (x – 2) < 0 we get x = 1, 4. So, x = 1



Hence sum of roots = 4



Alternatively,



Assuming |x – 2| = Z, this equation is now z2 + z – 2 = 0

1.166 

  Quantitative Aptitude and Data Interpretation _

_

_



Or, (z + 2) (z – 1) = 0, Hence z = –2 or 1.



Taking z = –2 is not possible since z = |x – 2|

2(2​√2 ​ ) 2 + 2​_√2 ​  ______ 2 – 2​_√2 ​  ______ _______ ​   – ​   = ​  _ ​   = 2  ​   ​  2​√2 ​  2​√2 ​  2​√2 ​ 



Taking z = 1, or, |x – 2| = 1, so x = 3 and x = 1.

[Using (a+b) (a-b) = a2 – b2]

And these are the only real roots of this equation. So sum of real roots = 1 + 3 = 4

37. (3)  Let one root be α(+ve) then other = 2α

23. (1)  All the terms in the equation x2 + 7 |x| + 12 = 0 are positive [terms like x2, 7 |x| and 12]. Sum of positive terms cannot be equal to zero. It shows there will not be any real root for this equation.

m is a multiple of 3 and –ve.

–m = 3α 38. (1)  m + c = 2, since m = –6 so, c = 8

24. (3)  x2 – kx + 5 = 0 has 3 as a root ⇒ 32 – k × 3 + 5 = 0 ⇒ K = 14/3

Equation = X2 – 6X + 8 = 0 ⇒ (X – 4) (X – 2) = 0 ⇒ X = 4 or 2

25. (3)  Use AM ≥ GM.

39. (2)  Let the roots be –21 and 11

26. (5)  For roots to be equal, D = b2 – 4ac = 0



Equation is X2 + 10X – 231 = 0 ⇒ (X + 21) (X – 11) = 0



2 – 4ac _________ b______ 100 + 924 ​  2 ​   = ​   = 1024  ​  1 a



b/2a = 10/2 = 5



b2 – 4ac = (2p)2 – 4 × 9 × 4 = 0 → p = ±6

27. (1)  1; Let x1, x2 be the roots of x2 + px + qr = 0

Let x2, x3 be the roots of x2 + qx + pr = 0



Let x1, x3 be the roots of x2 + rx + pq = 0



Common roots are x1, x2 and x3.



Now, x22 + px2 + qr = 0 and x22 + qx2 + pr = 0



⇒ (p – q) x2 + r(p – q) = 0 ⇒ (p – q) (x2 – r) = 0 ⇒ x2 = r



Similarly, x1 = q and x3 = p



So, x1 + x2 + x3 = p + q + r

|X 1 – X2| = |±2| = 2

(not multiple of 100)

40. (2)  Treating both the equations as independent equations:

D for 1st equation = b2 – 4ac



D for 2nd equation = b2 + 4ac



At least one of these two D will be positive, and hence atleast two roots will be positive.

43. (1)  By putting a = 1, 0, or –1 etc., we get both roots of eqn less than 3. hence a is less than 2.

28. (2)  2; f(x) = ax2 + bx + c

44. (1)  By putting k = 1, we get equation as (x2 + x + 1)2

Since roots are greater than unity, a × f(1) > 0

45. (4)  a2 + aa + b = a2 + ba + a ⇒ a = 1

f(1) > 0 [a > 0] ⇒ a + b + c > 0



30. (4)  4  α + β = –1, αβ = 1, γ + δ = –3, γδ =1.

46. (4) 120 ___ ​  x   ​ of the planned distance.



Also γ² +3γ + 1 = 0 and δ² + 3δ + 1 = 0



Now, (α – γ) (β + δ) (α + δ) (β – γ) = [αβ – γ (α + β) + γ²] [αβ + δ (α + β) + δ²] = (1 + γ + γ²) (1– δ + δ²) = (–2γ) (–4δ) as γ² + 3γ +1=0



δ² + 3δ + 1 = 0 ⇒ 8γδ = 8

31. (2)  Go through the options. 32. (1)  Let y = 23x Then y 2 + y – 6 = (y + 3) (y – 2) = 0

Since y > 0, y = 2 = 23x



3x = 1 → x =

1 3

y 33. (2)  Let y = 3z. so we can say 3y – = 24. Solving this we see that y = 3 9, so z = 2. So, Desired expression, 42 = 16. 34. (2)  Rearrange the expression to have:

1_ 1_ 1_ __________ __________ _________   _ ​  + ​    _ ​  + ​    _   ​ ​  1 + ​√2 ​ + √ ​ 3 ​  1 + ​√2 ​ – √ ​ 3 ​  1 – √ ​ 2 ​ + √ ​ 3 ​ 

_ _ _ _ 1_ 1 + ​√2 _​ – ​√3 ​ _+ 1 + ​√2 ​ _+ ​√3 _​  _________ + ​    _ ​  =​ ____________________       ​ 1–√ ​ 2 ​ – √ ​ 3 ​  ((1 + ​√2 ​)  + ​√3 ​)  ((1 + ​√2 ​ – ​√3 ​  _ _ _ _ 1–√ ​ 2 ​ ​ 3 ​_ + 1 – ​√2 ​_ + √ ​ 3 ​_  _______________________ _ – √

+ ​          ​ ((1 – ​√2 ​ ) +​√3 ​ ) ((1 – √ ​ 2 ​ ) – √ ​ 3 ​ 

Putting α = 1 in equation, we get 1 + a + b = 0.

48. (3)

a + b = 24, a – b =8 ⇒ a = 16, b = 8



Required equation is the one whose sum of the roots is 24 and product of the roots is 128. Quadratic equation = x2 – (sum of roots)x + product of roots = 0



x² – 24x + 128 = 0.

So, ab = 128

49. (3)

The equation ax² + bx + c = 0 has real roots if b² – 4ac > 0.



(3) ⇒ (x – 1) (2x – 5) = 0 ⇒ b² – 4ac = 49 – 40 = 9 > 0.

50. (4). 51. (3)

–3 7 __ ___ α + β = ​   ​ , αβ = ​   ​  2 2



(α + 2) (β + 2) = αβ + 2α + 2β + 4 = αβ + 2 (α + β) + 4



19 –3 –3 7 = ___ ​   ​ + 2 × __ ​   ​ + 4 = ___ ​   ​ + 11 = ___ ​   ​ = 9.5 2 2 2 2

52. (4)

Let α, β be roots of the equation x² – x + m = 0



⇒ α + β = 1, αβ = m

Equations 

Let 2α, γ be the roots of the equation x² – x + 3m = 0

⇒ 2α + γ =1, 2αγ = 3m m __ (i) ⇒ α + ​ α ​  = 1

(ii) ⇒ α² – α + m = 0 3m ___ ⇒ 2α + ​   ​ = 1 2α



⇒ 4α² – 2α + 3m = 0



Using A and B,

⇒ m = 2α



So, 2αγ = 3m ⇒ γ = 3, or, 2α + γ = 1 ⇒ α = –1



α+β=1⇒β=2



α = –1, β = 2, γ = 3 ⇒ m = –2.

  1.167

53. (2)  Assume f(x) = ax2 + bx + 6 -------------(A) -------------(B)



Since equation 1 has imaginary or real and equal roots and f(0) = 6 >0, so f(x) ≥ 0 for all real x.



f(3) ≥ 0 ⇒ 9a + 3b + 6 ≥ 0 ⇒ 3 (3a + b) ≥ –6



⇒ (3a + b) ≥ –2



So least value of (3a + b) is –2.

c h a p t e r

  10

Sequence and Series

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   What is Progression and their types?   Definitions and properties   Kind of questions which are asked in the CAT   Method of solving questions

  SEQUENCE AND SERIES If the terms of a sequence are written under some specific conditions, then the sequence is called a Progression. With respect to CAT preparation, however, we will confine ourselves only to the following certain and standard series of progression: 1.  Arithmetic Progression 2.  Geometric Progression 3.  Harmonic Progression

Arithmetic Progression A succession of numbers is said to be in Arithmetic Progression (AP) if the difference between any term and the previous term is constant throughout. This constant difference is known as common difference and is denoted by ‘d’.

nth term of an Arithmetic Progression nth term t n = a + (n–1)d where a is the first term, d is the common difference and n is the number of terms. Example  1 Example 

1

The 5th term of an AP is 15 and the 9th term is 23. Find the 14th term. Solution Solution

5th term of an AP = a + 4d and 9th term of the same AP = a + 8d. Solving these two equations, we get a = 7 and d = 2 Hence 14th term = a + 13d = 33



Sequence and Series  Example  2 Example 

  1.169

2/(1+log10y) = 1/(1+log10x) +1/(1+log10z)

2

If the 9 times the 9th term in AP is equal to 15 times the 15th term in the AP what is the 24th term?

[1 + (1+log10x) + 1+ (1+log10z) ] = __________________________ ​      [(1+log10x)    (1+log z)] ​ 10 = [2+log10xz ]/(1+log10x) (1+log10z)

Solution Solution

9th term of AP = a + 8d and 15th term of the same AP = a + 14d

Obviously, this is not going to fetch us the answer. Checking option (b) now

Given is 9 (a+8d) = 15 (a+14d) ⇒ 9a + 72d = 15a + 210d

[1/(1+log10y)]2 = [1/(1+log10x)] [1/(1+log10z)]

⇒ 6a = – 138 d ⇒ a = – 23d ––––––(1)

= [1/(1+ log10(x+z) + log10xz)]

24th term = a + 23 d

Again we are trapped and any solution is not in sight.

Using equation (1), we get a + 23 d = 0

Checking option (c) now 1/(1+log10x ), 1/(1+log10y) and 1/(1+log10z) are in HP then 1+log10x, 1+log10y and 1+log10z will be in AP.

Properties of AP If a, b, c, d,……………are in AP, then 1. a + k, b + k, c + k, d + k……will be in AP, where k is any constant.

So, log10x, log10y and log10z will also be in AP. Hence, 2 log10y = log10x + log10z ⇒ y2 = xz which is given.

2. a – k, b – k, c – k, d – k……will be in AP, where k is any constant.

So, (c) is the answer.

In the above two cases, the common difference will be the same as earlier.

Alternatively, we can apply the following process also:

3. ak, bk, ck, dk……will be in AP, where k is any constant.

So, 1+log10x = 1, 1+log10y = 2 and 1+log10z = 3.

In this case, new common difference will be k times the earlier common difference. b c d 4. __ ​ a  ​, __ ​   ​  , ​ __  ​, __ ​   ​  will be in AP, where k ≠ 0. k k k k In this case, new common difference will be __ ​ 1k ​  times the earlier common difference. Example  3 Example 

Assume x = 1, y = 10 and z = 100 as x, y, z are in GP. ⇒ Thus we find that since 1,2 and 3 are in AP, we can assume that 1+log10x , 1+log10y and 1+log10z are in AP. ⇒ Hence, by definition of an HP we have that 1/(1+log10x ), 1/(1+log10y ) and 1/(1+log10z ) are in HP. So, option (c) is the answer.

3

If x, y, z are in GP, then 1/(1+log10x), 1/(1+log10y) and 1/(1+log10z) will be in

Sum of n terms of an Arithmetic Progression

1.  AP

n ​  [2a+(n–1)d)], where n = no. of terms, a = 1st term Sn = ​ __ 2 and d = common difference.

2.  GP

3.  HP

4.  Cannot be determined Solution Solution

Going through options. Checking option (a), the three will be in AP if the 2nd expression is the average of the 1st and 3rd expressions. This can be mathematically written as:

Example  4 Example 

4

If the sum of the first 11 terms of an arithmetic progression equals that of the first 19 terms, then what is the sum of the first 30 terms? 1.  0 3.  1

2.  –1 4.  Not unique

(CAT 2004)

1.170 

  Quantitative Aptitude and Data Interpretation

Solution Solution

Alternatively, using average method, average = (1st no. + last no.)/2

Given t1 + t 2 + … + t11 = t1 + t 2 + … + t19 (for an A.P.)

10 + 94  = 52 Average = _______ ​  2 ​  So, sum = Average × Number of nos. = 52 × 13 = 676

19 11 ​ [2a + (11 –1)d] = ___ ​ 2 ​ [2a + (19 – 1)d ⇒ ​ ___ 2 ⇒ 22 a  + 110d = 38 a + 342 d ⇒ 16 a + 232 d = 0

Example  6 Example 

⇒ 2a + 29 d = 0 30 ​ [2a + (30 – 1)d] = 0 ⇒ ​ ___ 2 ⇒ S30terms = 0

Consider the set S = {1,2,3,…,1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements? (1)3 (4)7

Example  4 Example 

5

Find the sum of AP 3, 5, 7, ………………50 terms.

7

(2)4 (3)6 (5)8            (CAT 2006)

Solution Solution

Using arithmetic progressions, having n elements. Solution Solution

Tn = a + (n–1)d

Here n = 50, d = 2 and a = 3.

⇒ 1000 = 1+ (n–1) d ⇒ 999 = (n–1)d

n ​ [2a+(n–1)d)] = 25 × [2×3+(50–1)2)] Using formula Sn = ​ __ 2

Or, 999 = 33×37

= 25 × 104 = 2600 However, we can find out the sum of any AP in a better way through Average also. 3 + 101 Last term of this series = 101, so average = _______ ​  2 ​   = 52 So, sum = Average × No. of numbers = 52 ×50 = 2600 L   × n, where F is the first term, L is the Hence, Sn = _____ ​ F 2+ ​ last term and n is the no. of terms of that AP.

(n–1) = 3,37,9,111,27,333,999 i.e. 7 cases

Geometric Progression A succession of numbers is said to be in Geometric progression if the ratio of any term and the previous term is constant. This constant ratio which is common to any of the two terms is known as common ratio and is denoted by ‘r’. Example 7 Example

i. 1, 2, 4, 8,.,.,.,.,.,.,.,.,., Common ratio of series (i) is 2.

Example  5 Example 

6

What is the sum of all the two–digit numbers which when divided by 7 gives a remainder of 3? (CAT 2003) Solution Solution

This series is like → 10, 17, 21, …..94. Here n = 13, d = 7 and a = 10 Using the formula for sum Sn = __ ​ n2 ​ [2a+(n–1)d)], sum = 676

nth term of a Geometric Progression nth term t n = arn–1 where a is the first term, r is the common ratio and n is the number of terms.

Properties of GP If a, b, c, d,……………are in GP, then 1. ak, bk, ck, dk……will be in GP, where k is any nonzero constant.

Sequence and Series  b c d 2. ​ __a  ​, __ ​   ​  , ​ __  ​, __ ​   ​  will be in GP, where k is any non-zero k k k k constant.

  1.171

Solution Solution

Distance covered before first rebound = 120 m

In the above two cases, common ratio will be same as earlier. 3. If a GP of even number of terms is given, then its common ratio will be the same as ratio of sum of all the even terms and sum of all the odd terms.

Sum of n terms of a Geometric Progression a(1 – rn) Sn = ​ _______ ​ when r≠1 1 – r    Sn = na

when r = 1

Where n = no. of terms, a = 1st term and d = common difference.

120 4/5

120m

120.4/5. 4/5.

Floor

4  ​and then And then the ball bounces to a height of 120×​ __ 5 falls from the same height. Next time ball will go up by 4 4 __ 120×​ __ 5 ​ ×​ 5 ​  m and then will fall from the same height. So, total distance covered 4 __ 4 4 __ = 120 + 2×120×​ __ 5 ​ +2×120× ​ 5 ​ ×​ 5 ​  +………….∝. 4 __ 4 __ 4 = 120 + 2 ×120(​ __ 5 ​ +​ 5 ​ ×​ 5 ​ +…………∝) __ ​ 45 ​ ____ = 120 + 240 ​  __4  ​  1080 m 1– ​ 5 ​

Sum of Infinite Geometric Progression So far, we have done the summation of n terms of a GP. Now there lies the need of a separate expression for the sum of Infinite GP. In case of AP, since either the terms are always decreasing and going till –∝ or always increasing and going till +∝ so, summation of infinite terms in AP will be either –∝ or +∝. However the case is not same in GP    This need of a formula for infinite GP can be seen with the following example: 5 5 5 10, 5, , , , ........ 2 4 8 POINT TO REMEMBER If in an infinite GP every term is equal to the sum of all the terms that follow, then its common ratio = 1/2 Sum of Infinite GP = 1____ ​  –a r ​, where –1< r < 1.

Example  8

Example  8

After striking the floor, a ball rebounds to 4/5th of the height from which it has fallen. What is the total distance that it travels before coming to rest if it is gently dropped from a height of 120 m?

a  ​th of  Alternatively, if the ball rebounds to ​ __ b original height H, then total distance covered = a+b H × ____ ​ a–b  ​. In the above example, Total distance covered = 120 × ____ ​ 4+5  ​= 1080 m 5–4

Example  9

Example  9

On 1 January 2004 two new societies S1 and S2 are formed, each nnumbers. On the first day of each subsequent month, S1 adds b members while S2 multiples its current numbers by a constant factor r. Both the societies have the same number of members on 2 July, 2004. If b = 10.5n, what is the value of r? (CAT 2004) 1.  2.0

2.  1.9

3.  1.8

4.  1.7

Solution

Solution

There w ill be an increase of 6 times. Number of members S1 will be in A.P. On 2 July , 2004, S1 will have n + 6 b members = n + 6 × 10.5 n = 64 n Number of members in S2 will be in G.P On 2 July, 2004 Number of members in S2 = nr6 They are equal, Hence 64 n = nr6 ⇒ 64 = r6 ⇒ r = 2

1.172 

  Quantitative Aptitude and Data Interpretation

Example  10 Example 

Solution Solution

10

The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10n, on the nth day of 2007 (n = 1, 2, … 100). And then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, …,, 365). On which date in 2007 will the prices of these two varieties of tea be equal? 1.  May 20

2.  April 10

3.  June 30

4.  May 21

5.  April 11

(CAT 2007)

1 ​  will be in AP. a, b, c are in HP, so, __ ​ 1a ​  , __ ​ 1  ​and ​ __ c b a+b+c a+b+c a + b + c ________  , ​   ​   and ​ ________  will be in AP. Or, ​ ________ a ​  c ​  b a+b b+c a+c  , 1 + _____ ​   ​   and ​ _____   will be in AP. Or, 1 + ​ _____ a ​  c ​  b a+b b + c _____ a + c _____ ,  ​  a ​  ,  ​  c  ​  , are in AP. Hence _____ ​  a ​  b c , and ​ _____ ​     ​     ​ , will be in HP. So, _____ ​  a   ​ , _____ b+c c+a a+b Alternatively, these kinds of problems can be done by assuming values also. Let us take 1, 1/2, 1/3 (which are in HP)

Solution Solution

From 100 + 0.10 n = 89 + 0.15n, n will be definitely greater than 100 Price of Darjeeling tea on 100th day and onwards = 100 + 0.10 (100) = Rs 110 Now, price of Ooty tea will be Rs 110 when 89 + 0.15n = 110

_____ ​  a   ​ = 6 b+c b 3 ​  _____ ​ a + c ​ = ​ __ 8 c 2 ​  _____ ​     ​ = ​ __ a+b 9 Now, when we check these values for AP, GP and HP,

⇒ 0.15 n = 21 ⇒ n = 140

5 9 8 ​  is the AM of ​ __ __ we find that ​ __ 3 6  ​and ​ 2 ​ .

Therefore prices will be equal on 140th day i.e., 20 May

So, obviously the given terms are in HP.

Hence, [1]

Properties of HP

3. Harmonic Progression a, b, c, …..are said to be in HP if reciprocals of these terms 1 ​  , __ 1 __ 1 that is, ​ __ a ​ b  ​, ​ c ​  are in AP. It is noteworthy here that no term of an HP can be equal to zero.

nth term of a Harmonic Progression nth term of HP = 1/ (nth term of the corresponding AP)

Example  11 Example 

11

b c a   ​ , _____ If a, b and c are in HP, then ​ _____ ​     ​ , _____ ​     ​ are in b+c c+a a+b 1.  AP

2.  GP

3.  HP

4.  Cannot be determined uniquely

If a, b, c and d are in HP, all of them are distinct then (i)  a + d > b + c (ii)  ad > bc

Sum of n terms of a Harmonic Progression There is no standard formula for finding out the sum of n terms of a HP.

  ARITHMETICO GEOMETRIC SERIES A series is said to be in Arithmetico Geometric Series if its each term is the product of the corresponding terms of an AP and a GP. Example 12 Example

1, 2x, 3x2 , 4x3,……………..

Sequence and Series  In the above series, first part of this series is in AP (1, 2, 3, 4,….) and 2nd part is (x0, x1, x2 , x3,….) in GP.

Sum of n terms of any Arithmetico Geometric Series(AGS) The sum of n terms of any AGS a, (a+d)r, (a+2d)r2 ,…….. is given by

  1.173

So, if three terms a, b and c are in GP, then their ________ 3 ​ a × b × c ​  GM = b = √

Harmonic Mean If two numbers a and b are in HP then their HM

(1 – rn–1) ___________ [a + (n – 1)d] ​ 1 a– r ​ + dr ​ _______   – ​   ​    – r . rn, if r ≠ 1. Sn = ____ 1 – r ​  1–r

2ab = _____ ​    ​  a+b

​ n2 ​  [2a + (n–1)d], if r = 1 Sn = __

Relationship between AM, GM and HM

Sum of infinite terms of any Arithmetico Geometric Series(AGS)

1. AM, GM and HM will be in GP for any given set of numbers.

d×r S ∝ = ____ ​ 1 a– r ​ + ______ ​     ​, | r | < 1 (1 – r)2

So, GM is the geometric mean of this series. _________ And, GM = √ ​ AM × HM ​  (True of only two numbers)

  MEANS

2. AM ≥ GM ≥ HM (True for any number of numbers)

Arithmetic Mean a+b It two numbers a and b are in AP then their AM = ​ _____   2 ​  In general, if a, b, c,………………n terms are in AP, then a + b + c + ………n terms their AM = ______________________ ​         n ​

NOTE - For AM/GM/HM to be calculated of a set of numbers, number are not required to be in AP/GP/HP respectively.

  SUM OF N TERMS OF SOME SPECIAL SERIES

Example  13

Example  12 If a, b, c, d, e and f are the AM’s between 2 and 12, then find the value of a + b + c + d + e + f.

In this part of Progression, we will see the sum of some other special sequences.

1.  Sum of 1st n natural numbers

Solution Solution

If a, b, c, d, e and f are the AM’s between 2 and 12, then find the value of a + b + c + d + e + f.

( 

)

P+Q ​  2 ​     ​n Sum of n AM’s between P and Q = ​ ______

( 

)

12  ​ 2 +2 ​    ​6= 42 Hence sum =​ ______

Geometric Mean If two numbers a and b are in GP then their ___ GM = ​√ ab ​  In general, if a, b, c,………………n terms are in GP, then their ____________________________ n ​ a × b × c ×………………n.terms ​       GM = √

n(n+1) Sn = ______ ​  2 ​    Hence

n(n+1) S = 1 + 2 + 3 + ….+ n = ______ ​  2 ​    S=1 n

2.  Sum of the squares of 1st n natural numbers n(n+1)(2n+1) Sn = ____________ ​       6 ​ Hence =

n S=1

n(n+1)(2n+1) S2 = 12 + 22 + 32+ ……..+ n2 = ____________ ​       6 ​

3.  Sum of the cubes of 1st n natural numbers

( 

)

2

n(n+1) Sn = (Sum of 1st n natural numbers) = ​ ______ ​  2 ​     ​ 2

  Quantitative Aptitude and Data Interpretation

1.174 

It means:

Solution Solution

1 +2 +3 = 2(1+2+3) = 6 = 36 3

3

3

2

2

13 +23+33 +43 = (1+2+3+4)2 = (10)2 = 100 So, 13 +23+33 +43+............ n terms = (1+2+3+...........n terms)2 2 n(n+1)     = ______ 2

​ 

 ​

4.  22 + 42 + 62 +............ + n terms 2n (n + 1) (2n +1) 3 Example  14 Example 

13

Find the sum to n terms of the series 11 + 103 +1005 + ……… 1.  10/9(10 –1) –1 2.  100/99(10 –1) + n n

n

2

3.  10/9(10n–1)+ n2 4.  None of these

Ideally, in these problems, rather going by the mathematical process of solving, we should use options. Checking option (1), Put n = 1. 10/9(10n–1) –1 = 9, so it is not correct. Checking option (2), Put n = 1. 100/99(10 n –1) + n 2 is not equal to 11, so it is also not correct. Checking option (3), Put n = 1. 10/9(10n–1)+ n 2 = 11. But just because this option satisfies n = 1, we should not assume it to be correct. Let us check it for n = 2. Option (3) gives us 104. So, it is the answer. Normally, in these cases, checking the options till n = 2 guarantees the answer, but sometimes we need to check it till n = 3.

  Exercise  1 1. Sum of 15 terms of an AP is 600, and the common difference is 5. Find the first term. 1.  4 4.  6

2.  5 5.  None of these

3.  3

2. An AP has 23 terms, sum of the middle three terms is 144 and the sum of last three terms is 264. What is its16th term? 1.  102 4.  72

2.  64 5.  None of these

3.  82

3. In the above question, what will be the sum of 1st four terms? 1.  40 4.  64

2.  52 5.  None of these

3.  32

4. Find the sum of the first 15 terms of the series whose nth term is (4n+1). 1.  485 4.  630

2.  495 5.  None of these

3.  505

5. If the sum of the reciprocals of the first seven terms of a harmonic progression is 70, find the 4th term of the HP. 1.  2/15 4.  5/12

2.  1/10

3.  3/7

6. A series is simultaneously in AP and GP. Which of the following options is true?

1. Set of common ratios of all the possible GPs have only one element. 2. Set of common ratios of all the possible GPs have more than one element but a finite value be there. 3. Set of common ratios of all the possible GPs have infinite elements. 4.  Options (1) and (2) 5.  None of these

can can will can

7. A series is simultaneously in AP and GP. Which of the following options is true? 1. Set of common differences of all the possible APs can have only one element. 2. Set of common differences of all the possible APs can have more than one element but a finite value will be there. 3. Set of common differences of all the possible APs can have infinite elements. 4.  None of these 8. The series 1, 4…. to n terms is an 1.  AP 4.  AP or HP

2.  GP 3.  HP 5.  Cannot be determined

9. Find the sum to 200 terms of the series 1+ 4 + 6 + 5 + 11 + 6 +………...

Sequence and Series  1.  30200 4.  42800

2.  29800 5.  None of these

3.  26400

1.  3 4.  –3

2.  1 5.  –1

  1.175

3.  0

10. What is the 2nd term of an AP whose 8th and 12th terms are respectively 39 and 59?

19. An infinite GP has first term ‘x’ and sum 5. Then x belongs to

1.  8 4.  11

1.  x < –10 4.  x > 10

2.  6 5.  7

3.  9

2.  –10 < x < 0 3.  0 < x < 10 5.  None of these

11. The 4th and 10th term of a GP are 1/3 and 243 respectively. What is the 2nd term of this GP?

20. Consider the following pyramid of natural numbers:

1.  3 4.  1/9



2.  1 5.  None of these

3.  1/27



12. Find the sum to n terms of the series 2.  n(n+1)(2n+2)(n+2)/4 4.  n(n+1)(n+2)(n+3)/4

1

2

4

7

1.2.3+2.3.4+3.4.5+…….. 1.  (n+1)(n+2)(n+3)/3 3.  n(n+1)(n+2) 5.  None of these



3

5

8

6

9

10......

......................................................................................and so on. Find the sum of numbers in the nth row of this pyramid. 1.  n2 4.  (n2 + 1)/2

2.  n(n+1)/2 3.  n (n2 + 1)/2 5.  None of these

13. (p + q)th term of G P is x and (p – q)th term is y. What is the pth term of this GP? _____ ____ __ 1. ​√xy ​   2.  3√ ​ x 2 y ​   3. ​√x 3 y 2 ​   4.  x + y 5.  None of these

21. Three non-zero real numbers form an AP and the squares of these numbers taken in the same order form a GP. What is the number of all possible common ratio of the GP?

14. The sum of the series (5a + 7b) + (8a + 5b) + (11a + 3b) + (14a + b) + .... upto 25 terms is

1.  0 4.  3

1.  1225a + 275b

2.  1025a – 425b

3.  1025a + 425b

4.  1225a – 275b

22. Three positive real numbers a, b and c are in AP such that abc = 4. What is the minimum value of b? __ __ 1. ​√2 ​   2.  3√ ​ 2 ​   3.  22/3 4.  23/2 5.  None of these

5.  None of these 15. There are two geometric progressions that satisfy the following conditions: the sum of the first three terms is 52; the third number is 9/4 times the sum of the first two. Find the sum of the first terms in the two progressions.

2.  1 5.  4

3.  2

23. Which of the following statement is always true? (statements are related to AP and terms are having their general notations.)

3.  48

1.  t5 + t8 = t1 + t12 2.  t8 = a + 8d 3.  t1 + t2=t3 4.  only 1 and 2 5.  None of these

16. How many pairs of positive integers x, y are possible such that y < x < 1000 and AM of x, y = GM of x, y+ 2?

24. If the sum of the 10th, 20th, 30th terms of an AP is equal to the 58th term, what is the ratio of the sum of the 10th, 20th and 30th terms to the sum of the 5th, 10th and 15th terms?

1.  28 4.  58

1.  2 4.  31

2.  38 5.  68

2.  5 5.  7

3.  29

17. In the quadratic equation ax + bx + c = 0, if D = b − 4ac and α + β, α2 + β2, α3 + β3 are in GP where α, β are the roots of ax2 + bx + c = 0, then 2

1.  D ≠ 0 4.  D = 0

2.  bD = 0 5.  None of these

2

3.  cD = 0

18. Given 2x – y + 2z = 2, x – 2y + z = –4 and x + y + k z = 4, what is the value of ‘k’ so that the given system of equations has no solution?

1.  2 : 1 4.  2 : 9

2.  20 : 9 5.  32 : 9

3.  19 : 9

25. A GP consists of 1000 terms. Sum of the terms occupying the odd places is P1 and the sum of the terms occupying the even places is P2. Find the common ratio of this GP. 1.  P2/ P1 4.  (P2 + P1)/ P2

2.  P1/ P2 3.  (P2 – P1)/ P1 5.  None of these

  Quantitative Aptitude and Data Interpretation

ANSWER KEYS

1.176 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

1

4.

2

5.

2

6.

1

7.

1

8.

5

9.

1

10.

3

11.

3

12.

4

13.

1

14.

2

15.

5

16.

3

17.

3

18.

2

19.

3

20.

3

21.

4

22.

3

23.

1

24.

3

25.

1

HINTS AND EXPLANATIONS 1. (2)  Average of an AP with 15 terms = 8th term = a + 7d (assume) = 600/15 = 40 [Where a = 1st term and d = common difference] So, 1st term = 8th term – 7d = 40 – 35 = 5 2. (2) Method 1: Assume 1st term = a, 2nd term = a + d, 3rd term = a + 2d and so on…. Sum of middle three terms = Term 11 + term 12 + term 13 = (a + 10d) + (a + 11d) + (a + 12d) = 3a + 33d = 144 → a + 11d = 48 …………………..(1)     Sum of last three terms = Term 21 + term 22 + term 23 = (a+20d) + (a+ 21d) + (a+22d) = 3a + 63d = 264 → a + 21 d = 88………………………(2)



So, average = 4 × 8 +1 =33

Sum of 15 terms = Average × number of terms = 33 × 15 = 495 5. (2) Reciprocal of HP will be in AP. If there are 7 terms in an AP, then 4th term will be its average or arithmetic mean.   Sum = 70, hence average = 10 = 4th term of this AP   So, 4th term of HP = 1/10 6. (1) A series can be simultaneously in AP and GP both only if all the terms of this series are same.   For example – 2, 2, 2, 2, 2,…………………………. 7. (1)  See the solution to Q6 above. 8. (5) To identify any series, we should have atleast three terms.   This series can be a GP as well as an AP currently.

Solving equation 1 and equation 2, we get d = 4, a = 4. So 16th term = a + 15 d = 64

9. (1)

Method 2:

Method 1:

If in an AP, there are 23 terms then12th term will be its average as well as the average of middle three terms. So, 12th term = average of middle three terms = average of 23 terms = 144/3 = 48 Similarly, 22nd term will be the average of last three terms. So 22nd term = 264/3 = 88 Now 22nd term – 12th term = 10 d (d being the common difference) = 40 → d = 4

16th term = 12th term + 4d = 48 + 16 = 64

3. (1)  Sum of 1st four terms = 4 + 8 + 12 + 16 = 40 4. (2) Method 1:

nth term = 4n +1 → 1st term ‘a’ = 5 (putting n = 1)



Common difference ‘d’ = 4. Now sum of 15 terms can be calculated using the formula for ‘n’ terms of an AP.

Method 2: 8th term of this AP will be its AM or average

Given series is a combination of two APs. The 1st AP is (1 + 6 + 11 +…) and the 2nd AP is (4 + 5 + 6 +…….) Since the terms of the two series alternate hence each of the APs contain 100 terms. S= (1 + 6 + 11 +……to 100 terms) + (4 + 5 + 6 + ……to 100 terms) = 100/2[2.1 + 99×5] + 100/2[2×4 + 99×1] = 50[497 + 107] = 50[604] = 30200. Method 2: We can treat every two consecutive terms as one. So we will have a total of 100 terms of the nature: (1 + 4) + (6 + 5) + (11 + 6) ….can be taken as 5, 11, 17… Now, a = 5, d = 6 and n = 100 Hence the sum of the given series is S = 100/2[2×5 + 99×6] = 50[604] = 30200 Method 3: After identifying the clubbed series as: 5, 11, 17…

Sequence and Series  The series can be represented as a general term: 6N –1 (where N represents term). Sum of 100 terms of series with general term 6N –1 100 × 101 = ∑100– – 100 = 30200. N=1 (6N – 1) = 6 × 2 Method 4: After we have identified the general term 6N – 1, we can have 100th term = 6×100 – 1 = 599

x 2 + y 2 + 2xy 4 __ + 16 + 16 √ ​ xy ​ 

__ = xy +4 + 4 √ ​ xy ​ ⇒ x 2 + y 2 + 2xy = 4xy

__ Or, x 2 + y 2 – 2xy = 16 + 16 √ ​ xy ​  __ _______ __ __ Or, (x – y) 2 = 16 (1 + √ ​ xy ​ ⇒ x – y = 4 ​√1 ​ + ​√1 + ​√xy ​ ​   X – y is a multiple of 4. Now we can put the values to find it out.

Average of this series = (1st term + last term)/2 = (5 + 599)/2 = 302

17. We get (α2 + β2)2 = (α + β) (α3 + β3) ⇒ aβ(α – β)2 = 0

Sum = 302 × 100 = 30200

So, C×D = 0

10. (3) Difference between 12th term and 8th term = 4d (where‘d’ is common difference) = 20

S∞ =

  So, d = 5 → a =4

19. ⇒ 1– r = x/5 ⇒ r = (5 – x)/x exists only if |r| < 1

  2nd term = 9

  For n = 1, value should be 1 × 2 × 3 = 6  For n = 2, Value should be 1 × 2 × 3 + 2 × 3 × 4 = 6 + 24 = 30 13. nth term of GP = arn–1

x =5 1–r

So, –1 < (5 – x)/x < 1

12. (4)  Go through the options.



  1.177

(p + q)th term of GP = ar(p+q–1) = x .....(i) (p – q)th term of GP = ar(p–q–1) = y .....(ii)

__ ​ xy ​  Multiply (i) by (ii), we get xy = a².r²(p–1) ⇒ arP–1 = √ __ So, pth term = ​√xy ​ 



14. Sum = (5a + 8a + 11a + .......) + (7b + 5b + 3b + .....) = (25/2) [2 × (5a)] + (25–1) × 3a] + (25/2) [2 × 7b + (25 – 1) (–2b)] ⇒ Sum = 1025a – 425b 15. So we have the following system of equations

Or, –10 < –x < 0 ⇒ 0 < x < 10 20. Go through the options. 21. Let the numbers are a – d, a, a + d. Now (a – d)2, a2, (a+d)2 are in GP ⇒ a4 =(a – d)2 × (a + d)2 __ d4 – 2a2d2 = 0 ⇒ d = 0, ± √ ​ 2 ​ a 22. Given is abc = 4 We know that minimum value of a + b + c will be obtained when a=b=c ⇒ b3 = 4 ⇒ b = 22/3 24. Sum of the 10th, 20th, 30th terms of an AP is equal to the 58th term, hence 3a + 57 d = a + 57 d. So, a = 0 and d can be anything not equal to zero.

a1 + a1r + a1r 2 = 52

   Now, we have to find out the ratio 3a + 57 d and 3a + 27 d, or, we have to find out the ratio 57 d : 27 d = 19 : 9.

a1r 2 =

9 (a + a1r) 4 1 The two solutions for (a1, r) are (4,3) and (64, –3/4)

25. Take any small sample of 4 terms of any GP viz., 1, 2, 4 and 8. Its common ratio = 2 = (8 + 2)/(1+4)

So the sum of the first term of each series is 68.

  And this will be true for any number of terms as long as we are taking total number of terms as even(in this question, it is given as 1000). However, if the total number of terms is given as odd, we cannot find the common ratio in this way, because number of odd terms ≠ number of even terms.

16. We know that AM = is AM = GM ⇒

x+y

x+y 2

2

__ and GM = ​√xy ​ Given

__ = ​√xy ​ +2 Squaring both the sides,

c h a p t e r

  11

Function, Graphs and Maxima Minima You should have a thorough understanding of the following:   What is Function?   What is maxima and minima and how are they calculated?   Some standard graphs and their shifting   Ways of representing a function and questions associated   Method of solving questions

  FUNCTION Function is a rule which associates two or more than two variables. Function can be understood with the help of some very basic examples: i.  Area of circle (A) = πr2, where r is the radius. So, Area of circle is dependent upon value of radius of the circle. We can write this mathematically as, A = f (r) ii. If the distance (d) is constant, then time taken (t) to cover that distance (d) will be dependent on the value of speed (v). This can be written mathematically as,

Some special functions 1.  Modulus function y = |x| It is defined as y = x ; if x >0 y = –x; if x , then |2x + 3| 2 = 2x + 3

3 2 1 -4 -3 -2 -1 0 1 2 3 4 -1 -2 -3

So. 2x + 3 = 9, or, 2x = 6. So, x = 3 Case ii. When (2x + 3) < 0, or, x < –(2x + 3)

x

3 , then |2x + 3| = 2

So. –(2x + 3) = 9. or, –2x = 12

Example  3 Example 

So, x = –6

What is the value of x in the following expression [x]2 ≤ 16?

Example  2 Example 

6

What is the value of ‘x’ if x2 + 5|x| + 6 = 0? Solution Solution

Taking x > 0, x2 + 5|x| + 6 = x2 + 5x + 6 = (x + 2) (x + 3) =0 Or, x = –2 and x = –3 But as we have assumed that x>0, so x = –2 and –3 are not admissible. Taking x < 0, x2 + 5|x| + 6 = x2 – 5x + 6 = (x–2) (x–3) =0 Or, x = 2 and x = 3 But as we have assumed that x f(x) for all the values of x. In this case, ‘a’ is called the point of maximum and f(a) is known as the maximum value or the greatest value or the absolute maximum value of f(x).

For example, in case of y = f(x) = |x|, we will have the maximum value of y as + α. Minimum: Let f(x) be a function with domain D ⊂ R. Then f(x) is said to attain the minimum value at a point ‘a’ if f(x) > f(a). In such a case, the point ‘a’ is called the point of minimum and f(a) is known as the minimum value or the least value or the absolute minimum value of f(x). Let us first see the maximum and minimum values of some very basic functions:

y = f(x)=x

y = f(x)=x2

1 y = f(x)= x

Maximum

+∝

+∝

+∝

+∝

+∝

Minimum

–∝

0

–∝

–∝

0

Example  9 Example 

12

What is the maximum and minimum value of y = f(x) = |x + 3|? Solution Solution 

12

We have y = f(x) = |x + 3| | x + 3| > 0 ⇒

f(x) > 0 for all x ε R

So the minimum value of f(x) is 0, which is attained at x = -3. To find out the maximum value, it can be seen that y = f(x) = |x + 3| can be made as big as we wish to make. So, maximum value of y is +∝.

4.  Finding maximum or minimum value of product/ sum of two or more than two variables when sum/product of these variables is given i. If sum of two or more than two variables is given, then there product will be maximum when value of all the variables are equal.

  1.183

y = f(x)= logex

y = f(x)= |x-2|

Example  10 Example 

13

Find the x + y = 8.

maximum

1.  8

2.  16

Solution Solution 

13

value

of

xy

subject

3.  20

to

4.  24.

Maximum value of xy will occur when x = y = 4 So, maximum value of xy = 4 × 4 = 16

5.  Using Arithmetic Mean, Geometric Mean and Harmonic mean to find maxima and minima i.  AM ≥ GM ≥ HM   [For any number of terms] ii.  (GM)2 = AM × HM  [For only two terms] Example  11 Example 

14

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then which of the following is true regarding the values of N = (a + b) (c + d)? 1.  0 < N < 1 2.  1 < N < 2 3.  2 < N < 3 4.  0 < N < 1 Solution Solution 

14

Using A. M. > G.M. 1 1 [(a + b)+ (c +d) ] ≥ [(a + b)+ (c +d)]1/2 = 2 ≥ (N)1/2 2 Also, (a+b) (c+d) ≥ 0 So, 0 < N < 1

1.184 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  1 1.  9 4.  12

1. f(x) = |x|3 is

1.  Odd function 2.  Even function 3.  Neither odd nor even function 4.  Both odd and even function 5.  cannot be determined

9. If f (t) = 1.  t3 4.  t2

2. Sum of two odd functions is always

2.  4.5 5.  10

3.  0

t3 + 2 f (t) + f (–t) then is equal to t –1 f (t) – f (–t) 1

2.  5.  2tt

3.  t

10. If f(x)=2x2+6x-1 and g(x)=|x+5| then the value of f[g{f(g(-6))}] is:

1.  Odd function 2.  Even function 3.  Neither odd nor even function 4.  Both odd and even function 5.  cannot be determined

1.  225 4.  359

3. Sum of an odd function and an even function is always 1.  Odd function

2.  249 5.  125

3.  341

11. If f(x) = x3+1 and the value of the expression f(2x) – 2f(x) = 383, the value of x is: 1.  1 4.  6

2.  0 5.-1

3.  4

2.  Even function Direction for questions 12 to 15:  Read the passage below and solve the questions based on it.

3. Neither odd nor even function 4.  Both odd and even function 5.  cannot be determined Direction for questions 4 and 5:  Read the instruction given below and solve the questions based on it. A function g(x) is defined as g(x) = log (h(x)) where h(x) is any function of x. Then

The pages of a book are numbered 0,1,2,……P, P >0. There are four categories of instructions that direct a person in positioning the pages in the book. The instruction types with their meanings are given below: i.  OPEN – Position the book at page number 1. ii.  CLOSE – Position the book at page number 0. iii. FORWARD, n – From the current page, move forward by n pages. If, in this process, page number P is reached, stop at P.

4. For what value of h(x), h(x) = h(g(x))? 1.  10 4.  x

2.  log x 5.  1

3  10x

5. What would be the value of g(g(x)) for h(x) = 10 ? x

1.  log x 4.  1

2.  10 5.  None of these

3.  10x

iv. BACKWARD, n – From the current page, move backward by n pages. If, in this process, page number 0 is reached, stop at page no. 0.

6. If (p, q) is a solution for the equations given below, what is the maximum value of p2 + q2?

In each of the following questions, you will find a sequence of instructions. Let p1 be the page number before the instructions are given and p2 be page no. after executing all the instructions given.

2p2 + 5pq + 3q2 = 2 6p2 + 8pq + 4q2 = 3

12. FORWARD, 30; BACKWARD, 12. Which of the following statements is true? 1.  p1 = p2, if P = 12 and p1 = 0 2.  P = 25, provided p1>0 3.  p1>35, provided P = 100 4.  p1 = 40, provided P =30

7. Find the area of the region enclosed by the graphs of and x = 4 above the x-axis.



1.  9 4.  4.5

13. BACKWARD, 7; FORWARD, 7. Which of the following statements is true?

1.  5/11 4.  5/8

2.  5/2 5.  None of these

2.  6 5.  2

3.  5/4

3.  4.5

8. Find the area enclosed by the graph y = |X + 3| with the coordinate axes in square units.

1.  p1 = p2, if p1 ≥ 7 2.  p1 = p2, if p1 >0

  1.185

Function, Graphs and Maxima Minima  3.  p2 =7, provided P>0 4.  p1>p2, provided P > 0 14. FORWARD, 15; FORWARD, 15. Which of the following statements is true? 1.  p2 – p1 = 30, only if p1= 0 2.  p2 – p1 = 30, only if p1= 1 and P>30. 3.  p2 – p1 = 15, only if p1= 0 and P=31. 4.  p2>p1, if P >0. 15. FORWARD, 5; BACKWARD,4. Which of the following statements is true?

Direction for questions 21 to 23:  Given below are three graphs made up of straight line segments shown as thick lines. In each choose the answer as

1.  If f(x) = 3 f(-x) 2.  If f (x) = -f(-x) 3.  If f(x) = f(-x) 4.  If 3f (x) = 6 f(-x), for x > 0 5.  None of these

21.

1.  p2 = p1 + 4 provided 1 2, then what is the value of f fr(–r) + fr+1(–r)? 1.  –1 4.  ½

2.  0 5.  None of these

1 3.  18 (–r) +

r–1

3.  1

  Quantitative Aptitude and Data Interpretation

ANSWER KEYS

1.186 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

1

3.

3

4.

3

5.

5

6.

2

7.

3

8.

2

9.

3

10.

4

11.

3

12.

1

13.

1

14.

2

15.

3

16.

1

17.

4

18.

3

19.

5

20.

3

21.

3

22.

4

23.

2

24.

3

25.

1

HINTS AND EXPLANATIONS 1. (2)  f(x) = |x| is even function. So, f(x) = |x|3 will also be even. Alternatively we can verify for f(x) = |x|3 putting (–x) at the place of x to see that f(x) = f(-x). 2. (1)  This is a standard result. Can be verified by putting (–x) at the place of x to see that f(x) = f(-x). 3. (3)  This is a standard result. Can be verified by putting (–x) at the place of x to see that f(x) ≠

f(-x), and f(x) ≠ - f(-x). Hence neither odd nor even function.

4. (3)  Let h(x) = 10x.

Then g(x) = log (h(x)) = x thus h(g(x)) = 10x.



f(x) = xn + 1 = 1001, so xn = 1000



Hence n = 3.



f(20) = 203 + 1 = 8001

19. (5)  In this case, f(x) = g(x) is possible only if the domain of the respective functions are same. Now, either solve it or go through the options. 20. (3)  g(x) = f(x+1) = |x-2+1| + |x-3+1| + |x-4+1| = |x-1| + |x-2| + |x-3|

Obviously, this is neither odd nor even.



Alternatively, we know the graph of this function will neither be symmetrical to axis or origin.

5. (5)  For h(x) = 10x we get g(g(x)) = x. 6. (2)  Multiply the first equation by 3 and the second by 2 and then subtract 2nd from the 1st one to get:

-6p2 – pq + q2 = 0 ⇒ (-3p + q) (2p+q) = 0



So, the solutions are: q = 3p and q = -2p



Put these in the original equation to get the values of the equations.

10. (4)  g(x) = |x+5| ⇒ g (–6) = |–6 + 5| = 1

f(g(–6)) = 2 (1)2 + 6 (1) – 1 = 7



g(x) = | 7 + 5 | = 12



f[g{f(g(-6))}] = 2 (12)2 + 6 (12) – 1 = 359

11. (3)  If f(x) = x3+1 and the value of the expression f(2x) – 2f(x) = 383, the value of x is:

f (2x ) = (2x)3 + 1 = 8x3 +1



2 f (x) = 2 x3 +2



f(2x) – 2f(x) = 8x3 +1 – (2 x3 +2) = 6 x3 – 1 = 383



⇒ x3 = 64

21. (3)

From the graph , x = 2



⇒ f(2) =1 and x = –2 ⇒ f (–2) =1



Hence f(x) =f (–x)

22. (4)

From the graph, x = 1 ⇒ f(–2) and x = –1



⇒ f(–1) = 1



Thus, f(1) = 2 (–1). Hence, 3f(x) = 6(–x)

23. (2)

From the graph, x = 4



⇒ f(4) = –2 and x = – 4 ⇒ f(–4) = 2



Thus, f(4) = –f (–4). Hence, f(x) = –f(–x)

24. (3)  f (2) =

⇒x=4

18. (3)  Let f(x) = xn + 1, so f(1/x) = (1/xn) + 1 1 1 = f(x) + f satisfies the value of f(x) Checking it for f(x) f x x assumed.



Answer is

1 3 4 7 , f 2 (2) , f 3 (2) , f 4 (2) = f 5 (2) = 3 4 7 1

1 8

25. (1)  f(–1) = 0, f(0) = 1, f(–2) = –1

1 8

Function, Graphs and Maxima Minima 

  1.187

  EXERCISE  2 1. The set of all positive integers is the union of two disjoint subsets: {f(1), f(2),…., f(n),….} and {g(1), g(2),…., g(n)…), where f(1) < f(2) x 5.  None of these

For three distinct real numbers x, y and z, let

2.  4 5.  None of these

1.  y=a+bx 4.  y=a+bx+ ebx

7. Under which of the following conditions is f(x,y) necessarily greater than g(x,y)?

Direction for questions 8 to 10:  Answer the questions based on the following information.

F(x + 1, y + 1) = f (x, f(x+1, y) 1.  2 4.  1

6. Which of the following expressions yields a positive value for every pair of non-zero real numbers (x,y)? 1.  f(x,y) -g (x,y) 2.  f(x,y)-(g(x,y))2 3.  g(x,y)-(f(x,y))2 4.  f(x,y)+g(x,y) 5.  None of these

2.  1 5.  8

3.  16

Direction for questions 6 and 7:  Answer the questions based on the following information. For real numbers x and y, let f(x,y) = Positive square root of (x+y), = (x+y)2 if (x+y)0.5 is real otherwise. g(x,y) = (x+y)2 = - (x+y) If (x+y)0.5 is real otherwise.



f(x,y,z) = Min(Max(x,y), Max(y,z), Max(z,x)) g(x,y,z) = Max(Min(x,y), Min(y,z), Min(z,x)) h(x,y,z) = Max(Max(x,y), Max(y,z), Max(z,x)) j(x,y,z) = Min(Min(x,y), Min(y,z), Min(z,x)) m(x,y,z) = Max(x,y,z) n(x,y,z) = Min(x,y,z)

8. Which of the following is necessarily greater than 1?

1.  [h(x,y,z) - f(x,y,z)]/ j(x,y,z) 2.  j(x,y,z)/h (x,y,z) 3.  f(x,y,z) / g(x,y,z) 4.  [f(x,y,z)+h(x,y,z)-g(x,y,z)]/j(x,y,z) 5.  None of these

9. Which of the following expressions is necessarily equal to 1? 1.  [f(x,y,z)-m(x,y,z)]/ [g(x,y,z)-h(x,y,z)] 2.  [m(x,y,z)-f(x,y,z)/[g(x,y,z)-n(x,y,z)] 3.  [j(x,y,z)-g(x,y,z)]/j(x,y,z) 4.  [f(x,y,z)-h(x,y,z)]/ f(x,y,z) 5.  None of these 10. Which of the following expressions is indeterminate? 1.  [f(x,y,z) – h(x,y,z)]/[g(x,y,z)-j(x,y,z)] 2. [f(x,y,z)+h(x,y,z)+g(x,y,z)+j(x,y,z)]/[j(x,y,z)+h(x,y,z))m(x,y,z) – n(x,y,z)] 3.  [g(x,y,z) – j(x,y,z)]/ [f(x,y,z)-h(x,y,z)] 4.  [h(x,y,z) – f(x,y,z)]/ [n(x,y,z)-g(x,y,z)] 5.  None of these 11. If r – 6 = 1 and 2q – 12 = 8 what is the minimum posq sible value for r ?

1.188 

  Quantitative Aptitude and Data Interpretation

2 1.  5

2. 

2 17

4.  2

5.  None of these

3. 

10 17

15. The robot reaches point (6,6) when a sequence of three instructions is executed, the first of which is a GOTO (x,y) instruction, the second is WALK X (2) and the third is WALK Y (4). What are the value of x and y?

Direction for questions 12 to 14:  Answer the questions based on the following information.

1.  2,4 4.  2,2

Let x and y be real numbers and

16. The robot is initially at (x,y) , x>0 and y - F (f(x,y)). G (f(x,y)) 3.  F (f(x,y)). G (f(x,y)) ≠ F (f(x,y)). G (f(x,y)) 4.  F (f(x,y)). G (f(x,y)) = F (f(x,y)). G (f(x,y)) 5.  None of these 2.  2 5.  4

3.  4,2

2.  1 5.  3

3.  x+y

17. Let x and y be two positive numbers such that x + y=1. Then the minimum value of is x +

13. What is value of f (G(1,0)), f(F(f(1,2))), G (f(1,2))? 1.  3 4.  0

2.  0,0 5.  2, 0

3.  1

14. Which of the following expressions yields x2 as its result? 1.  F (f(x,-x)). G (f(x,-x)) 2.  F (f(x,x)). G (f(x,x)).4 3.  -F (f(x,x)). G (f(x,x)) ÷ log2 16 4.  f (x,x). f(x,x) 5.  None of these Direction for questions 15 and 16:  Answer the questions based on the following information. A robot moves on a graph sheet with X and Y-axis. The robot is moved by feeding it with a sequence of instructions. The different instructions that can be used in moving it, and their meanings are: Instruction

Meaning

GOTO (x,y)

Move to point with coordinates (x,y) no matter where you are currently

1.  12 4.  13.3

1

2

x

2.  20 5.  16

1 + y + y

2

3.  12.5

18. Consider a triangle drawn on the X-Y plane with its three vertices of (41,0), (0,41) and (0,0), each vertex being represented by its (X,Y) coordinates. What is the number of points with integer coordinates inside the triangle (excluding all the points on the boundary)? 1.  780 4.  741

2.  800 5.  None of these

3.  820

19. A telecom service provider engages male and females operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs 250 and Rs 300 per day respectively. In addition, a male operator gets Rs 15 per call he answers and female operator gets Rs 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job? 1.  15 4.  10

2.  14 5.  8

3.  12

WALK X (p) Move parallel to the X-axis through a distance of p, in the positive directions if p is positive , and in the negative direction if p is negative

20. If a, b, c are the sides of a triangle, then what is the maximum value of the expression

WALK Y(p)

1.  1 4.  5/2

Move parallel to the Y-axis through a distance of p, in the positive direction if p is positive, and in the negative direction if p is negative.



a b +c

+

b c+a

+

c a +b

?

2.  3/2 5.  None of these

3.  2

21. The minimum value of 3x + 4y, subject to the conditions x2y3 = 6 and x and y are positive, is

Function, Graphs and Maxima Minima  1.  10 4.  12

2.  14 5.  10

3.  13

24. The minimum value of (x-a)(x-b) is

2.  1 5.  2

(a – b)2 4

(a – b)2 5.  None of these 4 25. A right circular cylindrical container closed on both sides is to contain a fixed volume of motor oil. Suppose its base has diameter d and its height is h. The overall surface area of the container is minimum when 4 1.  h = πd 2.  h = 2d; 3.  h = d 3 4.  H = d/2 5.  None of these

3.  0

23. For how many values of x, is the equality: │││x–2│–3 │–1│=0, true? 2.  2 5.  None of these

ANSWER KEYS

3. 

4. 

= x8 + x6 – x4 – 2x3 – x2 – 2x + 9 is

1.  1 4.  0

2.  0

1.  ab

22. The minimum value of f (x) 1. 5 4.  9

  1.189

3.  3

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

2

4.

4

5.

3

6.

4

7.

1

8.

4

9.

1

10.

2

11.

2

12.

5

13.

3

14.

3

15.

3

16.

1

17.

3

18.

1

19.

4

20.

3

21.

1

22.

1

23.

5

24.

4

25.

3

HINTS AND EXPLANATIONS 1. (2)  g(1) = f[f(1)] + 1 = 2. Since f(1) has to be 1, else all the integers will not be covered. F(n) is the set of odd numbers and g(n) is the set of even numbers.



Or, (r–6) = –11, r= -5



|2q –12| = 8 ⇒ 2q -12 = 8, q= 10

2. (2)  f(1,2)=f(1,.1);



Or 2q –12 = –8, q= 2.



q 10 = –2 Hence, minimum value of r = –5



Now f(1,1) = f[0,f(1,0)] = f[0,f)] = f(0,2) = 3. Hence, f(1,2) = f(0,3) =4.

4. (2)  f(1) = 1, f(2) = 7, f(3) = 19, f(4) = 43. The difference between successive terms is in series 6, 12, 24, 48,….., i.e., they are in GP. Hence,

f (100) = (1) + f

r n– 1 r–1

2 –1 2– 1

12. (4)  Take some values of x and y and put in the given expression find which satisfies the answer choices. 13. (3)  f (G ( f (1,0 ))), f (G ( f (1,2))) = f (G ( f ( )1,0)), f (3, 3)

n

= 1 +6

= 6 × 29 – 5

= f (G ( f (1,0))) = f (1,0) =1.

6. (4)  Use choices. (a), (b) and (c) could be both negative as well as positive, depending on the values of x and y. 7. (1)  For (a), x, y < -1. Then value of f(x,y) = (x+y)2 and value of g(x,y) = - (x+y). Substituting any value of x,y 0, y > 0 1

, value of expression =

25

+

25

=

25



Taking x = y =



It can be easily verified as it is the least value among options.

2

4

4



If f = 8, then m = 15



If f = 9,10,11 then m will not be an integer while f = 12 then m will be 10.



By putting f = 8 and m = 15, A = 18800. When f = 12 and m = 10 then A = 18100.



Hence the number of males will be 10.

2

18. (3)  The equation forming from the data is x + y < 41

Values which will satisfy this equation are



(1,39), (1,38)……… (1,1)



(2,38), (2,37),…….(2,1)



.



x - 2-3 = 1, or, x - 2 = 4,



(39,1)



If x - 2 >0, then x = 6, and if x – 2 0, then x - 2= (x-2)



Or,x - 2-3 = -1, or, (x – 2) = 2, or, x = 4.





=

39 × 40 2

= 780

19. (4)  Let us from both the equations first:

23. (5)  x – 2–3 –1= 0, or, x – 2–3 = 1, or,



40m+50f=1000



If x – 2 < 0, x - 2= - (x-2)



250 m + 300 f + 40 × 15m + 50 × 10 × f = A



So, x - 2-3 = -1, or, -(x-2) = 2, or, 2 – x = 2, so x = 0.



850 m + 8000 f = A



So, four values of x are possible.



Where m and f are the number of males and females and A is the amount paid by the service provider.



Then the possible values for f are 8,9,10,11,12

24. (4)  Make a quadratic equation in the format of z2 + y. Minimum value of z2 = 0, so, minimum value = y.

c h a p t e r

  12

Permutations, Combinations and Probability  LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Difference between Permutation and Combination   Different cases of Permutation and combinations   Probability   Application of P and C to derive more formula   Kind of questions which are asked in the CAT   Method of solving the questions

  MEANING OF PERMUTATION AND COMBINATION Permutation is the number of ways in which a set or number of things can be ordered or arranged and Combination means the number of ways in which a group of things can be chosen from a larger group without giving regard to their arrangement. Let us understand this through an example: Suppose there are four different batsmen A, B, C and D. And we have to select a group of three batsmen out of these four batsmen. Now, we can select any combination of three batsmen so that no set of batsmen has all the three batsmen same. These set of batsmen will be—ABC, BCD, ABD, ACD. This is a case of combination as for every set

of selection of three batsmen, order of selection does not play any role (i.e., we can select anybody first or second or third and it creates no difference in the final selection as well as the total number of selections). Now, if we try to define their batting order also, i.e., who bats first and 2nd and so on, then corresponding to every selection of a set of three batsmen, we will have six different arrangements of their batting. It can be seen below that corresponding to selection of ABC as a team, following is the list of different batting orders: ABC, ACB, BAC, BCA, CAB, CBA. Now this is a case of permutation since order of occurrence has become important. Since there are four different ways of selecting a group of three batsmen and every selection can be arranged in 6

1.192 

  Quantitative Aptitude and Data Interpretation

different ways, so total no. of ways of arranging 3 batsmen (or, distinct things) out of 4 batsmen (or, distinct things) = 4 × 6 = 24 ways.

Standard Meanings and Definitions n! =Product of all the natural numbers from n to 1 = n (n–1) (n–2) (n–3)………× 3 × 2 × 1. 0! = 1 Note – Factorials are defined only for whole numbers, and not for negative numbers or fractions(≠ whole numbers).

ii. One girl can be chosen from 10 girls in 10 ways. Now corresponding to every selected girl, any one of 15 boys can be selected in 15 ways. It can be seen in the following presentation: Girl selected (Assume name of the girls are G1,G2,G3, ….G9, G10 ) – G1 Boy selected (Assume name of the boys are B1, B2, B3, ….B14, B15 )– B1, Or B2, Or B3 ,., Or B15. So, corresponding to G1, total number of selections of a boy = 15 Corresponding to G2, total number of selections of a boy = 15

Fundamental Principle of Counting: Two basic theorems

Corresponding to G3, total number of selection of a boy = 15

1. Multiplication theorem–If there are two jobs in such a way that one of them can be done in m ways and when it is completed in any of the ways out of m ways, second job can be completed in n ways, then the whole job can be done in m × n.

Corresponding to G15, total number of selection of a boy = 15

2. Addition theorem–If there are two jobs in such a way that one of them can be done in m ways and second one can be done in n ways independently, then either of the jobs can be done in (m+n) ways.

… …

…

…

…

So, total number of ways of selecting a team of one boy and a girl = Total number of ways of selecting a girl × Total number of ways of selecting a boy = 10 × 15 = 150 In this case, just by selecting a girl or a boy, work has not been completed. So, it’s a multiplication case.

  PERMUTATIONS Example  1

Example  1 There are 10 girls and 15 boys in a class. In how many ways i. a class representative can be selected? ii. a team of two students can be chosen with one girl and one boy?

Solution Solution

i. A class representative can be a girl or a boy. Now, one girl can be selected from 10 girls in 10 ways (any of the girls can be selected) and one boy can be selected from 15 boys in 15 ways (any of the boys can be selected). So that ways of selecting a class representative includes either selecting a boy or a girl. So, the total number of ways of selecting a class representative = 10 + 15 = 25 In this case, the moment a girl gets selected, the job is complete. It’s a different story that there are some more ways of doing this by selecting a boy also. So, it is a case of addition.

As we have seen, each of the arrangements that can be made by taking some or all elements out of a number of things is called a Permutation. Permutation implies “arrangement” or “that order of the things” is important. The permutations of three things a, b and c taken two at a time are ab, ba, ac, ca, cb and bc. Since the order in which the things are taken is important, ab and ba are counted as two different arrangements. The number of permutations of n things taking r at a time is denoted by nPr.

  COMBINATIONS As we have seen, each of the groups or selections which can be made by taking some or all out of a number of things is called a Combination. In combinations, the order in which the things are taken is not important. The combination of three things a, b and c taken two at a time are ab, bc and ca. Here, ab and ba are same because the order in which a and b are taken is not important. What is required is only a combination including

Permutations, Combinations and Probability  a and b. The words “combination” and “selection” can be used without any differentiation. The number of combinations of n things taking r at a time is denoted by nCr. Out of n things kept in a bag, if we select r things and remove them from the bag, we are left with (n – r) things inside the bag, that is, whenever r things are selected out of n things, we automatically have another selection of the (n – r) things. Hence, the number of ways of making combinations taking r out of n things is the same as selecting (n – r) things out of n given things, i.e.,

n

Cr = nCn–r

Some Standard Examples of   Permutation and Combination

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Example  3

Example  3 In the above question, how many times a particular child will go? 1.  72

2.  45

3.  90

4.  36

Solution

Solution

Consider the case for any particular child C1: Since C1 has already been selected, so out of the rest 9 children Munchun will be required to select 2 more children. This can be done on 9C2 ways. So, option (4) is the answer.

Permutation  Words Formation, Number Formation, Circular Permutation etc. Combination  Selection of a team, forming geometrical figures, distribution of things (except some particular cases).

Example  4

    Still, sometimes the questions may not explicitly state if what you have to find out is a case of permutation or a case of combination. In that case, the nature of what is to be found out will decide whether it is the number of permutations or the number of combinations.

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

    Before we move ahead, lets make it clear once again that whenever we are using nCr and nPr, our assumption is that all the things are distinct i.e., no two of them are same.

Example  2 Example 

1.  200

2.  216

3.  235

4.  256

Solution Solution

2

Munchun has 10 children. She takes 3 of them to the zoo at a time as often as she can, but she does not take the same three children to the zero more than once. How many times will Munchun be required to go to zoo? 1.  120

Example  4

2.  45

3.  90

4.  180

Solution

Solution

Number of times (read ways) 3 children(read distinct things) can be selected from 10 children(read distinct things) = 10C3.

Let there be m boys and n girls n(n – 1) ​  2 ​    nC2 = 45 = _______ ⇒ n(n – 1) = 90 ⇒ n = 10 m(m – 1) ​  2 ​   = 190 mC2 = 190 ⇒ ________ ⇒ m(m – 1) = 380 ⇒ m = 10 Number of games between one boy and one girl

So, she will be required to go to zoo 10C3 times.

= 10C1 × 20C1 = 10 × 20 = 200

So, option (1) is the answer.

Hence option (1).

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1.194 

Some Important Derivations

4. Number of permutations (arrangements) of n different articles taking r at a time when articles can be repeated any number of times = n × n × … r times = nr.

1. Number of arrangements of n things of which p are of one type, q are of a second type and the rest are distinct. ​  n!   ​  ______ p!.q!.r!

i. Number of circular permutations (arrangements) of n different articles = n – 1 .

2. Number of permutations of n distinct things where each one of them can be used for any number of times (i.e., repetition allowed).

ii. Number of circular arrangements of n different articles when clockwise and anti-clockwise arrangements are not different i.e. when observation can be

  In general, the number of perambulations of n things, taken r at a time when each thing may be repeated once, twice,.... up to r times in any arrangement is nr.

made from both sides = n – 1 . 2 6. Number or combinations of n different articles taken r at a time is denoted by nCr



3. Total number of combinations

Out of n things, the number of ways of selecting one or more things: where we can select 1 or 2 or 3...... and so on n things at time; hence the number of ways is nC1 + nC2 + n C3 + ....... nCn. = 2n–1, where n is the number of things.

4. Distributing given things (m + n) into two groups where one group is having m things and other one n things:

(m + n)! Cm. = ​ _______ ​     n!.m!

5. Circular permutations:

n . r n–r 7. Number of selections of r articles (r ≤ n) out of n identical articles is 1. and nCr =

8. Total number of selections of zero or more articles from n distinct articles = nC0 + nC1 + nC2 + …nCn = 2n. 9. Total number of selections of zero or more articles from n identical articles = 1+1+1+… to (n+1) terms = n + 1.

m+n

If we take m = n, then the above expression will denote “Distributing 2m things equally between two distinct groups = 2mCm.

10. Number of ways of distributing n identical articles among r persons when each person may get any number of articles = n+r –1Cr – 1.

However, when the groups are identical, then we will be required to divide the above result by 2!.

11. Number of ways of dividing m + n different articles between two persons containing m and n articles respectively m+n = m+nCn × mCm = mn 12. Number of ways of dividing 2m different articles

(2m)!  ​(Refer to word forHence, it becomes in that case ______ ​ 2!m!.m!   mation examples)

2m mm2 13. Number of ways of dividing 3m different articles among

each containing m articles =

Important Formulae/Derivations 1. If nCx = nCy then either x = y or x + y = n. 3. (a)  Number of permutation of n different articles taken r at a time is denoted by nPr and nPr =

n n–r

(b) Number of permutations of n different articles taking all at a time = n. (c) Number of permutations of n articles, out of which p are alike and are of one type, q are alike and are of second type and rest are all different =

=

n p q

.

3m . m m m 14. Number of ways of selecting n distinct articles taken r at a time when p particular articles are always included = n–pCr–p

three persons each getting m articles =

2. n = 1.2.3 …n;

15. nCr–1 + nCr = n+1Cr 16. npr = r.n–1pr–1 + n–1Pr 17. 0! = 1

Some Standard Formats of Questions Word Formation–As we know that order of occurrence of letters decide the formation of words, so word formation is one standard example of Permutation.

Permutations, Combinations and Probability  Let us understand with the help of some examples: Example  5

Example  5

Example  6 Example 

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6

How many 4–lettered distinct words can be formed from the letters of the word ‘EXAMINATION’?

How many words can be formed with the word ‘LUCKNOW’ when

Letters are – A – Twice

i.  No restriction is there.

N – Twice

ii.  L is the 1st letter of the word.

E, X, M, T, O – Once

iii.  All the vowels are together

Words will be of three types:

I – Twice

iv.  L always occurs before U v. L always occurs before U and U always occurs before W. Solution

Solution

i. Total number of distinct letters = 7 (L, U, C, K, N, O, W)    So, total number of words that can be formed = 7!  ow we can arrange only 6 letters(As place of ii.  N L is restricted),    So, total number of words that can be formed = 6! iii. U and O should be together, so we will assume these two letters to be tied up with each other.   Now we have 6 distinct things to be arranged – (L, UO, C, K, N, W)    So, number of arrangements = 6!   But place of U and O can be interchanged between themselves.   So, total number of words that can be formed = 6! × 2! v. Occurrence of all the letters in the word are having equal likelihood, so in half of the cases L will occur before U and in the remaining half, U will occur before O.

Solution

Solution

i. All distinct = 8P4 (Distinct letters are – A, I, N, E, X, M, T and O) ii. Two same, two distinct Selection of one pair out of three pairs (A, I, N) can be chose in 3C1 ways. Now rest two distinct letters can be chosen in 7C1 ways. Total number of words = 3C1 × 7C2 × __ ​ 4! ​  2! iii. Two same and are of one kind, two same and are of other kind = Out of three pairs of letters (A, I, N), we can select two pairs in 3C2 ways. Total number of words = 3C2 × _____ ​  4!   ​  2! ×2! Answer = summation of all the above three cases. Number Formation–Number Formation is another standard example of Permutation. Here, we will introduce Box Diagram method of solving the questions. If a three digit number is to be constructed, then we will use Hundred’s Place

Ten’s place

Unit’s place

If a four digit number is to be constructed, then we will use

  So, total number of words that can be formed = 7!/2

Thousand’s Place Hundred’s Place Ten’s place Unit’s place

vi. There are six possible arrangements (3!) corresponding to L, U and W. However only one

And so on.

  out of these six will be in the prescribed order: L always occurs before U and U always occurs before W.

While solving questions related to Number Formation, we should have two things very clearly in our mind:

  So, corresponding to 7! arrangements, no. of ways in which the condition will be satisfied = 7!/3! ways.

i. While using box diagram, we should start with the digit which is having any restriction, i.e., some condition is imposed on that digit.

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ii. Thousand’s place cannot be filled with 8 or 9.

Example  7

Example  7 How many different 3-digit numbers can be formed using the digits 1,2,3,4 and 5 i. when repetition is not allowed,

For unit’s digit – When it is filled with 9, thousand’s place can be filled in 7 ways namely any digit from 1 to 7, and remaining two places can be filled in 8 × 7 = 56 ways.

ii. when repetition is allowed?

So, total number of numbers formed in this way = 56 × 7 = 392

Solution Solution

  Now, if unit’s place is filled with any of the four digits 1, 3, 5 or 7, the thousand’s place can be filled in 6 ways (0 will be excluded), and remaining two places can be filled in 8 × 7 = 56 ways.

Below given Box represents the respective positioning of digits in a three digit number. Hundred’s Place

Ten’s place

Unit’s place

i. Since repetition of the digits is not allowed, we can fill Unit’s place in 5 ways, Ten’s place in 4 ways and Hundred’s place in 2 ways. 3

4

5

Using Multiplication Theorem, Total number of numbers which can be formed = 5 × 4 × 3 = 60 Alternatively, 3 digits can be selected out of 5 digits in 5P3 = 60 ii. Since repetition of the digits is allowed here, we can fill each of the hundred’s, ten’s and Unit’s place in 5 ways.

So, total number of numbers formed in this way = 56 × 6 × 4 = 1344 So, total number of numbers = 392 + 1344 = 1736

Example  9 Example 

9

How many natural numbers less than a million can be formed using the digits 0, 7 and 8? Solution Solution

Numbers formed would be of Single digit, Two digits, Three digits, Four digits, Five digits and six digits. Single digit numbers = 7 and 8 For two digits numbers,

5 5 5 Using Multiplication Theorem, Total number of numbers which can be formed = 5 × 5 × 5 = 125

2

3

= 2 × 3 = 6 numbers For three digits numbers, 2

Example  8 Example 

8

How many odd integers from 1000 to 8000 have none of its digits repeated? Solution Solution

There are two restrictions operating in this questions: i. For a number to be odd, unit digit should be either 1 or 3 or 5 or 7 or 9.

3

3

= 2 × 3 × 3= 18 numbers For four digits numbers, 2

3

3

3

= 2 × 3 × 3×3 = 54 numbers For five digits numbers, 2

3

3

3

3

= 2 × 3 × 3 × 3 × 3 = 162 numbers

Permutations, Combinations and Probability  For six digits numbers, 2

3

3

3

3

Solution Solution

3

= 2 × 3 × 3 × 3 × 3 × 3 = 486 numbers So, total number of numbers = 728

Circular Permutation Let us see the arrangement of three people A, B and C in a circle –

A C

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B

    What we can observe here is that arrangements ABC, BCA and CAB are same. And similarly arrangements ACB, CBA and BAC are the same. So, there are only two permutations in this case of circular permutation. To derive the formula for Circular Permutation, We first fix the position of one thing. Then the remaining (n – 1) things can be arranged in (n – 1)! ways. Hence, the number of ways in which n distinct things can be arranged in a circular arrangement is (n – 1)!

Clockwise and anti-clockwise circular arrangements Number of circular arrangements of n distinct things is (n – 1)! if there is difference between clockwise and anti clockwise arrangements and (n – 1)!/2 if there is no difference between clockwise and anti-clockwise arrangements.

i. Total number of persons = 9. These 9 persons can be arranged around a circular table in 8! ways. ii. Assuming all the Americans to be one group, we have 6 things (5 Indians + 1 group) to be arranged around a circular table which can be arranged in 5! ways. However, these 4 Americans can be arranged in 4! ways among themselves. So, total number of arrangements = 5! × 4! iii. Since there is no restriction on Indians, first of all we arrange the 5 Indians. 5 Indians can be seated around a table in 4! ways. Now the Americans will sit in between two Indians, i.e., 5 places. 4 Americans can be seated on these 5 places in 5P4 ways. iv. Total number of arrangements when there is no restriction = 8! and number of arrangements when all the four Americans sit together = 5! × 4! So, total number of arrangements when all the four Americans do not sit together = 8! – (5! × 4!.) Example  11 Example 

11

How many diagonals will be there in an n–sided regular polygon? Solution Solution

An n-sided regular polygon will have n vertices. And when we join any of these two vertices (nC2) we get a straight line, which will be either a side or a diagonal. So, nC2 = Number of sides + number of diagonals = n + number of diagonals n(n – 3) Hence, number of diagonals = nC2 – n = _______ ​  2 ​    Above written result can be used as a formula also.

Example  10 Example 

10

In how many ways, 5 Indians and 4 Americans can be seated at a round table if

Example  12

i. There is no restriction

There is an n–sided polygon (n>5). Triangles are formed by joining the vertices of the polygon. How many triangles can be constructed which will have one side common with the polygon?

ii. All the four Americans sit together iii. No two Americans sit together iv. All the four Americans do not sit together?

Example  12

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Solution Solution

An n–sided polygon will be having n vertices. Triangles having one side common with the polygon = Number of selection of three vertices out of which two are consecutive (If we select A5 and A6 as the two vertices, then A7 or A4 should not be the third vertex because it will constitute two sides common triangle). = n × ( n – 4 )C1

Let a, b, c, d, e be the number of stations between A and S1, S1 and S2, S2 and S3, S3 and S4 and B respectively. Then, a + b + c + d + e = 8

…(1)

Where a ≥ 0, b ≥ 1, c ≥ 1, d ≥ 1, e ≥ 0 Let x = a, y = b – 1, z = c – 1, t = d – 1, w = e Now x + y + z + t + w = a + b + c + d + e – 3 = 8–3=5 Or x + y + z + t + w = 5, where x, y, z, t, w ≥ 0 …(2) Required number = number of non negative integral solutions n+r–1Cr= 5+5+–1C5 = 9C5 = 126

Example  13

Example  15 Example 

If each permutation of the digits 1,2,3,4,5,6 is listed in increasing order of magnitude, the 289th term will be

There are 4 identical oranges, 5 identical apricots and 6 identical alphanso in a fruit basket. In how many ways can a person make a selection of fruits from among the fruits in the basket?

Example  13

1.  326541

2.  341256

3.  356241

4.  314256

Solution Solution

289 = (2×5!) + (2×4!) + 1 So, the number will be 341256.

15

Solution Solution

Zero or more oranges can be selected out of 4 identical oranges in 4 + 1 = 5 ways. Zero or more apricot can be selected out of 5 identical apricots in 5 +1 = 6 ways. Zero or more can be selected out of 6 identical alphanso in 6 + 1 = 7 ways.

Example  14

Example  14 There are 12 intermediate stations between two places, A and B. In how many ways can a train be made to stop at 4 of these 12 intermediate stations provided no two of which are consecutive?

∴ Total number of selections when all the three types of fruits are selected (the number of any type of fruit may also be zero) = 5 × 6 × 7 = 210. But in one of these selections number of each type of fruit is zero and hence this selection must be excluded. So, Required number = 210 – 1 = 209.

Solution Solution

1st Method: Let S1, S2, …, S8 denote the stations where the train does not stop. The four stations where the train stops should be at any four of the nine places indicated by cross. 9.8.7.6 ∴ Required number = 9C4 = ______ ​   ​   = 126 3 2nd Method: Let S1, S2, S3, S4 be the four intermediate stations where the train stops. a S1 b S2 c S3 d S4 e

1. Maximum No. of point of intersection among ‘N’ straight lines = NC2 2. Maximum No. of points of intersection among ‘N’ ­circles = NP2

  PROBABILITY Probability is the measure of uncertainty. Let us understand this with the help of a simple example of dice: As all of us know, a dice is well-balanced cube with its six faces marked with numbers from 1 to 6, one number on one face.

Permutations, Combinations and Probability  Lets throw a die once. What are the possible outcomes? Clearly, a die can fall with any of its faces uppermost. The number on each of the faces is, therefore a possible outcome and all the outcomes are equally probable. Hence it is as likely to show up a number, say 2 as any other number 1, 3, 4, 5,or 6. Since there are six equally likely outcomes in a single throw of a die and there is only one way of getting a particular outcome (say 2), therefore the chance of the number 2 coming up on the die is 1 by 6. In other words, the same phenomena is known as — Probability of getting 2 in a single throw of die is 1/6. We write this as P(2)= 1/6 Similarly, when an ordinary coin is tossed, it may show up (H) or tail (T). Hence, the probability of getting a head in a single toss of a coin is given by P(H)= ½

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Exhaustive number of cases The total number of possible outcomes of a random experiment in a trial is known as the exhaustive number of cases. For example For example

(i) In throwing of a die the exhaustive number of cases is 6, since any one of the six face marked with 1,2,3,4,5,6 may appear on its upper face.

Mutually exclusive events Events are said to be mutually exclusive if the occurrence of any one of them prevents the occurrence of all others, i.e., if no two or more than two can occur simultaneously in the same trial.

Equally likely events

Terms Associated with Probability

Events are equally likely if there is no reason for an event to occur in preference to any other event

Trial and elementary events When we repeat a random experiment under identical conditions, then the experiment is known as trial and the possible outcomes of the experiment are known as elementary events.

For Forexample example

(i) Tossing of a coin is a trial and getting head or tail is an elementary event. (ii) Throwing of a die is a trial and getting 5 on its upper face is an elementary event.

For Forexample example

While throwing a coin, chances of occurring of Head or Tail are equally likely event.

Favourable number of cases The number of cases favourable to an event in a trial is the number of elementary events such that if any one of them occurs, we say that the desired event happens. In other words, the number of cases favourable to an event in a trial is the total number of elementary events such that the occurrence of any one of them ensures the happening of the desired event.

Compound events Events obtained by combining two or more elementary events are known as the compound events. A compound event is said to occur if one of elementary events associated with it occurs.

For example For example

In throwing of a die, the number of cases favourable to the appearance of a prime number is 3 viz., 2, 3 and 5.

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1.200 

Independent events

Example  17 Example 

Events are said to be independent if the happening (or non-happening) of one event is not affected by the happening (or non-happening) of others.

Six die are thrown simultaneously. Find the probability that all of them show the same face.

For example, if two cards are drawn from a well-shuffled pack of 52 cards one after the other with replacement, then getting an ace in the first draw is independent to getting a jack in the second draw. But, if the first card drawn in the first draw is not replaced, then second draw is dependent on the first draw. Similarly, if we toss two coins one by one(or even simultaneously), then occurrence of head or tail on one of the coins is independent of the outcome of the other coin.

Solution Solution

2

Sample space of throwing six dice = 6 × 6 × 6 × 6 × 6 × 6 = 66 . All die are showing the same face implies that we are getting same number on all the six die. The number of ways for which is 6C1. 6 C1 1 Hence, required probability = ​ ___  ​ = 66 6 5

Probability of an Event P(E) Now, Probability of an event E, written as P(E), is defined as Example  18

number of outcomes fovourable to E P(E) = _________________________________________ ​            ​ Total number of possible outcomes (Sample Space)

REMEMBER THAT

1.  0 ≤ P(E) ≤ 1 2.  P(E) + P’(E) = 1

Example  3 In the above question, find the probability that all of them show different face.

Solution Solution

Total number of ways in which all die show different numbers on their top–faces is same as the number of arrangement of 6 numbers 1, 2, 3, 4, 5, 6 by taking all at a time. So, number of favourable cases = 6! 6!  Hence required probability = ​ __  ​  66

Example  16

Example  1 In a single throw of two die, what is the probability that the sum on the top face of both the die will be at least 10?

Solution Solution

When two die are thrown, sum of the numbers appearing on the faces can be anything from 2 to 12. To find out the number of favourable cases we will be required to find out the cases in which sum is at least 10. Following are the cases–(5,5), (6,4), (4,6), (6,5), (5,6), (6,6) So, total number of favourable cases = 6 Total number of possible outcomes = 6 × 6 = 36 Hence probability = 6/ 36 = 1/6

Example  19 Example 

4

Five persons entered the lift on the ground floor of an 8–floor apartment. Assuming that each one of them independently and with equal probability can leave the lift at any floor beginning with the first. What is the probability that all five persons are leaving the lift at different floors? Solution Solution

Apart on the ground floor, there are 7 floors. A person can leave the lift at any of the seven floors. Hence, total number of ways in which each of the five persons can leave the lift at any of the 7 floors = 75.

Permutations, Combinations and Probability 

  1.201

So, sample space = 75

Addition Theorem

Five persons can leave the lift at five different f loor 7 P5 ways.

If A and B are two events associated with a random experiment, then

P(A

B) = P(A) + P(B) – P(A ∩ B)

Corollary: If the events are mutually exclusive, then B) = P(A) + P(B) ∩

7 P Hence the required probability = ___ ​  55 ​  7

∩

P(A

So, favourable number of ways = 7P5.

Addition theorem can be extended for any number of events. Example  20

Example  5

7 1. ​ ___ 12  ​  

9 2. ​ ___ 12  ​ 

1 3. ​ ___ 12  ​  

11 4.  ​ ___ 12 ​  

(JMET 2005)

Solution

Solution

Probability that you will win at least one prize = 1 – probability that you will not win any prize. 5C3 ___ ​ 11 ​  = 1 – ​ ____ 10C   ​ = 12 3

Odds in Favour and Odds in Against Number of favourable cases Odds in Favour = _________________________ ​          ​ Number of Unfavourable cases Number of Unfavourable cases Odds in Against = _________________________ ​           ​ Number of favourable cases

Understanding and/or To understand the role played by And/Or in our calculation, let us take the example of throwing an unbiased die. Let A and B be two events associated with it such that A = getting an even number, B = getting a multiple of 3. Then A = {2,4,6}, and B={3,6}. We now define a new event “A or B” which occurs if A or B or both occur i.e., at least one of A, B occurs. Clearly the event “A or B” occurs if the outcome is any one of the outcomes {2,3,4,6}. Thus, the event “A or B” is represented by the subset A U B. Similarly, “A and B” means occurrence of both A and B which is possible if the outcome is {6}. Hence it is represented by the subset A ∩ B.

Example  21

Example  6 A basket contains 20 apples and 10 oranges out of which 5 apples and 3 oranges are defective. If a person takes out 2 at random what is the probability that either both are apples or both are good?

Solution Solution

Out of 30 items, two can be selected in 30C2 ways. So, total number of cases = 30C2. Consider the following events: A = getting two apples’; B = getting two good items Required probability = P (A B) = P(A)+P(B) – P(A∩B) ∩

If you have 3 tickets to a lottery for which 10 tickets were sold and 5 Prizes are to be given, the probability that you will win at least one prize is:

There are 20 apples, out of which two can be drawn in C2 ways. 20 C2   ​ ∴ P(A) = ​ ____ 30 C2

20

There are 8 defective pieces and the remaining 22 are good. Out of 22 good pieces, two can be selected in 22C2 ways. 22 C2   ​ ∴ P(B) = ​ ____ 30 C2 Since there are 15 pieces which are good apples out of which 2 can be selected in 15C2 ways, therefore P (A∩B) = Probability of getting 2 pieces which are 15 C2   ​ good apples= ​ ____ 30 C2 From (i) Required probability = P(A) + P(B) – P(A∩B) 20 C2 22C2 15C2 316   ​ ​ ____  ​ ​ ____  ​ ____ ​   ​  ​ ____ 30 C2 + 30C2 – 30C2 = 435

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  Quantitative Aptitude and Data Interpretation

Conditional Probability

Solution Solution

Let A and B be two events associated with a random experiment. Then, the probability of occurrence of A under the condition that B has already occurred and P (B) ≠ 0, is called the conditional probability and it is denoted by P(A/B).

Out of 52 cards, one card can be drawn in 52C1 ways. Therefore, exhaustive number of cases = 52C1 = 52

Thus, P(A/B) = Probability of occurrence of A given that B has already happened.

i. There are 4 kings in a pack of cards, out of which one can be drawn in 4C1. Therefore, favourable number of cases = 4C1 = 4. so the required probability

Similarly, P (B/A) = Probability of occurrence of B given that A has already happened.

4 ___ 1 = ​ ___ 52  ​ = ​ 13  ​ 

Sometimes, P (A/B) is also used to denote the probability occurrence of A when B occurs. Similarly, P (B/ A) is used to denote the probability of occurrence of B when A occurs.

ii. There are 28 cards in a pack of cards which are either a red or a king. Therefore, one can be drawn in 28 C1 ways. Therefore, favourbale number of cases = 28 C1=28.

Following examples illustrate various meanings of these notations

28 ​ = ___ 7  ​  ​ 13 So the required probability = ___ ​ 52 iii. There are 2 cards which are red and king, i.e., red kings. Therefore, favourable number of cases

Example  22

Example  7 A bag contains 5 white and 4 red balls. Two balls are drawn form the bag one after the other without replacement. Consider the following events. A = drawing a white ball in the first draw, B = drawing a red ball in the second draw. Now, P (B/A) = Probability of drawing a red ball in second draw given that a white ball has already been drawn in the first draw. Since 8 balls are left after drawing a white ball in first draw and out of these 8 balls 4 balls are red, therefore 1 P (B/A) = __ ​ 48  ​=​ __ 2 ​  Note that P (A/B) is not meaningful in this experiment because A cannot occur after the occurrence of B.

Example  24

Example  9 An urn contains 9 blue, 7 white and 4 black balls. If 2 balls are drawn at random, find the probability that i. Both the balls are blue ii. One ball is white.

Solution Solution

There are 20 balls in the bag out of which 2 balls can be drawn in 20C2 ways. So the total number of cases (sample space) = 20C2 = 190. i. There are 9 blue balls out of which 2 balls can be drawn in 9C2 ways. Therefore, favourable number of cases = 9C2 = 36.

Some More Examples

36  ​ = ___ ​ 18 So the required probability = ___ ​ 190 95 ​ 

Example  23

Example  8 One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability than the card drawn is i. a king ii. either red or king iii. red and a king

2 ___ 1 = 2C1 = 2. So the required probability = ​ ___ 52  ​ = ​ 26  ​ .

Contd…

ii. There are 7 white balls out of which one white can be drawn in 7C1 ways. One ball from the remaining 13 balls can be drawn in 13C1 ways. Therefore, one white and one other colour ball can be drawn in 7C1 × 13C1 ways. So the favourable number of cases = 7 C1 × 13C1 = 91. 91 So the required probability = ___ ​ 100  ​ 

Permutations, Combinations and Probability  Example  25 Example 

  1.203

Solution Solution

10

Three persons A, B and C are to speak at a function along with five others. If they all speak in random order, the probability that A speaks before B and B speaks before C is 1.  3/8

2.  1/6

3.  3/5

4.  None of these

A    r/2

Solution Solution

The total number of ways in which 8 persons can speak is 8 P8=8!. The number of ways in which A, B and C can be arranged in the specified speaking order is 8C3. There are 5! ways in which the other five can speak. So, favourable number of ways is 8C3 × 5!. 8 C3 × 5!. __  = ​ 16  ​ Hence, required probability = ​ _______ 8! ​ 

B Assume that the radius of the bigger circle is r, and the radius of the inner circle is r/2. Point will be closer to circumference than to the centre if point is lying in the segment B.

Example  26

Example  11

Area of segment B = ¾ πr2

There is a point inside a circle. What is the probability that this point is closer to the circumference rather than to the centre?

So, probability of point being closer to the circumference = ¾ πr2/πr2 = ¾

  EXERCISE  1 1. How many words can be formed by using the letters of the word ‘MANGO’? 1.  5! 4.  5C5

2.  5!/2 5.  None of these

3.  4!

2. How many words can be formed by using the letters of the word ‘PATNA’? 1.  5! 4.  5C5

2.  5!/2 5.  None of these

3.  4!

3. A cricket team consisting of 11 members is to be selected out of 15 members squad. In how many ways can the team be selected? 1.  15P11 4.  11!

2.  15C11 5.  None of these

3.  15!

5. In Q3, out of 15 members, player A does not want to play with player B (both A and B are the part of 15 member squad). In how many different ways team can be selected? 1.  15P11 4.  14P10

2.  15C11 5.  None of these

3.  14C10

6. In how many ways can 15 B.Sc. and 13 I.Sc. candidates be arranged in a line so that no two I.Sc. candidates may occupy consecutive positions? 1.  15!×13! 3.  13! × 16P12 5.  None of these

2.  15! × 16P13 4.  2!×15!×13!

4. In the above question, out of the 15 members, one of them is a wicket keeper and has to be selected in the team. In how many ways the team can be selected?

7. How many words can be formed with the word ‘LUCKNOW’ which are having L and W as the terminal letters? 1.  6! 2.  5! × 2 3.  7! – 2 4.  6! – 2 5.  5!

1.  15P11 4.  14P10

8. How many words can be formed with the word ‘LUCKNOW’ in which W always occurs before U?

2.  15C11 5.  None of these

3.  14C10

1.204 

  Quantitative Aptitude and Data Interpretation

1.  5! 4.  6! × 2

2.  7!/2 5.  None of these

3.  6!/2

9. Using digits 2, 4, 5, 6, 7, 9 how many two digit numbers can be formed without repetition? 1.  36 4.  12

2.  30 5.  None of these

3.  24

10. Using digits 2, 4, 5, 6, 7, 9 how many three digit numbers can be formed without repetition? 1.  360 4.  120

2.  300 5.  None of these

3.  240

11. How many arrangements can be formed out of the letters of the word EXAMINATION so that vowels always occupy odd places? 1.  6400 4.  12000

2.  36300 5.  None of these

3.  72400

12. Let n be the number of different five-digit numbers, divisible by 4 with the digits 1,2,3,4,5 and 6, no digit being repeated in the numbers. What is the value of n? 1.  144 4.  96

2.  168 5.  None of these

3.  192

13. Ten points are marked on a straight-line and 11 points are marked on another straight-line how many triangles can be constructed with vertices from among the above points? 1.  495 4.  2475

2.  550 5.  595

3.  1045

14. For a scholarship, at the most n candidate out of 2n+1 can be selecte 4. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is 1.  3 4.  5

2.  4 5.  2

3.  6

15. One red flag, three white flags and two blue flags are arranged in a line such that: I.  No two adjacent flags are of the same colour. II.  T  he flags at the two ends of the line are of different colours. In how many different ways can the flags be arranged? 1.  6 4.  2

2.  4 5.  3

3.  10

16. Sama has forgotten her friend’s seven-digit telephone number. She remembers the following: the first three digits are either 635 or 674, the numbers is odd, and the number 9

appears once. If Sama were to use a trial and error process to reach her friend, what is the minimum number of trials she has to make before she can be certain to succeed? 1.  10000 4.  3006

2.  4230 5.  None of these

3.  3402

17. Ten students are participating in a race. In how many ways can the first three prizes be won? 1.  920 4.  720

2.  680 5.  None of these

3.  820

18. If the different permutations of the word Examination are listed as in a dictionary, how many items are there in this list before the first word starting with E? 1.  9062800 4.  905200

2.  907200 5.  None of these

3.  908200

19. Find the number of arrangement of the letters of the word ‘ALGEBRA’ without altering the relative position of the vowels and the consonants. 1.  80 4.  72

2.  48 5.  None of these

3.  64

20. There are four similar balls and four similar boxes. Ball are required to be put in boxes. In how many ways the can balls be put inside the boxes? 1.  8 4.  6

2.  4 5.  None of these

3.  5

21. There are five identical sweets to be distributed between 2 children out of five children present. In how many ways can this be done? 1.  80 4.  60

2.  40 5.  None of these

3.  50

22. There is an n–sided polygon (n>5). Triangles are formed by joining the vertices of the polygon. How many triangles can be constructed which will have no side common with the polygon? 1.  n+2C3 – n 3.  nC3 – n 5.  None of these

2.  nC3 – n × ( n – 4 )C1 – n 4.  n × ( n – 4 )C1

23. There are 12 points in a plane out of which 5 are collinear. How many straight lines can be made out of these points? 1.  62 4.  57

2.  63 5.  None of these

3.  58

24. In an examination of 5 papers, a student is required to pass in each of the subjects to be declared qualifying the examination. In how many ways a student cannot qualify the examination?

Permutations, Combinations and Probability  1.  32 4.  64

2.  31 5.  2

3.  63

  1.205

31. In how many ways can 4 men and 4 women be seated in a row so that the men and women are alternate?

25. What is the number of five digit numbers having at least one digit repeated?

1.  28 4.  2.4!.4!

1.  67820 4.  59760

32. There is a regular decagon. Triangles are formed by joining the vertices of the polygon. What is the number of triangles which have no side common with any of the sides of the polygon?

2.  32180 5.  None of these

3.  27880

26. What is the maximum number of points in which three straight lines and three circles can intersect? 1.  32 4.  64

2.  27 5.  21

3.  63

27. In how many ways a father can divide Rs 50 among his ten children so that each of the children gets at least Rs 3 (only integral number of Rs can be given)? 1.  50C10 4.  29C9

2.  50C9 5.  None of these

3.  29C10

28. The letters of the word ‘COCHIN’ are permutated and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before ‘COCHIN’ in the dictionary is 1.  360 4.  48

2.  192 5.  None of these

3.  96

29. The value of

(  )(  ) (  )(  ) (  )(  )

​ ​ 30 ​   ​​ ​ 30 ​  ​– ​ ​ 30 ​   ​​ ​ 30 ​  ​+ ​ ​ 30 ​   ​​ ​ 30 ​  ​ 0 10 1 11 2 12

(  )(  )

(  )

30 2. ​ ​ 15 ​   ​

(  )

4. ​ ​ 31 ​  ​ 10

3. ​ ​ 60 ​  ​ 30

(  )

5. ​ ​ 30 ​  ​ 20

30. A rectangle with sides (2m – 1) and (2n – 1) is divided into squares of unit length by drawing parallel lines as shown in the diagram. What is the number of rectangles possible with odd side lengths?

1.  15C3 4.  9C3

2.  11C3 5.  None of these

3.  9C4

3 4. A conference attended by 200 delegates is held in a hall. The hall has 7 doors, marked A, B, … G. At each door, an entry book is kept and the delegates entering through that door sign it in the order in which they enter. If each delegate is free to enter any time and through any door he likes, how many different sets of seven lists would arise in all? (Assume that every person signs only at his first entry.)

1.  1749 4.  1954

2.  199P5 5.  None of these

3.  199C5

3.  m2n2

2.  528 5.  1353

3.  1221

36. Number of positive integral solution of abc = 30 is 1.  27 4.  54

2.  81 5.  None of these

3.  243

37. A train going from Cambridge to London stops at nine intermediate stations. Six persons enter the train during the journey with six different tickets of the same class. How many different sets of tickets they may have had? 1.  11C5 4.  1729

1.  (m+n+1)2 2.  4m+n–1 4.  mn (m+1) (n+1) 5.  None of these

3.  44

35. Two number are selected at random from 1,2,3…10 and are multiplied. Find the number of ways in which the two numbers can be selected so that the product thus obtained is divisible by 3.

(  )

(  )

2.  300 5.  120

3.  4!.4!

33. There are 12 intermediate stations between two places A and B. In how many ways can a train be made to stop at 4 of these 12 intermediate stations no two of which are consecutive?

1.  206C6 4.  206P6

30 30 ​ 30 ​   ​is, where (​  __ ​ nr ​  )​= nCr is: ……… + ​ ___ ​ 20  ​  ​​ ___ 1. ​ ​ 30 ​  ​ 10

1.  50 4.  294

2.  36 5.  8P4 × 2!

2.  35C6 5.  None of these

3.  45C6

38. Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five

1.206 

  Quantitative Aptitude and Data Interpretation

1.  3C1.4C2.6! 4.  3C1.4C2

balls. In how many different ways can we place the balls so that no box remains empty? 1.  119 4.  210

2.  150 5.  186

3.  180

40. Find the number of n – digit number formed with the digits 1,2,3…,9 in which no two consecutive digits are same.

39. An eight oared boat is to be manned by a crew chosen from 11 men of whom 3 can steer but cannot row and the rest cannot steer. In how many ways can the crew be arranged if two of the men can only row on bow side?

ANSWER KEYS

2.  3P1.4P2 3.  3P1.4P2.6! 5.  None of these

1.  9n–1 4.  9n

2.  9.8n–1 5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

2

3.

2

4.

3

5.

5

6.

2

7.

2

8.

3

9.

2

10.

4

11.

5

12.

3

13.

3

14.

1

15.

1

16.

3

17.

4

18.

2

19.

4

20.

3

21.

4

22.

2

23.

4

24.

2

25

5

26

2

27.

4

28.

3

29

1

30.

3

31.

4

32.

1

33.

3

34.

4

35.

1

36.

3

37.

3

38.

2

39.

3

40.

2

3.  9.8n

Permutations, Combinations and Probability 

  1.207

HINTS AND EXPLANATIONS 1. (1) There are five distinct letters. So total number of arrangements = Words formed = 5!

11. EXAMINATION

 Vowels are – E, A, I, A, I, O and consonants are – X, M, N, T, N



3. (2) Total number of members (n) = 15, team to be selected (r) = 11 Hence nCr = Total ways to select the team = 15C11

 There are six odd places:– vowels can be arranged in–6!/ (2! × 2!)



 There are five even places now:– Consonants can be arranged in – 5! / 2!

4. (3) One member has already been selected in the team. So out of 14 members now, 10 players to be selected.



  Total number of ways will be product of these two.

2. (2) There are total five letter, out of which A appears twice.



  So total number of words formed = 5!/2!

  Total ways to select the team = 14C10

6. (2) Since there is no restriction on B. Sc candidates, we would start with them only (take this as a thumb rule):

  15 B. Sc candidates can be arranged in 15! (15P15) ways.



 Now, to make an arrangement such that no two I.Sc. students are sitting together, we can make each of them sit in between two B.Sc. candidates.



 Total places in between B. Sc. Candidates = 16 (consider the ends too).



 Out of these 16 places, we can arrange 13 I.Sc. candidates in = 16 P13



  Total number of arrangements = 15! × 16P13

7. (2) We have to arrange only 5 letters (As place of L and W are restricted),

  So, Number of arrangements = 5!



 Place of L and W can be interchanged between themselves.



 So, total number of words that can be formed = 5! × 2!

12. The last two digits can be 12, 16, 24, 32, 52, 56, and 64, i.e., 8 possibilities.

Remaining digits can be chosen in 4P3 = 24 ways hence, total number of such five digit numbers = 24 × 8 = 192.

13. The answer is 10C2 ×11+ 11C2 × 10 = 45 × 11 + 55x 10 = 1045. 14. Out of (2n+1) candidates, selection of at least one candidate is given by (22n+1–1) ways. Hence, in our case, 22n+1–1= 63 or 22n+1 = 64 = 26 or n = 2.5 since a cannot be a fraction, n = 3. 15. The possibilities are W@W@W@ (or) @W@W@, where 2 blue and 1 red flag occupy the space marked as @. Hence, the total permutation is 2(3!2!) = 6. 16. There are two possible cases. The number 9 comes at the end, or it comes at position 4,5, and 6. For the first

8. (3) Total number of arrangements without any restriction = 7!

9 ___ case, the number would look like: 635… ​     ​ …9. 674 In both these cases, the blanks can be occupied by any of the available 9 digits. (0,1,…,8). Thus, total possible numbers would be 2× (9 × 9 × 9) = 1458. For the second case, the number 9 can occupy any of the given position 4,5, or 6, and there shall be an odd number at position 7. Thus, the total number of ways shall be 2[3(9 × 9 × 4)]=1944. Hence, the answer is 3402.



 In half of the cases, W will come before U and in other half U will come before W.

17. (4)



  So, required number = 7!/2



Out of 10 students, the first three prizes can be won in



10! ___ 10! _______ 10P3 = ​     ​  ​   ​ = 10 × 9 × 8 = 720 ways. (10 –3)! 7!

9. (2)  Unit place can be filled in 6 ways (Since total no. is 6)

 Tens place can be filled in 5 ways (as we have used one digit and reputation of digits is not allowed)

18. (2)

  Hence, required total nos. are 6 × 5 = 30.



10. (4)  Unit place can be filled in 6 ways (Since total no. is 6)

 Tens place can be filled in 5 ways (as we have used one digit and reputation of digits is not allowed)



  Hundreds place can be filled in 4 ways



  Hence, required total nos. are 6 × 5 × 4 = 120

Starting with A and arranging the other ten letters, A, E, I, I, M, N, N, O, T X (not all distinct, I occurs twice, N occurs twice), there are



10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. ________________________________ ___ ​ 10! ​ = ​        ​    2 ×2 2!2



= 907200 words.

1.208 

  Quantitative Aptitude and Data Interpretation

The number of items in the list before the first word starting with E is 907200.

19. (4)



23. Required number of straight lines = 12C2 – 5C2 + 1 = 57 24. With respect to each of the subjects, there can be two outcomes— either pass or fail.

There are 7 letters, of which two are A’s and the rest are all different. The vowels A, A, E occupy 1st, 4th and 7th places. The number of ways in which they can be



So, out of 5 subjects, total number of outcomes = 2 × 2 × 2 × 2 × 2 = 32

3! __ arranged in these places is ​    ​3. 2!



There is only one way to qualify – passing in all the subjects.



So, number of ways a student cannot qualify = 32 – 1 = 31

The consonants L, G, B, r are all different. The number of ways in which they can be arranged in the remaining places in 4!. Since each way of arranging the vowels can be associated with each way of arranging the consonants, we find that the total number of arrangement = 3 × 4! = 3 × 24 = 72.

20. Since the balls and the boxes are identical, it does not matter which ball is going to which box. What matters is how many balls (and not which balls) are there in how many boxes (and not which boxes):

25. Total number of five digit numbers = 90,000

Total number of five digit numbers without any digit repeated = 9 × 9 × 8 × 7 × 6 = 27216



So number of numbers having atleast one digit repeated = 62784

26. Three lines can intersect among themselves = 3C2 = 3 points

Three circles can intersect among themselves = 3P2 = 6 points



So the possible ways are – (4, 0, 0, 0), (3, 1, 0, 0), (2, 2, 0, 0), (2, 1, 1, 0), (1, 1, 1, 1)



Every line can cut 3 circles in 6 points ⇒ 3 lines can cut 3 circles in 18 points



Understand that (3, 1, 0, 0) = (0, 1, 3, 0) = (0, 0, 3, 1) = Same arrangement



Total points of intersection = 3 + 6 + 18 = 27 points



So total number of ways = 5

21. Let us 1st choose the children whom the sweet is to be distributed = 5C2

Since the sweets are identical, it does not matter which sweet is going to who? What matters is number of sweets only.



So the possible ways are = (5,0), (4,1) (3,2) (2,3) (1,4), (0,5) = 6



Please understand that here the way (5,0) is not same as (0,5) because the child is distinct. So 1st child getting 5 sweets and second getting zero is different situation than 2nd child getting 5 and 1st child getting 0.



So total number of ways = 5C2 × 6 = 60

22. An n–sided polygon will be having n vertices. Triangles constructed out of these n vertices will be of three types – i. Having two sides common with the polygon, ii. Having one side common with the polygon, iii. Having no side common with the polygon. And total number of triangles formed will be nC3.

i. Having two sides common with the polygon – Out of total n vertices, any combination of three consecutive vertices will give us the triangle which is having two sides common with polygon = n



ii. Having one side common with the polygon – Number of selection of three vertices out of which two are consecutive (If we select A5 and A6 as the two vertices, then A7 or A4 should not be the third vertex because it will constitute two sides common triangle). = n × ( n – 4 )C1



 So, the total number of triangles having no side common with polygon = nC3 – n × ( n – 4 )C1 – n

27. 1st distribute Rs 30 to 10 children (10 × 3 = 30)

Remaining Rs 20 can be distributed to 10 children is ways.

C10–1

20 + 10 – 1

29. Option 1 is the answer.

The given expression is the coefficient of x20 in the product of (1+x)30(1–x)30 = (1–x2)30



= 30C10

30. There are 2m vertical (numbered 1, 2, ......., 2m) and 2n horizontal lines (numbered 1, 2, ....., 2n). To get the required rectangle, we should select two horizontal lines, one even numbered and one odd numbered and similarly two vertical lines. The number of rectangles is then mC1 . mC1 . nC1 . nC1 = m2n2

Alternate solution:



Number of rectangles possible is (1 + 3 + 5 + ...... + (2m – 1)) (1 + 3 + 5 + ...... + (2n – 1)) = m2n2

31. Four men (or four women) can be seated in 4! ways. Now four women can be seated in 4! Ways in between men to make the arrangement alternate. But women can come before the man making woman as the 1st person seating or men can come before women making man as the 1st person seating. See this below:

W1 M1

W2 M2

W3 M3 W4

M4

OR

M1 W4

W1 M2

W2 M3

W3 M4



So, total arrangements for women and men together = 4! 4! 2!

Permutations, Combinations and Probability 

  1.209

9. What is the probability that there are 52 Sundays in a leap year?

  EXERCISE  2 1. What is the chance of drawing an ace from a deck of cards?

1.  0 4.  1/7

1.  8/52 4.  4/52

10. What is the probability that there are 53 Sundays and 53 Saturdays in a leap year?

3.  2/52

2. Mayank and Amit are throwing an unbiased dice. If Mayank throws 1, what is the probability that Amit will throw a higher number? 1.  1/5 4.  2/6

2.  5/6 5.  ½

3.  2/12

3. A bag contains 4 red and 7 green balls. If three balls are drawn from the bag, replaced and once again three balls are drawn from the bag, what is the probability of obtaining 3 red balls on first drawing and 3 green balls on second drawing? 1.  14/5445 4.  7/27225

2.  14/27225 5.  None of these

3.  28/5445

4. One number is selected at random from first 25 natural numbers. What is the probability that it is a multiple of either 5 or 7? 1.  2/12 4.  1/5

2.  8/25 5.  None of these

3.  4/25

5.  None of these

2.  2/7 5.  1

3.  0

11. A and B are two possible events of an experiment such that P(A B) = 0.7 and P(A) = 0.4, then find P(B) given that A and B are mutually exclusive events. 1.  0.6 4.  0.5

2.  0.3 5.  0.25

3.  0.2

12. A bag contains eight items—3 cubes and 5 balls having painted in three different colours red, blue, and green. No two cubes have the same colour. An item is taken out from the box. What is the probability that this item is a cube having red colour? 1.  1/8 4.  7/8

2.  1/4 5.  1/3

3.  5/8

13. A bag contains 2 red, 3 green and 2 blue balls, 2 balls are to be drawn randomly. What is the probability that the balls drawn contain no blue ball? 5 1. ​ __ 7 ​  

5. If there coins are tossed at random. What is the chance that these will turn up head and tail alternately? 7 ​  1 ​   1 ​   3. ​ __ 1. ​ __ 2. ​ __ 8 8 4 3 ​   4. ​ __ 8

1.  1/7 4.  3/7

3.  0.5

∩

2.  16/52 5.  13/52

2.  1 5.  2/7

11 4. ​ ___ 21 ​  

10 2. ​ ___ 21 ​  

2 ​  3. ​ __ 7

5.  2/5

14. If the probability that A will live 15 years is __ ​ 78 ​  and that 9 B will live 15 years is ___ ​ 10  ​ , then what is the probability that both will live after 15 years?

6. A bag contains 5 green apples and 7 red apples. If two apples are drawn from the bag, what is the probability that one is red and other is green?

1 1. ​ ___ 20  ​  

63 2. ​ ___ 80 ​  

4.  ½

5.  None of these

1.  12/66 4.  2/35

15. A set A is containing n elements. A subset P of A is chosen at random. The set is reconstructed by replacing the elements of P. A subset of A is again chosen at random. The probability that P and Q have no common elements is n n 1.  2n 2. ​ __ ​ 34 ​    ​ 3. ​ __ ​ 35 ​    ​

3.  2/12

7. The probability of a problem being solved by A is 1/4 and B solving it is 1/5. If they try independently, then what is the probability that the problem is not solved? 1.  2/5 4.  2/9

2.  4/9 5.  1/3

3.  3/5

8. What is the probability that there are 53 Sundays and 53 Tuesdays in a leap year? 1.  0 4.  1/7

2.  1 5.  2/7

3.  0.5

(  )

4.  ½

(  )

5.  None of these

16. If events A and B are independent and P (A) = 0.15, P (A B) = 0.45, then P (B) = ∩

2.  35/66 5.  12/66

1 ​  3. ​ __ 5

6 1. ​ ___ 13  ​  

6 4. ​ ___ 23  ​  

6 2. ​ ___ 17  ​   5.  None of these

6 3. ​ ___ 19  ​ 

1.210 

  Quantitative Aptitude and Data Interpretation

17. The probability that a marksman will hit a target is given as 1/5. Then, his probability of atleast one hit in 10 shots is 1  ​   1. ​ ___ 610 51 4. ​ ___ 101  ​  

19. If the probability of rain on any given day is 50%. What is the probability that it rains on exactly 3 days in 5-days period?

50 3. ​ ___ 101  ​ 

49 2. ​ ___ 101  ​  

1.  8/125 4.  2/25

5.  49/50

4.  5/8

5.  3/17

ANSWER KEYS

2.  3/8

3.  8/25

20. The probability that an event A happens in one trial on an experiment is 0.4. Three independent trials of the experiment are formed. The probability that the event A happens at least once is

18. Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that one of the objects occupy the place corresponding to its number? 1.  17/24

2.  5/16 5.  3/25

3.  1/2

1.  0.934

2.  0.784

4.  0.343

5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

2

3.

3

4.

2

5.

2

6.

2

7.

3

8.

1

9.

2

10.

1

11.

2

12.

1

13.

1

14.

2

15.

5

16.

2

17.

2

18.

3

19.

2

20.

2

3.  0.548

HINTS AND EXPLANATIONS

  So probability = 4/52

2. (2) Amit can throw a higher number – 2, 3, 4, 5, 6 (Total cases = 5)

  Hence probability = 5/6

4. (2)  Multiples of 5 = 5, 10, 15, 20, 25 (5 numbers)

  Multiples of 7 = 7, 14, 21 (3 numbers)



  Multiples of 7 and 11 both = None



  Hence total number of multiples of 5 or 7 = 8



  Hence required probability = 8/25

5. (2)  Sample space n(S)= 2³ = 8



 Number of ways in which desired event can happen n(E) = (H, T, H) (T, H, T) = 2 n(E) __ 2 __ 1 ____   So, required probability = ​   ​ = ​   ​  = ​   ​  n(S) 8 4

6. (2) Sample space = 12C2 = 66 Ways such that one is green and other one is red apple = 5C1 × 7C1 = 35

  Required probability= 35/66

7. (3)  Problem not getting solved by A = ¾

  Problem not getting solved by B = 4/5



 Since the events are independent, probability the problem is not solved = ¾ × 4/5 = 3/5

8. (1) Total number of days in a leap year = 366 days = 52 weeks + 2 days 52 weeks implies that there will be 52 Sundays, 52 Mondays ……..52 Saturdays. 2 extra days can be the pair of days like Sunday + Monday, or , Monday + Tuesday (7 such pairs can be made)etc.

 Since question asks about 53 Sundays and 53 Tuesdays, it is not possible. Hence probability = 0

9. There has to be 52 Sunday in a year. Here Probability = 1 10. See the solution to R8.

∩

1. (4) Total number of cards = 52, Total number of aces = 4

11. (2)  P(A B) = 0.7 = P (A) + P (B) – P (A∩B)

 Since A and B are mutually exclusive events, P (A∩B) = 0

Permutations, Combinations and Probability 

  P (B) = 0.7 – P (A) = 0.7 – 0.4 =0.3

12. (1) The probability of drawing a cube from the bag = 3/8

  Now, the probability of cube to be red = 1/3



  Hence, probability of drawing red cube



3 1 __ 1 __ __   = ​ ​    ​× ​   ​   ​= ​   ​  8 3 8

( 

)

9 ___ 63 7 ___ __ 14.   P (A) × P (B) = ​   ​  × ​    ​ = ​   ​  8 10 80 15. (5) 16. (2)

10

(  )



4 __ shots is ​ ​   ​    ​ 5



So, probability that atleast once target will be hit



4 __ = 1 – ​ ​   ​    ​1 0 5

(  )

1 __ 19. (2) Prob. that is rains on the 1st day = ​   ​  2

1 __ Prob. that it rain on the 2nd day = ​   ​  2



1 __ Prob. that it rains on the 3rd day = ​   ​  2



1 __ Prob. that it rains on the 4th day = ​    ​ 2



1 __ Prob. that it rains on the 5th day = ​    ​ 2



P (A ∩ B) = P (A) × P (B) = 0.15 × P(B)



P (A



0.45 = 0.15 + P(B) – (0.15) × P (A ∩ B)



= 0.15 + P (B) (1–0.15) = 0.15 + 0.85 P(B)



0.85 P(B) = 0.45 – 0.15 = 0.30 Þ P(B)



Prob. that it rains on the any day in a 5–day period



0.30 ___ 30 ___ 6 ____ = ​   ​  . = ​   ​ = ​    ​ . 0.85 85 17



5 1 ___ ___ = ​    ​ , So, P(Exactly 3 days) = ​    ​  16 32

B) = P (A) + P (B) – P (A ∩ B)

∩

17. (2)

  1.211

20. (2)



4 1 1 __ __ __ P(A) = ​   ​ , P ( A ) = a – ​   ​  = ​   ​  5 5 5



Required Probability = 3C1 (0.4)(0.6)2 + 3C2 (0.4)2 (0.6) + 3C4 (0.4)3



The probability that he will not hit the target in 10



= 3 (0.144) + 3 (0.096) + 1 (0.064) = 0.784.

c h a p t e r

  13

Miscellaneous

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Calendars, Logarithm, Inequality and Height and Distance   Definitions and properties   Kind of questions which are asked in the CAT   Method of solving the questions

1.  CALENDAR We know that Any non-leap year contains 365 days = 52 weeks + 1 day And leap-year contains 366 days = 52 weeks + 2 days This 1-day and 2 days extra added to any year create changes in the calendar and this is the reason why calendar of Nth year will not be same as N+1th year. Before we proceed ahead, we should be very clear about two things: i. Which years are leap years? It takes the earth about 365.2422 days to go around the sun, but a normal calendar year is only 365 days. The extra fraction of a day added up four

times makes four years (or, four revolution of earth around sun) 1460.9688 days, but four calendar years would only be 1460 days. That 0.9688 is almost a whole day, so every four years we add an extra day to our calendar, February 29. We call that year leap year. To make things easier, leap years are always divisible by four: 2004 and 2008 will both be leap years. For hundreds of years, people used a calendar called the Julian calendar that followed this rule, adding a leap year every four years. However, because 0.9688 isn’t exactly a whole day, the Julian calendar slowly began to disagree with the real seasons. In 1582, Pope Gregory fixed this problem by ordering everyone to use a new set of rules. These rules are named the Gregorian calendar, after him. They work like this:

The Gregorian Calendar Rule

Examples

Miscellaneous 

  1.213

Year

1972

1973

1974

1975

1976

Excess days

2

1

1

1

2

Every fourth year is a leap 2004, 2008, and 2012 are year. leap years.

Since no. of excess days are 7, so the days of the year 1972 and year 1977 will be same from 1st of January to 28th of February.

However, every centenary 1900 and 2100 are not leap year is not a leap year. years.

ii. For any (leap-year+1) year

In case of centuries, every 2000 and 2400 are leap four hundred years, there’s a years. leap year after all.     In layman terms, all the century years divisible by 400 will be leap years and all the non-century years divisible by 4 will be leap years. So, leap year next to 2096 AD is 2104 AD and not 2100 AD. Because 2000, 4000, 6000, etc. are leap years and 1000, 3000, 5000, etc. are not, the number of leap days in each millennium alternates between 242 and 243, with the first, third, etc. millennia (i.e., 1-1000, 2001-3000, etc.) having 242 leap days, and the second, fourth, etc., (i.e., 1001-2000, 3001-4000, etc.) having 243 leap days. ii. How the days of consecutive years change? Due to any non-leap year, calendar of next year go ahead by 1 day and due to any leap year, calendar of next year goes ahead by 2 days, but this change in calendar will be there only before 29th February. It can be seen through the example given below: 1991

1992

1993

1st January

Sunday

Monday

Wednesday

28th February

Tuesday

Wednesday

Friday

1st March

Wednesday

Friday

Saturday

    In the above example, we have assumed that 1st January of 1991 is Sunday. 1991 and 1993 are non-leap years and 1992 is a leap year. If now we try to find out the symmetricity of calendars, we can see this in the following way: i. For any leap-year Let us see, for example, the case of 1972.

Year

1973

1974

1975

1976

1977

1978

Excess days

1

1

1

2

1

1

Since no. of excess days are 7, so calendar of year 1973 and 1979 will be same for whole year. iii. For any (leap-year+2) year Year

1974

1975

1976

1977

1978

1979

Excess days

1

1

2

1

1

1

Since excess days are 7, so calendar of year 1974 and 1980 will be same till 28th of February. iv. For any (leap-year+3) year Year 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985

Excess 1 days

2

1

1

1

2

1

1

1

2

1

Since no. of excess days are 14, so calendar of year 1975 and 1986 will be same for whole year. This whole mechanism can be summed up in following way: Nature of year

No. of years after which 1st January will be same

Leap year

5

Leap year + 1

6

Leap year + 2

6

Leap year + 3

11

So, 1st January of 1972 and 1st January of 1977 will be on same day. If 1st January of 1973 and 1st January of 1979 will be on same day and so on. Exception – No century year, which is not a leap year, should be included in this calculation. Example  1 Example 

1

Sum of dates of last Monday of previous month and 1st Thursday of next month is 38. If both the dates are of the same year, then which month is the current month?

1.214 

  Quantitative Aptitude and Data Interpretation

Solution Solution

Sum of dates of last Monday of previous month and 1st Thursday of next month is 38 is possible only if last Monday is 31st and 1st Thursday is 7th.(Since if we take 30+8 = 38, then 30 can be last Monday of any month but 8th can not be the 1st Thursday of any month)     So, 31st of last month is a Monday. Hence 7th of current month - 14th of current month –21st of current month -28th of current month will be a Monday.     Now, if current month is a month with 30 days, then 5th of next month will be a Monday, so 7th of next month cannot be a Thursday.     If current month is a month with 31 days, then 4th of next month will be a Monday, so 7th of next month will be a Thursday.     Finally, we can conclude that previous month and current month, both are having 31 days. Since both the dates are of the same year, so current month is August.

Finding day of a date by using a reference date Let us see this with the help of an example: If 9th Dec of 1972 is Sunday, then which day it will be on 14th December 1998? Process:  There are several processes to do this calculation: 1. Year method, 2. Days method, 3. Actual calculation method 1. Year Method – We use the above given table to find out about any of the years. 9.12.1972 – Sunday 1.1.1973 – Tuesday (It is a Leap year + 1 year) So, 1.1.1979 – Tuesday, (It is a Leap year + 3 year)

1.1.1973 – Tuesday Due to 1973, calendar will go ahead by 1 day, similarly due to 1974 – 1 day, due to 1975 – 1 day and due to 1976- 2 days. So, in four years, calendar will go ahead by 5 days. Using unitary method, in four years, calendar will move ahead by 5 days. So, in 24 years calendar will move ahead by 30 days. Hence calendar will move ahead by 2 days. So, 1.1.1997 will be two days ahead of Tuesday i.e., Thursday. Now, it is calculation as given in Year Method. 3. Actual Calculation method–With the help of this method, we can find the actual day of any date of 20th century. To use this method effectively, we need to remember the Month Codes of all the months. Let us learn this method by finding the date of 15th August 1947 – At 1st, add the Date + Month code of August + Last two digits of year +

( 

)

Last two digits of year ​ __________________ ​       ​ 4 ​  (Where [x] represents the greatest integer value of x.) So, corresponding to 15th August 1947 – 15 + 3 + 47 + 11 = 76 Now, divide this value by 7 to find out the remainder. If the remainder is 0 → then it is a Saturday If the remainder is 1 → then it is a Sunday If the remainder is 2 → then it is a Monday If the remainder is 3 → then it is a Tuesday If the remainder is 4 → then it is a Wednesday

So, 1.1.1990- Tuesday, (It is a Leap year + 2 year)

If the remainder is 5 → then it is a Thursday

So, 1.1.1996 – Tuesday

If the remainder is 6 → then it is a Friday

Now, we can find out all the next years one-by-one.

Here, remainder is 6, so 15th August 1947 was a Friday.(It should have been ‘Free’day)

1.1.1997 – Thursday 1.1.1998 – Friday – 31.12.1998 – 24.12.1998 – 17.12.1998 So, 14.12.1998 – Tuesday 2. Days method–We use the no. of excess days every year to find out the no. of days calendar will move ahead by.

List of Month Code: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Leap Year

0

3

4

0

2

5 0

3

6

1

4

6

Non-leap 1 year

4

4

0

2

5 0

3

6

1

4

6

Miscellaneous 

2.  INEQUALITIES While discussing equations and inequations in polynomials, we have seen what inequations are. However, while discussing inequalities here, our focus will be to discuss this concept in isolation with equations, for real numbers only.

  1.215

The two signs ‘>’ and ‘’ means ‘greater than’

As we can see, 10 is greater then 5 because 10 – 5 = 5 and 5 is greater than zero.

‘ N when M – N > 0

(ii) M is said to be less than N when M – N is negative.

‘≥’ means ‘greater than or equal to’

⇒ M < N when M – N < 0.

‘≤’ means ‘less than or equal to’ If ‘N’ is any real number, then value of ‘N’ will be either positive or negative or zero. When ‘N’ is positive, we write N >0; which is read ‘N is greater than zero’. Similarly When ‘N’ is negative, we write N < 0; which is read as ‘N is less than zero’. If ‘N’ is zero, we write N = 0 and in this case, ‘N’ is neither positive nor negative.

As we can see, -10 is less than -5 because -10 – (-5) = -5 and -5 is less than zero. However, in case of numbers inequalities can be understood through Number Line also. Number Line: The number line is used to represent the set of real numbers. Below is the brief representation of the number line:

Opposites 7

–

–

6

–

5

–

4

–

3

–

2

–

1

0

Negative integers Basics of Inequalities It is quite pertinent here to understand some of the very basic properties related to inequalities. These properties should be seen as the building block of the concepts of Inequalities. Assume all the numbers used here are real numbers. - For any two real numbers M and N, either M > N or M < N or M = N. If M > N, then N < M. •  If M > N and N > P, then M > P. •  If M < N and N < P, then M < P. •  If M > N, then M ± c > N ± c. •  If M > N and P > 0 then MP > NP. •  If M > N and P < 0, then MP < NP. •  If M < N and P > 0, then MP < NP. •  If M < N and P < 0, then MP > NP. •  If M > N and P > Q, then M + P > N + Q. •  If M < N and P < Q, then M + P < N + Q.

1

+

2

+

3

+

+

4

5

+

+

6

7

+

Positive integers • However, if M > N and P < Q, Or, M < N and P > Q then we cannot comment about the inequality between (M + P) and (N + Q). • If M > N and P > Q, then we cannot infer the inequality sign between (M - N) and (P - Q). Depending on the values of M, N, P and Q, it is possible to have (M - N) > (P - Q), (M - N) = (P - Q) or (M - N) < (P - Q) • The square of any real number is always greater than or equal to 0. • The square of any NON-ZERO real number is always greater than 0. • If N > 0, then – N < 0 and if M > N, then –M < -N. • If M and N are positive numbers and M > N, then (i)  1/M < 1/N (ii)  M/P > N/P if P > 0 and (iii)  M/P < N/P if P < 0

1.216 

  Quantitative Aptitude and Data Interpretation

•  For any two positive numbers M and N 2

2

If M > N then M > N . If M 2 > N2 , then M > N. If M > N, then for any positive value of n, Mn > Nn. •  For two positive numbers M and N If M/N < 1 then M < N

Solution Solution

3065 –2965 ​ ________    ​> 1 3064 –2964 As, 3065 – 2965 > 3064 + 2964 Or, 3064 (30-1) > 2964 (29+1)

If M/N = 1 then M = N

Or, 3064×29 > 2964×30

If M/N > 1 then M > N

Or, 3063 > 2963

•  Relationship between a number and its square root:

Hence option (4)

Let N be a natural number. √N = N, for N = 0 or N = 1 √N > N, for 0 < N < 1 √N < N, for N > 1 • Let A, G and H be the Arithmetic Mean, Geometric Mean and Harmonic Mean of n positive real numbers, then A ≥ G ≥ H. Equality occurs only when all the numbers are equal. • If the sum of two positive quantities is given, their product is greatest when they are equal; and if the product of two positive quantities is given, their sum is least when they are equal. • For any positive number, the sum of the number and its reciprocal is always greater than or equal to 2, i.e., x + __ ​ x1 ​ ≥ 2 where x > 0. The equality in this relationship will occur only when x = 1. Cauchy–Schwarz Inequality If a1, a2 , …….an and b1 b2 …bn are 2n real numbers, then

Example  3 Example 

3

If 13x + 1 < 2z, and z + 3 = 5y2 , then    (CAT 03) 1  x is necessarily less than y.  2. x is necessarily greater then y. 3.  x is necessarily equal to y.  4. None of the above is necessarily true. Solution Solution

We have 13x + 1 < 2z .... (1) and z + 3 = 5y2 .... (2) From (1) and (2) we get 13x + 1 < 2 (5y2 – 3) ⇒ 13x + 1 < 10y2 – 6

(a1b1 + a2b2 +….. + anbn)2 < (​a2​1​​ ​a2​2​​ +……​a2​n​ ​)(​b1​2​​ + b​ 2​2​​ ……​b2​n​ ​)

⇒ 13x < 10y2 – 7

With the equality holding if and only if

10y2 – 7 ⇒ x < _______ ​  13 ​    If y =1 then, we get x < 0.230



a a1 a2 = = ...... = n b1 b2 bn

Despite all the points given above, we should not let the LOGIC die. Most of the questions asked in CAT can be solved by using options and we won’t be in need of using any concept of Inequalities. But this should not be seen as a case in support of not-going through concepts. Example  2 Example 

2

30 –29 If R = ​ ________    ​, then    (CAT 05) 3064 –2964 65

65

1.0 y. This is not possible. Hence, correct answer is (4).

Example  4 Example 

4

If |b|≥ 1 and x = – |a| b, then which one of the following is necessarily true?   (CAT 03) 1.  a – xb < 0

2.  a – xb > 0

3.  a – xb > 0

4.  a – xb < 0

Solution Solution

Lets start assuming the values of a and b. Assume b = 2 and a = 1/2. Then x = – 1. Thus options 1 and 4 have been eliminated. Assuming a = –1 and b = –1, we get x = 1. Putting Ans.(2) the values in options 1 and 2, we get

3.  HEIGHTS AND DISTANCES General Theory on Heights and Distances Angle of elevation: If the object is above the horizontal level of the eyes i.e., if it is above the eye level), we have to turn our head upwards to see the object. In this process, our eyes move through an angle. Such an angle is called the angle of elevation of the object from our eyes. Angle of depression: Suppose a boy, standing on the roof of a building, observes a ball lying on the ground at some distance form the building. In this case, he has to move his head downwards to view the ball. In this process, his eyes again move through an angle. Such an angle is called the angle of depression of the object from the location of his eyes (figure.)

SOME TRIGONOMETRIC RATIOS and   FORMULAS 0o

30o

45o

60o

90o

Sin

0

1/2

1/√2

√3/2

1

Cos

1

√3/2

1/√2

1/2

0

Tan

0

1/√3

1

√3

∞

sin(–θ) = – sinθ; cos (–θ) = cosθ; tan(–θ) = – tanθ;

__ 1.  5​( ​√3 ​ + 1 )​ __ ​ 3 ​ – 1 )​ 3.  7​( √

__ __ 2.  6​( ​√3 ​ + √ ​ 2 ​  )​ __ 4.  8​( √ ​ 3 ​ – 2 )

Miscellaneous 

Solution Solution

h 60°

45° d

x tan 45° = _____ ​  h   ​  x+d or, h x + d

Similarly, tan 60° = __ ​ hx ​  __ or, h = x​√3 ​  Hence, x + d = x√3, So, x(√3-1) = d Car takes 10 mins in covering ‘d’ distance, so car will take 10/(√3-1) min in covering ‘x’[x = d/(√3-1)] distance. Now, t = 10/(√3-1)

__ (   ​ 3 ​ + 1 )​, Multiplying both numerator and denominator by ​ √ __ we get t = 5​( ​√3 ​ + 1 )​. Hence option (1).

Example  6

Example  6 The angle of elevation of the top of a tower from a point 60m from its foot is 30°. What is the height of the tower?

cot(–θ) = – cotθ; sec(–θ) = secθ; cosec(–θ) = – cosecθ; sin (90°–θ) = cos θ; cos(90° –θ) = sin θ

Solution Solution

Sin2θ = 2 Sinθ.Cosθ Cos2θ = 2 Cos2θ – 1 = 1 – 2 Sin2θ Example  5

Example  5

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?

  1.217

Let AB be the tower with its foot at A. Let C be the point of observation. Given ∠ACB = 30° and AC = 60 m B

C

30° 60 m

A

1.218 

  Quantitative Aptitude and Data Interpretation

From right triangle BAC: AB  ​ = tan 30° ​ ___ AC __ ⇒ AB = 60 tan 30° = 60​ ___ ​  1__   ​  ​= 20​√3 ​  ​ 3 ​  √

(  )

iii. For constant x, if base is lying in between 0 and 1, then log x becomes decreasing function. Otherwise it is an increasing function.

y

y = log2 x y = log3 x

Example  7

Example  7 Two pillars of equal height stand on either side of a road. At a point on the road between the pillars the elevation of the tops of the pillars are 60° and 30°. Find the height of the pillars if it is given that the width of the road is 150 m.

o

(1, 0)

x y = log 1/3 x y = log 1/2 x

Solution Solution

__ tan 60° = √ ​ 3 ​ = __ h/x tan 30° = 1/​√3 ​   = h / (150 – X) Solving we get: x = 37.5m, h=64.95 m.

Some Important Properties In case of all the following properties given ahead, we will be using the standard restrictions on logarithm. 1. loga(XY) = logaX + logaY

4. LOGARITHM The logarithmic function is defined as the inverse of exponential function. If any number N is expressed in the form ax then the index ‘X’ is called the logarithm of the number N to the base ‘a’. Thus, If N = a Then X = logaN. Generally logarithm of any number is calculated to the base 10. x

When base is not mentioned, it should be taken as 10.

If we don’t use the restrictions given regarding log of any number, then we can see a good number of contradictions about numbers. One of the examples of similar nature can be seen here: log (12) = log ( - 4 × - 3) = log (-4) + log(-3) Now on the Left Hand Side, we have a defined value, but on the right hand side we get a value which is not defined. It is all owing to the fact that loga(XY) = logaX + logaY is possible only if X > 0 and Y > 0. 2. loga(X/Y) = logaX - logaY 3. loga(Xk) = k logaX; loga

k

Restrictions with Logarithm of any number

4. loga1 = 0 (As a0 = 1)

For logarithm of any number to be defined, number should be greater than zero and base should be positive and not equal to 1.

6. logaX = 1 / logxa

i.e., For log logax to be defined, x > 0 and a > 0 as well a ≠ 1.

logaX = logbX / logba

It can be seen with the help of graph of log x also (given alongside).

⇒ logaX × logba = logbX

Following observations can be made from this graph i. Value of y can be negative for some value of x. ii. Value of x cannot be negative in any case.

X = 1/k × logaX

5. log xX = 1 7. Base change rule

8. a

(log a x )

=x

9. If a>1 and X>a, logaX>0 10. If 0 < x < y then log x < log y (i.e., log x is an increasing function). In particular if x > 1 then log x > 0 and if 0 < x < 1 then log x < 0.

Miscellaneous  11. If a > 1 and 0 < x < y then logax < loga y and ax < ay. If 0 < a < 1 and 0 < x < y then loga x > loga y and ax > ay. 12. Log of 0 and negative numbers is not defined.

  1.219

Worked out Examples Example  8 Example 

8

Find the number of digits in the expansion of 2150.

Characteristic and Mantissa The integral part of logarithm is called Characteristic and its decimal part is called Mantissa. Logarithms to the base 10 are called Common logarithms. The Characteristic of common logarithm can be found out by visual inspection. The Characteristics of the logarithm (base 10) of a number greater than 1 is less by one than the number of digits in the integral part and is positive. However if a decimal fraction number is less than1 but positive, its characteristic will greater by unity than the number of consecutives zeros immediately after the decimal point and is negative.

Solution Solution

Taking log = 150 log 2 = 150 × 0.301 = 45.01. Number of digits = 45 Greatest integer value = No. of digits

  EXERCISE  1 1. The total number of terms in the expansion of (x + a)100 + (x – a)100 after simplification is

7. Year 200X is a leap year. Which of the following year will definitely be a leap year again?

1.  202 4.  101

1.  200X+4 3.  200X+2

2.  51 5.  None of these

3.  50

2. The number of terms of terms in the expansion (x+y+z)10 is 1.  11 4.  55

2.  33 5.  None of these

3.  66

3. If 3×+1 = 6 log 2 3 then x is 1.  2 4.  log23

2.  3 5.  1

3.  log32

4. If log4 5 = 1 and log5 6 = b then what is the value of log3 2? 1 1. ​ ____    ​   2a+1

1 2. ​ ____    ​   2b+1

1 4. ​ _____      ​ 2ab–1

5. None of these

3. 2ab + 1

2.  log 3 5.  None of these

3.  1

6. What is the number of leap years in between any 100 consecutive years? 1.  24 4.  23

8. 10 June 1979, was a Sunday. Then 10 May 1972, was a 1.  Wednesday 4.  Friday

2.  Thursday 5.  Sunday

3.  Tuesday

9. In a certain year, the month of January had exactly four Wednesdays and four Sundays. Then January 1 of that year was a 1.  Monday 4.  Saturday

2.  Thursday 5.  Tuesday

3.  Friday

10. A. I was born in a century in which the last year of the previous century was leap year. B. I was born in the first year after the first leap year of the century. C. I was born after A B 1200 and before A D 2000

25 81 16 __ __ 5. Find the value of 3log ​ __ 80 ​+5log ​ 24 ​+7log ​ 15 ​.

1.  log 2 4.  log(1/3)

2.  200X+5 3.  200X+6 5.  cannot be determined

2.  25 3.  26 5.  Cannot be determined

What is the year of my birth? 1.  1405 4.  1705

2.  1505 5.  1655

3.  1605

11. If a < 22 and b > 12, then which of the following is always true? 1.  a > b 2.  a – b > 10 3.  a – b < 10 4.  a + b > 34 5.  None of these

1.220 

  Quantitative Aptitude and Data Interpretation

12. If x, y and z are such that x0, then

2. ​ __xz ​< _​ zy ​

1.  ____ ​ y >x 1 ​  

4.  xz _​ z ​

5. None of these

Direction for questions 13 to 16:  Find the values of x for which the inequality holds true.  

_____

13. x+2 < ​√  x+14 ​  1.  -2 ≤ x < 14

2.  -14 ≤ x < 2

3.  x≤ -2 or x>14

4.  x2

1.  1 ​ _ 15. ​ ___ 2 ​

1.  60(2+√3)m 4.  100(2+√3)m

 

2.  100​ √  3 ​   5.  None of these

24. A pole being broken by the wind, the top a struck the ground at an angle of 30° and a distance of the 21 m from the foot of the pole. Find the total height of the pole.

3.  –1 < x < 3, x ≠ 2

1.  2 < x < 5 4.  x < 2 or x > 5

3.  60°

22. A tower stands on a horizontal plane. A man on the ground 100 m from the base of the tower finds the angle of elevation of the top of the tower to be 30°. What is the height of the tower?

​ √  3 ​ 

2.  1 < x < 3, x ≠ 2

2.  2

2.  45° 5.  75°

23. When the sun is 30° above the horizontal, the length of shadow cast by a building 50 m high is

14. (x-1) (3-x) (x-2)2 >0

1.  1

1.  30° 4.  90°

1.  100 m 4.  100√2 m

5.  –14 < x < 3

1.  -52 2 2 | x | − | x | − 2 holds if and only if 1.  -1 < x < -2/3 or 2/3 < x< 1;

32. 1st January of Year 19XY and 1st January of year 19PQ are same day. It is also given that no other year before 19PQ has its 1st January on the same day as that of 1st January of 19XY. What is the minimum possible value of | PQ-XY|, where PQ and XY are the last two digits of the year?

2.  -1 < x < 1;

1.  5 4.  13

39. What are the values of x satisfying

2.  6 5.  7

3.  11

2.  6 5.  7

4.  x > 1 or x < -1 or – ​ _23 ​< x < _​ 23 ​ 5. None of these |x-2| ≤ 2 and |x+3| ≥ 4?

33. In the above question, what is maximum possible value of | PQ-XY|, where PQ and XY are the last two digits of the year? 1.  5 4.  13

3. ​ _23 ​< x < 1;

3.  11

1.  1 < x < 4

2.  1 ≤ x ≤ 4

4.  1 < x or x > 4

5.  None of these

Direction for questions 40 to 42:  Find the values of x for which the inequality holds true.

Direction for questions 34 and 35:  Read the passage below and solve the questions based on it.

x – 5x +  6  40. ​ ________ ​  0, d>0 and ​ __ba ​ < ​ __dc ​, then which of the following is true? a–c __ 1. ​ __ba ​ < ​ ____ ​ w and (ii)  If x > z, then y < w One of the following statements given below is a valid conclusion. Which one is it? 1.  If x < y then z < w 2.  If x < z then y > w 3.  If x > y + z then z < y 4.  If x > y + z then z > y 5.  None of these 15. If xy + x + y = 2, then which of the following is true?  x +1 x–1 x+2 1.   2.  ​ ___ ​ y+2  ​     ​>0 3. ​ ___ >0 y–1  ​ >1  y + 1 

(  )

x–2 4. ​ ___ y–2  ​> 0

17. The angle of elevation of the top of an incomplete vertical pole at a horizontal distance of 100 m from its base is 45o. If the angle of elevation of the top of the complete pole at the same point is to be 60o, then the height of the incomplete pole to be increased by

5.  None of these

3×5×7×....................×99 16. Let N = ​  _______________________         ​ 2×4×6×........................................100

Then which of the following is true regarding the value of N? 1.  1/3 < N < ½ 2.  1/5 < N < ¼ 3.  1/15 < N < 1/10

 

__

2.  10 ​ √ __3 ​ m   5.  25​ √  2 ​ m

3.  20 m

19. Amitabh makes a road trip to the Hooghly beach. If he averaged his speed 5kmph more, he could have decreased his time by 10%. On the other hand, if he averaged his speed 5 kmph less, the journey to the beach would have taken an extra hour. What is the distance from Amitabh’s home to the Hooghly beach? 1.  380 km 4.  360 km

2.  420 km 5.  390 km

3.  275 km

20. The length of a ladder exactly equals the height of a wall. If the ladder is placed on a 2 ft. tall stool placed 10ft. away from the wall, then its tip can just touch the top of the wall. The height of the wall is 1.  15 ft 4.  32 ft

2.  26 ft 5.  27 ft

3.  28 ft

21. A tree of height 21 m on a roadside broke at a certain height and fell in such a way that its top touched the other edge of the road. If the breadth of the road is 12 m, then the height above the ground at which the tree broke was 1.  12 m 4.  6.5 m

2.  6 m 5.  None of these

3.  9 m

22. If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of 2√3 metres along the ground then the angle(in degrees) that the sun makes with the ground is 1.  30o 4.  75o

2.  60o 5.  None of these

3.  45o

  1.225

Miscellaneous  23. In a chess tournament, each of the 5 players plays against every other player. No game results in a draw and the winner of each game gets one point and the loser gets zero. Then which one of the following sequences cannot represent the scores of the five players?

29. If logkN = 6, and log25k(8N)=3, then k is

1.  3,3,2,1,1 4.  4, 4,1,1,0

(logba . logca –loga) + (loga b logc b – logb b) + (loga c logb c – logc c) = 0. What is the value of abc?

2.  3,2,2,2,1. 5.  3,2,4,1,0

3.  2,2,2,2,2.

24. Let P, Q, R, S and T be statements such that if P is true then both Q and S are true, and if both R and S are true then T is false. We then have: 1.  If T is true then both P and R must be true. 2.  If T is true then both P and R must be false. 3.  If T is true then at least one of P and R must be true. 4.  If T is true then at least one of P and R must be false. 5.  None of these 25. If A, B, C and D are statements such that if at least one of A and B is true, then at least one of C and D must be true. Further, both A and C are false. Then

1.  12.5 2 _ 4.  (12.5) ​ 3 ​

3. ​ _52 ​

2.  (12.5)2 5.  None of these

30. If a, b, c are distinct positive numbers (≠ 1) such that

1.  1 4.  2

2.  0 5.  -2

3.  -1

31. If 4 log 9 3 + 9log 2 4 = 10 log x 8 , x εR, how many values can x take? 1.  0 4.  3

2.  1 5.  4

3.  2

32. How many values of x (x >1) satisfy the following equation? log2 x.log4 x.log6 x = log2x.log4 x + log2 x . log6 x + log4 x.log6 x.

1.  If D is false then B is false 2.  Both B and D are false 3.  Both B and D are true 4.  If D is true then B is true 5. None of these

1.  0 2.  1 3.  2 4.  More than 2. 5.  None of these

26. A club has 108 members. Two third of them are men and the rest are women. All members are married except for 9 women members. How many married women are there is the club?

33. A person walking along a straight __road towards a hill   observes at two points, distance ​ √  3 ​  km, the angles of elevation of the hill to be 30° and 60°. The height of the hill is __ __

1.  20 4.  30

2.  24 5.  32

3.  27

2.  1 5.  3

__

 

4.  ​√  3 ​ km

log a log b log c a b c 27. If ​ ____   ​= ​ ____  ​= ​ ____ c–a   b–c   a–b   ​then a b c is

1.  0 4.  2

1. ​ _32 ​km

3.  0.5

 

​√  3 ​ +1

2.  ​  _​ 23 ​ ​ km 3. ​ ____ ​ km 2    5.  None of these

√

 

34. The tops of two poles of height 20 m and 14 m of are connected by a wire. If the wire makes an angle 30° with the horizontal, then the length of the wire is

28. If x > 1, y > 1, z > 1 are three numbers in GP 1 1 1 then ​ ______   x   ​, ​ ______   y   ​, ​ ______   z   ​are in 1+log 1+log 1+log

1.  12m 4.  9 m

1.  AP

35. The angles of elevation of the top of a tower from points at distance A and B from the base and in the same line with it are complementary. If A> B, then height of the tower is

2.  HP 3.  GP 4.  AP or HP 5.  GP or HP

 

____

1. ​ √ ___ B–A ​     4. ​√  BA ​  

2.  10 m 5.  None of these

 

__

2. ​ √  B ​ /A 5. None of these

3.  8 m

 

_____

3. ​ √  B+A ​ 

  Quantitative Aptitude and Data Interpretation

ANSWER KEYS

1.226 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

3

3.

1

4.

1

5.

3

6.

2

7.

2

8.

1

9.

4

10.

4

11.

2

12.

2

13.

2

14.

4

15.

1

16.

3

17.

1

18.

4

19.

4

20.

2

21.

5

22.

2

23.

4

24.

4

25.

1

26.

3

27.

2

28.

2

29.

1

30.

1

31.

2

32.

2

33.

1

34.

1

35.

4

r e v i e w

t e s t

 4

Algebra This review test

based on the following chapters

  Set Theory   Equations   Sequence and Series   Function, Graphs and Maxima Minima   Permutations, Combinations and Probability   Miscellaneous

  INSTRUCTIONS 1. This test contains 20 questions. You have forty-five minutes to complete the test. 2. All questions carry four marks each. Each wrong answer will attract a penalty of one mark. 3. Do your rough work only on the Test Booklet and not on the Answer Sheet. 1. If the equation x³ – ax² + bx – a = 0 has three real roots, then it must be the case that 1.  b =1 2.  b ≠ 1 3.  a = 1 4.  a ≠ 1 5.  None of these 2. The number of non-negative real roots of 2x – x –1 = 0 equals

1.  0 4.  3

2.  1 5.  5

3.  2

3. When the curves y = log10x and y = x-1 are drawn in the x-y plane, how many times do they intersect for values x>1? 1.  Never 4.  Thrice

2.  Once 5.  More than thrice

3.  Twice

4. p and q are positive real numbers such that p + q = 6. What will be the maximum value of pq2? 1.  8 4.  9

2.  16 5.  None of these

3.  32

5. We have 1200 metres of fencing material, and wish to enclose two equal rectangular areas as shown in the diagram below:

1.228 

  Quantitative Aptitude and Data Interpretation

1.  P2/ P1 4.  (P2+ P1)/ P2

y

13. Let N = { x | x be a prime number and x < 30}. The number of distinct rational numbers whose numerator and denominator belong to set N is:

x What is the maximum area (m2) of the diagram given above that can be enclosed (2x is the total length and y is the breadth. Fencing has to be done between the rectangular areas too, as shown in the diagram. 1.  30000 4.  60000

2.  40000 5.  None of these

2 + 4x – ​ ≥ 7  2 6. Find x: ​ x_________ x+4   i.  – 5 ≤ x ≤ -4 ii.  x ≥ 3

1.  i only 4.  i and iii only

2.  1 5.  -2

3.  10C2 + 1

Direction for questions 14 to 16:  Read the passage below and solve the questions based on it.

iii.  x ≥ 2

i.  OPEN – Position the book at page number 1.

3.  128

8. If the quadratic equation px2 – qx + 5 = 0 does not have 2 distinct real roots, what is the minimum value of 5p + q? 1.  9 4.  3

2.  10P2 5.  None of these

The pages of a book are numbered 0,1,2,……P, P >0. There are four categories of instructions that direct a person in positioning the pages in the book. The instruction types with their meanings are given below:

2.  ii only 3.  i and ii only 5.  i, ii and iii only

2.  18 5.  An never equals 2

1.  10C2 4.  10P2 + 1

3.  50000

7. We define a function h on the integers h(x) = x/10, if x is divisible by 10, and h(x) = x+1 if x is not divisible by 10. If A0 = 1994 and An+1 = h(An), what is the smallest n such that An = 2? 1.  9 4.  1993

2.  P1/ P2 3.  (P2 - P1)/P1 5.  Cannot be determined

3.  -1

ii.  CLOSE – Position the book at page number 0. iii. FORWARD, n – From the current page, move forward by n pages. If, in this process, page number P is reached, stop at P. iv. BACKWARD, n – From the current page, move backward by n pages. If, in this process, page number 0 is reached, stop at page no. 0. In each of the following questions, you will find a sequence of instructions. Let p1 be the page no. before the instructions are given and p2 be page no. after executing all the instructions given. 14. FORWARD, 30; BACKWARD, 12. Which of the following statements is true? 1.  p1 = p2, if P = 12 and p1 = 0 2.  P = 25, provided p1>0 3.  p1>35, provided P = 100 4.  p1 = 40, provided P =30 5.  None of these

9. In an examination of 9 subjects, a student has to pass in more subjects than the number of subjects in which the student fails, in order to be successful. What is the number of ways in which a student can be unsuccessful?



1.  1024 4.  1124

15. BACKWARD, 7; FORWARD, 7. Which of the following statements is true?

2.  532 5.  792

3.  256

10. For what value of p, the area enclosed between y = x2 – 3 and y = px + 2 is the least? 1.  0 4.  2

2.  1 5.  -2

3.  -1

11. If x > y and y > 1, then the value of the expression log x (​ __​ xy ​  ) ​+ logy ​ __​ xy  ​  ​can never be 1.  –1 2.  –0.5 3.  0 4.  1 5.  None of these

(  )

12. A GP consists of 1001 terms. Sum of the terms occupying the odd places is P1 and the sum of the terms occupying the even places is P2. Find the common ratio of this GP.



1.  p1 = p2, if p1 ≥ 7 2.  p1 = p2, if p1 >0 3.  p2 =7, provided P>0 4.  p1>p2, provided P > 0 5.  None of these

16. FORWARD, 15; FORWARD, 15. Which of the following statements is true?

1.  p2 – p1 = 30, only if p1= 0 2.  p2 – p1 = 30, only if p1= 1 and P>30. 3.  p2 – p1 = 15, only if p1= 0 and P=31. 4.  p2>p1, if P >0. 5.  None of these

Review Test 4  17. A telecom service provider engages male and females operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of Rs 250 and Rs 300 per day respectively. In addition, a male operator gets Rs 15 per call he answers and female operator gets Rs 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 of the 12 female operators available for the job? 1.  15 4.  10

2.  14 5.  8



1.  If x < y then z < w 2.  If x < z then y > w 3.  If x > y + z then z < y 4.  If x > y + z then z > y 5.  None of these

19. If xy + x + y = 2, then which of the following is true?

(  )

(  )

1.  ​ ____ ​ x+1 ​    ​ > 0 y+1

2.  ​ ____ ​ x+2 ​    ​ > 0 y+2

x–2 ​ > 4.  ​ ____ y–2  0

x–1 ​ > 3.  ____ ​ y–1   0

5.  None of these

3×5×7×.......................×99 ______________________ ​         ​ 20. Let N = 2×4×6×.......................×100

3.  12

Then which of the following is true regarding the value of N?

18. Let x, y, z, w be positive real numbers, which satisfy the two conditions that



i.  If x > y, then z > w and ii.  If x > z, then y < w One of the following statements given below is a valid conclusion. Which one is it?

ANSWER KEYS

  1.229

1.  1/3 < N < ½ 2.  1/5 < N < ¼ 3.  1/15 < N < 1/10 4.  1/10 < N < 1/5 5.  1/15 < N

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

3

3.

2

4.

3

5.

4

6.

3

7.

1

8.

3

9.

3

10.

1

11.

4

12.

5

13.

4

14.

1

15.

1

16.

2

17.

4

18.

4

19.

1

20.

3

HINTS AND EXPLANATIONS 1. Use the choices. If b = 1, then the factors are (x-a) (x2 + 1). This cannot yield 3 real roots.



2. 2 - x – 1 = 0



x



Under the restriction 4x + 3y = 1200, the quantity 4x 2xy = 2x ​ 4 00 – ​ ___    ​  ​. 3

( 

)

We can therefore try to find a real number x which makes this quantity as large as possible.



⇒ 2x – 1 = x



If we put x = 0, then this is satisfied and if we put x = 1, then also this is satisfied.





Now we put x = 2, then this is not valid.



A1= h(A0) = h(1994) = 1995



A2 = 1996, ….



A6 = 2000



A7 = 200, A8 = 20, A9 = 2



Hence n = 9

3. For the curves to intersect, log10x = x-1 __​ 1 ​or xx =10 Thus, log10x = x

This is possible for only one value of x (2 Rs 2800 profit.

(b)  => Rs. 4125 profit



(c)  => Rs. 1100 profit



(d)  => Rs 2000 profit



(e)  => Rs. 2800 profit

5. From Rcomm, 100 × 50 = Rs 5000

From FRLD, 150 × 25 = Rs 3750.



Total sum for investing = 5000 + 3750 = Rs 8750



No. of INDSEC shares he can buy = 8750/35 = 250 shares

6. (4) After decreasing by 24% production of B type of cloth will be

25 –





Percentage increase =

7. (2) 

22 – 19 300 × 100 = ≈ 16% 19 19

40 + 29 + 23 23 = times 31 + 26 + 19 19

11 + 22 33 × 100 = × 100 = 64.7% 19 + 32 51

1994

1995

1996

1997

1998

0.61

0.57

0.85

0.68

0.70

14. (4)  Export value in 1997 is Rs 25000





Prod. of C = 108000 tonnes





Required difference = 65000 tonnes

11. (4)

25000 – 24000 24000



Rate of export in 1997=







∴ difference in export value = 25000 × 4.16% = Rs. 1040 (approx)

= 4.16%

15. (1) Percentage increase from 1994 to 1995 = (approx)



And that of from 1996 to 1997 =





Difference = 52% – 46% = 6%

16. (2)  Required Percentage =

6 × 100 = 46% 13

11 × 100 = 52% 21

3100 + 4200 × 100 ≈ 150% 2100 + 2800

18. (3) In the year 1994 and 1997, there is more production than demand and the rest year there is more demand than production.



∴ Ratio = 4 : 2 = 2 : 1

19. (1)  Required percentage =

3150 × 100 = 70% 4500

20. (4)  Required percentage =

2100 × 100 ≈ 67% 3100

8. (5)  Prod. of A = 173000 tonnes

10. (5)  % increase =

1998

17. (3) Required number = Avg demand – Avg production = 3435 – 3158 = 277

25 × 24 = 19 100



1997

13. (3)

3. (i) True. (50 + 45.5 + 48.3 + 55 + 53.2 + 57)/6 = Rs 51.5

1996

Value per 15 24 25 22 = 1.15 kg (in Rs) 11 = 1.36 18 =1.33 22 = 1.13 19

2. % increase in Rcomm = 57/50 × 100 = 114%

1995

63 – 60 3 × 100 = × 100 = 5% 60 60

21. (4)  Average consumption of metal B



20 + 25 + 20 + 25 + 27.5 + 30 = 147.5 ≈ 24.5 6 6

22. (3)  Reqd difference = 27500 – 22500 = 5000 tonnes

  Quantitative Aptitude and Data Interpretation

1.238  23. (4)

25. (4)  Percentage decrease

1988

1990

1991

1993

45

45

55

47.5

30 – 22.5 × 100 30



= 25%

  EXERCISE  2 Bar Chart Direction for questions 1 to 5: Go through the data given below and solve the questions based on it. Registration of vehicles (in thousands) in Mumbai over the years. 35

31

30 25

17 11

2.  17% 5.  21%

16

1.  14800 4.  16300

2.  15200 5.  None of these

3.  15800

5. Of the total vehicles registered during the period, what is the percentage of taxi’s approximately? 2.  66% 5.  69%

3.  78%

Direction for questions 6 to 10: Go through the data given below and solve the questions based on it.

13

12

3.  16%

4. Find the average number of taxi’s registered over the given years.

1.  54% 4.  62%

23

21

20 15

27

27

1.  12% 4.  18%

10

Installed capacity, production and imports of fertilizers in India (in 000 tonnes)

5 0 1994 Taxi

1995

1996

2.  2000 5.  None of these

3.  3000

2. What was the average of all the annual percentage increases in the number of registered taxi’s between 1993 to 1996? 1.  25% 4.  37%

2.  29% 5.  41%

8

2010-11

Total Vehicle

1. What was the difference between the number of other vehicles, registered in 1993 and 1997? 1.  1000 4.  4000

Fertilizers statistics

1997

In 000 tonnes

1993

3

2009-10

0

2

14

9 4

2007-08

14

10

3

2008-09

4

Imports

3.  31%

3. Find the difference between the percentage of taxi’s registered in 1995 with respect to the total vehicles and percentage of taxis registered in 1996 with respect to the total vehicles.

10

8 6

8

13 12

10

Production

12

14

16

Capacity

6. Capacity utilization (production/capacity) was lowest in the year 1.  2008-09 4.  2010-11

2.  2007-08 5.  None of these

3.  2009-10

Data Interpretation  7. Import of fertilizer in 2010-11 was approx. what percentage more than that of the previous years? 1.  172% 4.  167%

2.  158% 5.  179%

3.  147%

8. The availability of fertilizer is the sum of production plus import. The minimum difference in availability was between 1.  2007-2008 and 2008-2009 2.  2007-2008 and 2009-2010 3.  2007-2009 and 2009-2010 4.  2009-2010 and 2010-2011 5.  None of these 9. The increase in percentage capacity utilization in 20102011 over that in 2007-2008 was nearly 1.  4.7 4. 3.0

2.  3.4 5.  None of these

3.  4.2

  1.239

12. What is the required run rate for Pakistan to win the match after 40 overs, if Pakistan wins the match. (Disregard the data given for Pakistan in overs 40–50)? 1.  12.3 4.  13.8

2.  13.3 5.  12.8

3.  10.8

13. By how much run India has won the match? 1.  84 runs 4.  73 runs

2.  74 runs 5.  None of these

3.  63 runs

14. Between 10 to 30 overs (excluding 10th over) runs scored by Pakistan is what percentage of the runs scored by India between 0 to 20 overs (approx)? 1.  96% 4.  82%

2.  90% 5.  75%

3.  80%

15. Average run rate of India in 20–50 overs is what percentage of the average run rate of Pakistan in 20–50 overs?

10. The proportion of imported to production was highest in

1.  75% 4.  132%

1.  2007-2008 4.  2010-2011

2.  2008-2009 3.  2009-2010 5.  None of these

Direction for questions 16 to 20: Go through the data given below and solve the questions based on it.

Direction for questions 11 to 15: Go through the data given below and solve the questions based on it.

Graph shows the production of three type of minerals over the given years.

Runs scored by India and Pakistan (Pak) in 50 overs in the ODI played in world cup. 71

70

(run scored)

60

63

57

47

50

52

49

45

37

40

67

35

30 20

90 Production (in thousand tonnes)

80

0 0-10

10-20

20-30 Overs

30-40

40-50

3.  126%

84

80

80

72

70

63

60

56

50

30 24

28

54

49

47

40

34

51

57 48

55

51

42

30

20 10 0

10

2.  85% 5.  None of these

1990-91 1991-92 1992-93 1993-94 1994-95 1995-96

Zinc

Nickel

Lead

11. What is the average run rate of India after 30 overs?

16. What is the difference between annual average production of Nickel and Lead? 2.  9000 tonnes 1.  7000 tonnes 3.  11000 tonnes 4.  12000 tonnes 5.  None of these

1.  5.65 4.  6.25

17. The production of Zinc in 1994-95 is what percentage of its total production over the given years?

India

Pak

2.  5.49 5.  None of these

3.  5.26

  Quantitative Aptitude and Data Interpretation

1.240 

1.  22% 4.  30%

2.  25% 5.  35%

Note: (1) Profit = Sales – Expenses; Loss = Expenses

3.  27%

– Sales

18. Two fifth of the production of Nickel in 1992-93 is approximately what percentage of one-third of the production of Lead in 1995-96? 1.  50% 4.  80%

2.  60% 5.  100%

Profit occurs when sales > expenses, loss occurs when expenses > sales (2) Profit/loss should be added/subtracted to the company’s equity at the end of every year.

3.  70%

(3) All the data points above are as on 31st Dec of respective years. Initially, promoters infused an equity of INR 50 million on 1st Jan 1997 (the day when company was established).

19. Find the approximate percentage increase in the production of given minerals in 1992-93. 1.  12% 4.  18%

2.  15% 5.  20%

3.  16%

2 0. Which of the following statements is wrong? (i)  In 1993-94 the percentage increase in production of Nickel is 70%. (ii)  The ratio between the no. of years in which production of Lead is above average and below average is 2 : 3. (iii) Percentage fall in the production of Zinc in 199596 with respect to previous year is 15%. (iv) The average production of Nickel is 40 thousand tones (v)  None of these

21. What was the simple average growth rate per annum of sales between 1997 and 2000?

Direction for questions 21 to 25: Go through the data given below and solve the questions based on it.

1.  0 4.  3

Refer to the sales, expenses and equity graph of a company over a period of five years given below:

24. What net amount (in mn INR) was added to company equity over the 5 year period (excluding the initial equity)?

1.  25% 4.  15.5%

1.  1999 4.  1998

2.  2000 5.  None of these

3.  2001

23. How many years there was a loss? 2.  1 5.  None of these

1.  Rs 50 4.  Rs 200

250 200

2.  Rs 100 5.  None of these

3.  2

3.  Rs 150

25. In which year was the ratio of sales to expenses the lowest?

150

1.  1998 4.  2001

100

2.  1999 5.  None of these

50 1997

1999

1998

Sales

Expenses

ANSWER KEYS

0

3.  11.4%

22. In which year the ratio of equity to profit was the highest?

300

INR million

2.  8.33% 5. None of these

2000

2001

Equity

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

4

3.

2

4.

3

5.

2

6.

2

7.

4

8.

1

9.

1

10.

4

11.

5

12.

2

13.

5

14.

4

15.

4

16.

3

17.

1

18.

3

19.

4

20.

3

21.

5

22.

4

23.

3

24.

1

25.

2

3.  2000

  1.241

Data Interpretation 

HINTS AND EXPLANATIONS 1. (4) Diff. in other vehicles = (27 – 13) – ( 21 – 11) = 4000.

2. (4) 

100 400 1100 + + 11 12 16

58700 = 37% (approx.) 528 × 3

=

3 27 16 × 100 – × 100 = 87% – 70% = 17% (approx.) 3. (2)  31 23 5. (2)  Percentage of taxis =

79 × 100 ≈ 66% 119

2007-2008

2008-2009

2009-2010

2010-2011

66.7%

69.2%

71.4%

71.4%

2010-11 =



Average run rate of Pak after 20 overs = 4.53





Required per cent =





‘07 – 08 and ‘08 – 09 = (12 – 12) = 0





In ‘08 – 09 and ‘09 – 10 = 13 – 12 = 1000 tonnes





In ‚09 – 10 and‚ 10 – 11 = 17–13 = 4000 tonnes



Hence the change was lowest between 07–08 and 08 – 09

9. (1)  Difference in capacity utilization = 71.4 – 66.7 = 4.7

2007-08

2008-09

2009-10

2010-11

Value

0.5

0.33

0.30

0.80

11. (5)  Run scored in 30 overs = 57 + 63 + 45 = 165

∴ Average =





Run scored by Pakistan in 40 overs is = 171





In 10 overs required = 133





Hence run rate required = 13.3 runs per over

13. (5)  Total Indian score = 303 India win by = 83 runs

× 100 =

25 × 100 ≈ 18% 139 2 % 7

1997

1998

1999

2000

2001

Equity

100

150

100

50

100

Profit

50

50

–50

–50

50

Ratio

2

3

–2

–1

2



14. (4)  Indian score upto 20 overs is = 120



Pak score between 11 to 30 overs = 99





Required per cent

99 × 100 = 82.5% 120

Equity/Profit = highest for 1998.

24. (1) Profit/loss should be added/subtracted to the company’s equity at the end of every year.



165 = 5.5 30 12. (2)  Run required to win the match = 303 + 1 = 304



164–139 139

12 × 100 ≈ 70% 17

23. (3)  Loss years are 1999 and 2000.

Year



× 100 =

1 × 51 3

19. (4)  Required % =



10. (4)  Proportion of imported to utilized capacity.

Total Pak’s score = 220

2 × 30 5

22. (4)

8. (1)  Difference in availability of fertilizer between



84 × 100 ≈ 22% 379

17. (1)  Required percentage =

21. (5) Simple average growth rate in sales between 1997 and 2000 is zero, as the sales value remains same.

8–3 × 100 ≈ 167% 3



6.00 × 100 = 132.45% 4.53

20. (3)  Percentage fall in production of Zinc will be 14

7. (4)  Percentage change in import from 2009-2010 to



18. (3)  Required % =

6. (2)  Capacity utilization:



15. (4)  Average run rate of India after 20 overs = 6.1

Net amount of addition. 1997

1998

1999

2000

2001

50

50

–50

–50

50

25. (2) Year

1997

1998

1999

2000

2001

Ratio

1.33

1.25

0.75

0.8

1.5

1.242 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  3 Table Direction for questions 1 to 5: Go through the data given below and solve the questions based on it. Production of pressure cooker by different companies in different years (in lakhs). Company year

A

B

C

D

E

F

G

2000

20.5

19.4

23.2

18

17

16.7

14

2001

21.3

18.2

26.5

24.6

20

25

22

2002

16.9

17.6

20.4

22.2

23.5

27

24

2003

19

18

22

27

24

26

2004

35

27

26.4

25

21.2

2005

26.2

29

31.5

18

2006

28

27

26

2007

37

21.2

17.7

Science

Engineering

Appeared Passed Appeared Passed Appeared Passed

32156

4715

8694

1925

25.5

1992

14005

2239

33019

5019

8731

1864

18.7

35

1993

13152

1956

31438

4308

7846

2021

20

22

27

1994

10697

2132

28567

3974

9238

1738

19.2

23

24

32

1995

11648

2062

29348

4526

9465

1824

25

18.7

21

23

1996

9639

1862

32247

4413

8732

1638

2.  31.73% 5.  45.23%

2.  2004 5.  2007

2.  1.2 5.  1.6

2.  74% 5.  54%

Year

3.  2005

3.  1.3

3.  70.5%

Commerce

Total

Appeared

Passed

Appeared

Passed

1991

3169

620

57527

9416

1992

3724

584

59479

9706

1993

4018

675

56454

8960

1994

4269

694

52771

8538

1995

4293

712

54754

9124

1996

4485

730

55103

8643

3.  32.75%

4. Three fourth of the production by company B in 2007 is approximately what per cent of the five-sixth of the production by company D in 2001? 1.  67% 4.  77%

Arts

2156

3. The total production by company A is how many times of the total production by company D for all the given years? 1.  1.1 4.  1.5

Year

13508

2. In which year, the total production of all the companies taken together is maximum? 1.  2003 4.  2006

Number of candidates appeared and passed in different disciplines over the years.

1991

1. Find the percentage increase in the production of pressure cooker by the company F in 2005 with respect to 2000. 1.  29.23% 4.  43.29%

Direction for questions 6 to 10: Go through the data given below and solve the questions based on it.

6. What was the approximate percentage increase in the number of candidates passed under Engineering discipline from 1992 to 1993? 1.  18 4.  8

2.  26 5.  12

3.  32

5. In which of the following years, the percentage increase in the production of pressure cookers from previous year (all the companies taken together) is maximum?

7. In which of the following years was the percentage of candidates passed over appeared the maximum in the case of science discipline?

1.  2001 4.  2004

1.  1992 4.  1991

2.  2002 5.  2007

3.  2003

2.  1994 5.  1995

3.  1996

Data Interpretation  8. In which of the following disciplines was there a continuous increase in the number of candidates appeared over the years? 1.  Arts 2.  Commerce 4.  Science and Commerce 5.  None of these

3.  Science

9. In which of the following years was the percentage of candidates appeared in the Arts discipline approximately 20% w.r.t. total students appeared in Arts over the period? 1.  1995 4.  1992

2.  1996 5.  None of these

3.  1994

10. In which of the following years, in the number of candidates passed under Science discipline was 2.5 times of the candidates passed in the Engineering discipline? 1.  1992 4.  1996

2.  1994 5.  None of these

3.  1993

Direction for questions 11 to 15: Go through the data given below and solve the questions based on it. Numbers of five types of cars produced and rejected (in 000) Car

A

B

C

D

E

Year Prod Rej Prod Rej Prod Rej Prod Rej Prod Rej

5

2.  1 : 2 5.  None of these

1.  2 : 1 4.  4 : 3

  1.243

3.  3 : 4

14. The accepted E type car in 1998 is approximately what percentage more than the accepted A type car in 1996? 1.  120% 4.  175%

2.  135% 5.  185%

3.  142%

15. Find the difference between the total rejected cars in 1993 and 1995. 1.  2900 4.  6300

2.  5900 5.  None of these

3.  4900

Direction for questions 16 to 20: Go through the data given below and solve the questions based on it. Table given below gives the percentage of students passed and total number of students passed in five disciplines across 6 years–from 1994 to 1999. Discipline

Agr

Eng

Com

Arts

Sci

Year

%P No. %P No. %P No. %P No. %P No.

1994

45

1995

50 140 60 180 55 148 68 120 53 145

1996

52 120 64 205 58 150 65 115 52 90

1997

40

95

54 170 45 120 80 85 65 05

86

70 165 60 105 75 135 50 98

80

65 210 50 110 70 96 55 120

93

15

3

45

6.2

32

3.1

55

5.1

63

94

20

4.5

50

6.5

48

4.9

65

7.2

57 3.2

1998

55

95

23

4.2

55

5.7

57

5.8

71 8.5 58 4.1

1999

58 105 55 196 52 135 72 102 65 84

96

28

4.7

35

2.5

72

8.2

61

4.3 67 5.7

97

35

5.5

40

3.2

68

4.5

49

3.1

98

38

4.9

42

5.1

61

3.9

72 4.2 75 8.1

64 2.9

In the table shown, Prod = Produced and Rej = Rejected All the cars produced which are not rejected are accepted. 11. In which of the following years, percentage of type C selected cars was minimum? 1.  1993 4.  1996

2.  1994 5.  1997

3.  1995

12. In 1997, for how many types of cars was the rejection below 10%? 1.  5 4.  2

2.  4 5.  1

3.  3

13. In case of type C car, what is the ratio of the no. of years having above average production to number of years having below average production?

In the table shown Agr = Agriculture, Eng = Engineering, Com = Commerce, Sci = Science and % P= % passed. 16. In how many years was the percentage of students passed under all the disciplines more than 50? 1.  0 4.  3

2.  1 5.  4

3.  2

17. What was the approximate percentage increase in the no. of passed students under commerce discipline from 1998 to 1999? 1.  25 4.  35

2.  20 5.  50

3.  12

18. What was the percentage decrease in the no. of students passed under Arts discipline from 1995 to 1996? 1.  10 4.  5

2.  2 5.  None of these

3.  3

19. Approximately what was the difference in no. of students passed under science discipline from 1995 to 1996?

1.244 

  Quantitative Aptitude and Data Interpretation

1.  8 4.  4

2.  6 5.  14

21. For which of the following cars was the defect minimum in 1996?

3.  24

1.  Indica 4.  Zen

20. In which of the following years was the no. of students passed under Commerce discipline exactly equal to the total no. of student under Agriculture discipline in 1997? 1.  1995 4.  1996

2.  1994 5.  None of these

1.  160 4.  60

Direction for questions 21 to 25: Go through the data given below and solve the questions based on it.

Type year

Ford

Zen

P

D

P

D

P

D

1994

64

12

75

20

45

08 85 14

48

18

1995

80

08

90

12

30

09 95 16

94

14

1996

40

06

65

16

55

06 75 12

84

05

1997

95

09

80

18

25

05 70 10

78

09

1998

75

14

60

19

40

07 65 13

62

11

1999

112

16

55

15

60

04 80 15

37

10

P

1.  50000 4.  100000

2.  500000 5.  None of these

P D

1.  76500 4.  750000

2.  790000 5.  8000000

3.  100000

3.  780000

25. What was the approximate number of defective Indica type car in the year 1999? 1.  30500 4.  200000

2.  300000 5.  182000

In the table shown P= Production and D= % defective

ANSWER KEYS

3.  20

24. What was the approximate number of the Maruti type cars without defect in the year 1996?

Maruti

D

2.  40 5.  None of these

23. What was the difference in the production of Zen type car without defect in 1997 to 1999?

Total no. (in lakhs) of different types of cars produced and % defect under each type in the factory over the years (1994–1999). Matiz

3.  Ford

22. What was the percentage increase in the production of Ford type car from 1997 to 1998?

3.  1999

Indica

2.  Matiz 5.  Maruti

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

1

4.

4

5.

1

6.

4

7.

5

8.

2

9.

4

10.

5

11.

4

12.

2

13.

1

14.

5

15.

2

16.

3

17.

2

18.

5

19.

4

20.

2

21.

1

22.

4

23.

2

24.

5

25.

3

3.  180000

Data Interpretation 

  1.245

HINTS AND EXPLANATIONS 22–16.7 16.7

1. (2)  % increase =

3. (1)  2010-11 =

13. (1)  Average production of C type car over the years

× 100 ≈ 31.73%

203.9 = 1.1 times 179

2 5 15.9 4. (4)  × 100 = 100 ≈ 77% 20.5 1 24.6 × 3



Hence % age increase =

=





∴ Required ratio = 4 : 2 = 2 : 1 66.9 – 23.3 23.3

=

338 = 56.33 6

× 100 ≈ 185%

15. (2) Total number of rejected cars of all types in 1993 = 22400

6. (4) Increase in the number of candidates passed under engineering from 1992-1993 = 2021 – 1864 = 157.



14. (5) 

21.2 ×

32 + 48 + 57 + 72 +68 +61 6







And that in 1995 = 28300





Difference = 5900

16. (3) in 1996 and 1999. In 1995 and 1998, one of the disciplines = 50%.

157 × 100 ≈ 8% 1864

17. (2) 

7. (5)  Percentage of Science. candidates passed in 1995 Year

1991

1992

1994

1995

1996

% passed

14.66%

15.20%

13.91%

15.42%

13.68%

8. (2)  Visual inspection

18. (3)  % decrease =



19. (4) 

9. (4)  Percentage of candidates appeared in Arts discipline

= 53 × 120 – 100

120 – 115 × 100 120 5 120

× 100

52 × 115 100

= 64 – 60 = 4

20. (2)  In 1994 no. of students passed in Commerce

Year

1991

1992

1994

1995

1996

% value

18.59%

19.28%

14.72%

16.03%

13.27%

10. (5) Ratio of no. of candidates passed in Sc. to that of Engg. Year

1991

1992

1994

1995

% value

2.69%

2.13%

2.29%

2.48%

50 × 210 = 105 100





=





= no. of students in Agriculture in 1997

21. (1)  It is lowest for Indica. 22. (4)  Percentage increase =

15 × 100 = 60% 25

23. (2)  85% of 80,00,000 – 90% of 70,00,000

11. (4)

1993

1994

1995

1996

1997

90%

89%

89%

88%

93%

12. (2)



= 68,00,000 – 63,00,000 = 5,00,000

24. (5)  84,00,000 ×

95 = 79,80,000 ≈ 80,00,000 100

25. (3)  16% of 11200000 = 1792000 ≈ 1800000 A

B

C

D

E

15%

8%

6%

6%

4%

  Quantitative Aptitude and Data Interpretation

1.246 

  EXERCISE  4

Pie Chart Direction for questions 1 to 5: Go through the data given below and solve the questions based on it. 2,000 students secured admissions into the 2-year MBA programme beginning in 1997. Figure A given below provides the educational background of this batch of students. The same batch of students graduated in 1999 and had opted for different specializations as indicated in figure B given below. All the students who secured admission in 1997 passed out in 1999. Others 6% CA 4%

Human Resourse Management 7% Systems 18% Engineers Operations 12%  36% Arts 16%

Commerce

20%

Science 18%

A

General Management 16%

Finance 25% Marketing 22% 

B

Figure A:  When they entered in 1997. Figure B:  When they left in 1999. Note: 20% of Engineers and 10% of (Science + commerce) students were with some work experience before joining MBA programme. All others students were without work experience. 1. 40% of students with work experience specialized in Marketing. How many students with specialization in Marketing are without work experience? 1.  352 4.  88

2.  396 5.  None of these

3.  440

2. If 50% of engineers specialized in Systems, how many non-engineers specialized in Systems? 1.  360 4.  160

2.  0 5.  None of these

3.  100

3. What is the difference between the number of students specializing in Finance in 1999 and the number students who had CA or Commerce background? 1.  500 4.  40

2.  480 5.  None of these

3.  20

4. 24% of students of graduating class in 1998 specialized in finance. Find the % increase in the number of students specializing in finance from 1998 to 1999.

1.  1% 3.  3% 5.  None of these

2.  100/24% 4.  Cannot be determined

5. 30% of Engineers and 40% of Commerce students specialized in Finance. The remaining students who specialized in finance were Science graduates. What percentage of Science graduates opted for finance? 1.  24.66% 3.  38.68% 5.  None of these

2.  34.44% 4.  Cannot be determined

Direction for questions 6 to 8: Go through the data given below and solve the questions based on it. Data given below presents the exports from India to other countries/group of countries. Total exports value = $27562 mn

Other East Europe 1% OPEC 10% Russia 3% Japan 6% UK 6%

LDCs 27% Others 9%

Other EU 13%

US 20% Germany 5%

6. Exports to US is how much more than the export to UK? 1.  Data inadequate 2.  $ 13.3 cr 3.  Rs 13.3 cr 4.  $ 3665 million 5.  None of these 7. To which of the following countries/group of countries India’s exports were the highest during the given period? 1.  Other E U 4.  Japan

2.  US 5.  OPEC

3.  LDCs

8. During 1997-98 (Feb-Mar) if the exports is 20% of the exports during 1997-98 (Apr-Jan), find the value of exports to Japan for the period 1997-98 (Apr-Jan). 1.  $ 1852 mn 3.  $1940 mn 5.  None of these

2.  $ 1820 mn 4.  Cannot be determined

Data Interpretation  9. Ratio between export value to Russia and export value to Japan is equal to the ratio between which of the following pairs of countries?

1.  12886 4.  13792

1.  OPEC and US 3.  USA and OPEC 5.  None of these

Direction for questions 15 to 17: Go through the data given below and solve the questions based on it.

2.  Germany and LDCs 4.  Others and OPEC

E 10% D 18% C 22%

China 15%

B 26%

Chart 2 US 15%

11. What is the difference between the number of type C and D managers in the organization? 3.  984

12. Organization appoints another 600 type C managers without changing any other type of managers. What would be the approximate percentage of B now? 1.  24 4.  23

2.  56 5.  25

India 20%

Chart 1 shows the distribution by value of top 6 suppliers of MFA textiles in 1995. Chart 2 show the distribution by quantity of top 6 suppliers of MFA textiles in 1995. The total value is Rs 5760 million. The total production is 1.055 million tones.

A 24%

2.  820 5.  None of these

Pakistan 12%

Turkey 16%

The following diagram represents percentage figures of the five types of managers in a company. Total number of managers = 16400.

1.  656 4.  1312

Switzerland 20%

USA 17%

2.  $ 3452 mn 3.  $ 2756 mn 5.  Cannot be determined

Direction for questions 11 to 14: Go through the data given below and solve the questions based on it.

3.  14332

Chart 1

10. Half of India’s exports to US is consumed domestically and other half is re-exported to Japan. What is Japan’s total import of this commodity (approx)? 1.  $ 3031 mn 4.  $ 2544 mn

2.  13284 5.  None of these

  1.247

3.  21

Switzerland 11% Pakistan 16%

Turkey 15%

China 17%

India 26%

13. If the organization retrenches 2400 managers, what would be the approximate percentage of A type managers?

15. The country which has the lowest average price is

1.  26 4.  28

16. The country which has the highest average price is

2.  22 3.  32 5.  Cannot be determined

14. Next year, half of the total managers from B category, 25% of the managers from the A category will be promoted to higher positions inside the company. If there are no new recruitments in the company and no manager goes out of the organization, what is the total number of above five types managers in the company?

1.  US 4.  Switzerland 1.  US 4.  Switzerland

2.  India 5.  None of these 2.  India 5.  None of these

3.  Pakistan

3.  Pakistan

17. The average price in Rs per kilogram for Turkey is approximately 1.  3.20 4.  7.20

2.  4.60 5.  6.3

3.  5.60

1.248 

  Quantitative Aptitude and Data Interpretation

Direction for question 18 to 20: Refer to the pie-chart

18. What is the increase in sales of A over the five years?

The pie-charts show the market shares of various products in the year 1995 and 2000.

1.  $415 million 3.  $295 million 5.  None of these

below and answer the questions that follow.

E 20%

F 9%

A 16% B 17%

D 35%

19. What is the CAGR at which the market has grown for the period 1995-2000?

2000

1995

C 12%

1.  18% 4.  12%

B 14%

D 28%

Market Size = $ 2.3 billion

ANSWER KEYS

A 19%

E 17%

2.  $492 million 4.  $335 million

2.  10% 5.  13%

3.  6%

20. Which of the following has recorded maximum percentage growth during the given period?

C 13%

1.  A 4.  D

Market Size = $ 3.7 billion

2.  B 5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

2

3.

3

4.

4

5.

2

6.

5

7.

3

8.

2

9.

1

10.

5

11.

1

12.

5

13.

5

14.

2

15.

3

16.

4

17.

3

18.

4

19.

2

20.

1

3.  C

HINTS AND EXPLANATIONS 1. (1)  Students with work experience





= 36% × 20% × 2000 + 10% [38% of 2000]





= 2000 × [36% × 20% + 38% × 10%] = 220



Now Marketing students with work experience = 40% of 220 = 88







So, Marketing students without work experience = 440 – 88 = 352

So, Total Marketing students = 22% of 2000 = 440

2. (2)  Number of students specializing Systems = 360



Number of Engineers specializing Systems = 360



So number of non-engineers specializing Systems = 0



Alternatively, this question can be done by seeing only the percentage values too.

3. (3) Number of students specializing in Finance = 25% of 2000 = 500 Total number of CA = (20 + 4)% of 2000 = 480

or

Commerce

Difference = 500 – 480 = 20

4. (4) Since total number of students doing graduation in 1998 in not known, this question cannot be answered.







students

5. (2) Number of engineers who specialized in Finance = 30% × 36% × 2000 = 216

Number of Commerce students who specialized in Finance = 40% × 20% × 2000 = 160



So, number of Science graduates specializing in Finance = (25% of 2000) – 216 – 160 = 124









∴ % of Science students specializing in Finance 124 = × 100 = 34.44% 18% of 2000

6. (5)  Export to USA = 20% of $27562 mn





Therefore required difference = (20%–6%) of $27562 mn





8. (4) 

Export to UK = 6% of $27562 mn.

= 14% of $27562 m = $3858.68 mn

Data Interpretation  9. (1)  Ratio = 0.5 10. (5) Pie chart gives the total export from India to different places. Japan and other countries may be importing from other countries too. 4 11. (1)  Difference = 16,400 × = 656 100 12. (5)  B → 16,400 ×

26 = 4264 100



After 600 employees appointed



So, the total no. of employees = 17,000 4264 % of B = × 100 ≈ 25% 17000



13. (5) We don’t know that retrenchment happened from which area. So cannot be determined. 14. (2) Total percentage of managers to be promoted = 19%

Hence left in these five categories = 81%



Total managers left = 81% of 16400 = 13284

15. (3) To compare the price per kg (or to find lowest average price), we need, not calculate the actual price. Just calculate the ratio

  1.249

of the percentage figure given in the chart 1 and in chart 2. Minimum value of this comes for Pakistan. 16. (4) See the solution of above question. In this case, we need to find out the maximum value. 17. (3) Look at the options. There is only one option in between 5 and 6. Value will be somewhere between 5 and 6 (5760/1055). 18. (4) Sales of ‘A’ in 1995 = (0.16 × 2.3) billion = 368 million. Sales of ‘A’ in 2000 = (0.19 × 3.7 ) billion = 703 million. Therefore, increase in sales = 703 – 368 = $ 335 million. 19. (2)  Market size in 2000 = $ 3.7 billion.

Market size in 1995 = $ 2.3 billion.

1    3.7  5   – 1 × 100 = 10 % Therefore, growth rate =    2.3    

20. (1)  % growth is market share is more than the % growth in the market share of all others. Hence option (1) is the answer.

1.250 

  Quantitative Aptitude and Data Interpretation

  EXERCISE  5 Combination of Charts Direction for questions 1 to 4: Go through the data given below and solve the questions based on it. The given table below reports annual statistics of rice production in select states of India for a particular year. Total area

State

% of Area Under

6 4 34 10 19 4 9 20 5 31 13 31 24 28

20 60 20 60 50 80 80 60 80 40 70 50 70 80

1. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat? 2.  4 5.  None of these

3.  5

2.  8 5.  None of these

Proportion of population of seven village in 1995 F 15%

3.  6

G A 12% 13%

E 19%

D 16%

B 15% C 10%

The table gives the percentage of the population in that particular village below poverty line:

1.  Haryana and Punjab 2.  Punjab and Andhra Pradesh 3.  Andhra Pradesh and Haryana 4.  Uttar Pradesh and Haryana 5.  None of these 4. How many states have % area under rice cultivation more than 40% and population (in millions) more than 5? 2.  9 5.  None of these

6 32 56 83 53 21 80 51 24 60 62 97 166 76

Below given pie chart presents the percentage of population of Bachwaran block comprising of the following 7 villages—A, B, C, D, E, F and G. [for the sake of calculation assume fractional values are also possible]

3. Which two states account for the highest productivity of rice (tons produced per hectare of rice cultivation)?

1.  8 4.  11

(in millions)

12 48 68 12 19 19.2 21.6 24 24 24.8 27.3 48 67.2 112

2. An intensive rice producing state is defined as one whose annual rice production per million of its population is at least 400,000 tonnes. How many states are intensive rice producing states? 1.  3 4.  7

Population

(in million hectors) Rice Cultivation (in millions tons)

Himachal Pradesh Kerala Rajasthan Bihar Karnataka Haryana West Bengal Gujarat Punjab Madhya Pradesh Tamilnadu Maharashtra Uttar Pradesh Andhra Pradesh

1.  3 4.  6

Production

3.  10

Direction for questions 5 to 9: Go through the data given below and solve the questions based on it.

Village

% population below poverty line

A

55

B

48

C

36

D

60

E

42

F

43

G

49

Data Interpretation 

8. If the population of village C below poverty line in 1995 was 1520, what was the approximate population of village F in 1995? 1.  5800 2.  6300 3.  6400 4.  6500 5.  6200 9. The population of village C is 2000 in 1995. What will be the ratio of population of village C below poverty line to that of the village E below poverty line in that year? 2 4 6 1.  2.  3.  7 7 7 1 4.  5.  None of these 7 Direction for questions 10 to 12: Go through the data given below and solve the questions based on it. Following bar chart gives the distribution of greenland in the following countries. Total greenland area = 13,754 km2

50%

73

67

58

43

Malayasia 5%

Japan 9%

Canada 23% Pakistan 6%

China 25%

Brazil 16%

si a isi tan

n

Protected

Pa k

a la ya

Jap a

d ia

In

i na

da

Ch

na

41

10. What is the difference of protected and unprotected greenland (approx.)? 1.  30150 4.  26540

2.  32750 5.  None of these

3.  28450

11. Which country has the maximum protected greenland? 1.  China 4.  Canada

2.  Japan 5.  India

3.  Brazil

12. Protected greenland of India is what percentage of the protected green land of Pakistan? 1.  48% 4.  210%

2.  65% 5.  250%

3.  160%

Direction for questions 13 to 17: Go through the data given below and solve the questions based on it. The total population of the different states in 1993 is 25 lakhs. AP 9%

India 16%

Unprotected

78 34

il

40% 30% 20% 10% 0%

M

7. If in 1995 the total population of the seven villages together was 55,000, what will be population of village F in that year below poverty line? 1.  3000 2.  3600 3.  3550 4.  3400 5.  Cannot be determined

100% 90% 80% 70% 60%

Ca

6. If in 1997 the population of village D is increased by 10% and the population of village G is reduced by 5% from 1995 and the population of village G in 1995 was 9000, what is the total population of village D and G in 1997? 1.  19250 2.  21670 3.  22000 4.  22500 5.  None of these

Some of these greenlands are protected and remaining are unprotected. Following bar chart gives that distribution.

Br az

5. In 1996, the population of villages A as well as B is increased by 10% from the year 1995. If the population of village A in 1995 was 5000 and the percentage of population below poverty line in 1996 remains same as in 1995, find the population of village B below poverty line in 1996. 1.  3128 2.  3264 3.  3168 4.  3100 5.  None of these

  1.251

Karnataka 13%

UP 28%

Maharashtra 10% T.N 11%

Bihar 21% Kerala 8%

Sex-and-literacywise population ratio

  Quantitative Aptitude and Data Interpretation

1.252 

Sex

Literacy

M- F

Literate–illiterate

UP

4:3

3:8

Bihar

3:2

3:7

AP

4:3

2:1

Karnataka

4:5

3:4

Maharashtra

4:5

3:2

Tamil Nadu

3:4

7:3

Kerala

5:6

9:5

States

17. In Tamil Nadu, if 70% of the females are literate and 75% of the males are literate, what is the approximate number of illiterate in the state? 1.  75000 4.  80000

Following data gives the annual food production and annual fertilizer production during the period 1983–1991. Answer the questions based on it.

Food production

3.  24%

14. If in the year 1993 there was an increase of 10% population of U P and 12% of Bihar compared to the previous year, then what was the ratio of the population of UP to Bihar? 27 1.  32 4. 

23 42

31 2.  42

4. 

121 84

5.  None of these

ANSWER KEYS

2. 

3. 

100

100

50

50 1983 1984 19851986 1987 1988 19891990 1991

1.  1983-84 4.  1988-89

0

Fertilizer production

2.  1984-85 5.  1990-91

3.  1985-86

19. Fertilizer production in 1992 is expected to 1.  go up 2.  go down 3.  remain roughly the same as that of the previous year 4.  Cannot be determined 5.  None of these

3.  50%

242 43

150

150

18. In which of the following years is there an increase in food production with increase in fertilizer production?

16. What is the ratio of the number of females in Tamil Nadu to the number of females in Kerala? 21 138

200

200

All the values are multiples of 10.

5.  None of these

1. 

250

Food production

55 3.  84

2.  70% 5.  None of these

250

0

15. Women of Andhra Pradesh is approximately what percentage of the women of Tamil Nadu? 1.  60% 4.  55%

300

Fertilizer production

2.  25% 5.  22%

3.  77500

Direction for questions 18 to 20: Go through the data given below and solve the questions based on it.

13. Approximately what will be the percentage of total male in U P, Maharashtra and Kerala of the total population of the given states? 1.  20% 4.  28%

2.  76500 5.  74500

20. In which of the following years, the percentage growth over the last year in food production is maximum?

205 84

1.  1984 4.  1987

2.  1985 5.  1990

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

5

2.

5

3.

1

4.

4

5.

3

6.

5

7.

3

8.

2

9.

5

10.

5

11.

4

12.

4

13.

3

14.

5

15.

1

16.

4

17.

2

18.

1

19.

4

20.

5

3.  1986

Data Interpretation 

  1.253

HINTS AND EXPLANATIONS 4. (4) Following are the states satisfying the criterion: Andhra

Pradesh, Uttar Pradesh, Maharashtra, Tamil Nadu, Punjab, Gujarat, West Bengal, Haryana, Karnataka, Bihar, Kerala.

5. (3)  Population of village B in 1995 15 = 6000 12.5





= 5000 ×





Population of B in 1996 = 6600



Population = 3168

below

poverty



= 1520 ×





Required ratio =

2000 × 36% 3800 × 42%

= 16 +





≈

line

=

6600

×



=

24 ×25 ≈ 6 lakh 100 110% of 28% of 25 lakh 112% of 21% of 25 lakh

110 × 28 55 = 112 × 21 42 3 7 4 7





=

2000 × 20 = 4000 10 ≅ 45% (approx.)

11. (4)  Canada

16. (4)  Required ratio =



In Pakistan = 3550



7480 Required per cent = × 100 ≈ 210% 3550

13. (3)  Total males in UP, Maharashtra and Kerala 4 28 4 10 5 8 × + × + × = 7 100 9 100 11 100

7 6 11





=

of 9% of 25 lakh of 8% of 25 lakh

3×9 × 100 ≈ 60% 4 × 11 4

12. (4)  Protected land in India = 7480



25 100

48%

10. (5)  None of these



40 40 + 11 9

15. (1)  Required percentage =

100 15 × = 6333 36 10

9. (5) Population of village E in 1995 =



14. (5)  Required Ratio =

8. (2)  Population of village F in 1995



4 × 11 × 11 7×6×8

of 11% of 25 lakh of 8% of 25 lakh

=

121 84

17. (2) Total no. of illiterate in Tamil Nadu = (100 – 70) 30% of female + (100 – 75) 25% of males in the state.







30 4 25 3 + × × of 11% of 25 lakh 100 7 100 7 195 11 × × 2500000 ≈ 76500 700 100

PRACTICE EXERCISE  1 Region-wise distribution of sales (%)

Direction for questions 1 to 3:  Read the passage below and solve the questions based on it. The following table gives the result of Hero Cup football competition. Matches were played round robin (each team playing against another once) and the teams participated were Bihar, Punjab and Haryana. The table has some data missing: Match Won Drawn Lost Goals Goals played for against Bihar

2

Punjab

2

Haryana

2

1

2

4

3

7 1

18 16

2.  1 – 5 5.  none of these

15

14

14 12 10

12

11

11

8

6

6 4 2 0

1. What did the score card read in favour of Punjab in Punjab-Haryana match? 1.  2 – 5 4.  1 – 6

16

15

South South South East West East West

North North North East West

3.  1 – 4 Product-wise distribution of sales (%)

2. How many matches did Punjab lose? 1.  0 4.  0 or 1

2.  1 5.  none of these

3.  2 Product-wise distribution of sales(%)

3. How many goals did Haryana score? 1.  5 4.  7

2.  1 5.  none of these

3.  3

30

28

25

22

20

 irection for questions 4 to 7:  Read the passage below D and solve the questions based on it. The sales of a company in 2007–08 were Rs 1200 crore. The following charts represent the distribution of sales for various regions, product and distribution methods wise:

15

17 13

14

10

8

5 0

Textiles Pherma Computer Media Cement

Other

Practice Exercise 1 

Distribution of sales by various distribution methods. (%) 35

30

30

21 10

16

15 10

7

8

Dealers

Catalogue Direct Sale Online Franchises Others

4. If the computers are sold only through the dealers, how much of the dealers sales are made by products other than computers? 1.  Rs 48 crore 3.  Rs 252 crore 5.  none of these

2.  Rs 43 crore 4.  Rs 204 crore

5. In 2008-09 computers sales grow by 50% while the sales of dealers grows by 30%. If computers are sold only through dealers, what has been the percentage change in the sales of dealers of products other than computers? 1.  –20% 4.  +15%

2.  –45% 5.  none of these

3.  –55%

6. Cement sector has a total sales of Rs 3215 crore in the year. What is the market share of the company? 1.  9.55% 4.  11.55%

2.  10.45% 5.  none of these

3.  8.71%

  Direction for questions 7 to 11:  Go through the bar chart below and solve the questions based on it.

There are three constituents of product D­—A, B and C. When A, B and C are mixed in the ratio 1 : 2 : 3, D is formed. Following bar chart gives prices (in Rs) of 500 kg of constituent A, 1000 kg of constituent B and the average cost of 500 kg each of constituent A, constituent B and constituent C. 6000 5000 4000 A

3000

Average of A,B,C B

2000

1.  13 : 14 4.  4 : 3

2.  8 : 7 5.  none of these

3.  27 : 29

9. What was the percentage increase in price of C from 2006 to that in 2007? 1.  100% 2.  66.66% 3.  124% 4.  142% 5.  None of these

5

0

7. In which year was the price of C the highest? 1.  2005 2.  2006 3.  2007 4.  2008 5.  none of these 8. What was the ratio of price of C in 2005 to that in 2006?

25 20

  1.255

10. Vijay Shankar Pd. decides to buy 10 kg each of A, B and C. In which year will he pay the least amount of money? 1.  2005 2.  2006 3.  2007 4.  2008 5.  none of these 11. What was the cost of D in 2006 if 6000 kg of D is to be made? 1.  Rs 17250 2.  Rs 36450 3.  Rs 25500 4.  Rs 20750 5.  none of these Direction for questions 12 to 16:  Go through the table below and solve the questions based on it. Following table gives the details pertaining to the company’s employee appointment in three different wings at different levels and the salaries offered: G rads. Stands for graduate. A graduate has completed exactly 15 years of education. PG stands for post graduation and a post graduate has completed exactly 17 years of education. A person is not allowed to shift from one wing to another wing. Net salary = Gross Salary – taxes and other benefits NA is given when it is not eligible. 12. Ravi is a graduate and he joins in a wing at a particular level. What is the minimum time that Ravi will take to save Rs 200000, if 15% of his salary is deducted for tax and other benefits and he spends 50% of his net salary? 1.  34 months 2.  44 months 3.  56 months 4.  52 months 5.  None of these 13. Ravi’s friend Aftab, a post graduate joins at a middle management cadre. He joins that particular wing which will help him in saving maximum money in two years, given that 15% of his salary is deducted for taxation and other benefits and he spends 40% of his net income. Which wing he must have joined? 1.  Finance 4.  None of these

2.  Marketing 3.  HRD 5.  cannot be determined

1.256 

  Quantitative Aptitude and Data Interpretation Finance Wing

Marketing Wing

HRD Wing

Details/Level of entry

Entry Level

Middle Level

Top Level

Entry Level

Middle Level

Top Level

Entry Level

Middle Level

Top Level

Average gross salary drawn per month (in Rs)

5000

8000

18000

4000

7000

17000

5500

7500

15000

Minimum Work Ex required for a graduate (in years)

0

2

NA

0

3

5

0

2

NA

Minimum Work Ex required for a PG (in years)

0

1

2

0

0

2

0

0

2

Number of Grads. Employed

1000

100

NA

1000

70

1

40

1

NA

Number of PG employed

200

100

5

Nil

80

2

80

4

1

14. Ravi’s another friend Indrajeet is a fresh graduate. He is confused about his next career move that should he go for post graduation or to start working. He finally decides to calculate her total earnings in 5 years’ time in both cases for all wings and make his decision on that basis. Which of the following would be the best course of action assuming he keeps getting promoted immediately after meeting the minimum criteria? (cost of Post graduate program is Rs 250000 keeping all the other things constant.) 1.  Do post graduation and join marketing wing 2.  Do post graduation and join HRD wing 3.  Do not do post graduation and join HRD wing

4.  Do not do post graduation and join finance wing

16. Under a new policy to improve the profile of the company, it has been decided that no graduates will be recruited now and all graduates at entry level and middle level will be replaced with post graduates. Which wing has the best TPC at any level now (Use the definition of TPC from Q 20)? 1.  Finance 2.  HRD 3.  Marketing

5.  None of these

4.  Finance or Marketing

15. To facilitate the promotion of employees in a par-

5.  none of these

ticular wing from lower level (L1) to next higher level (L2), a mechanism has been devised. The whole of this mechanism has been developed by Mr Thomas

Direction for questions 17 to 20: Go through the chart given below and solve the questions based on it. Exports of Three Fruits from India

and hence it is named as Thomas profile co-efficient. Thomas profile co-efficient (TPC) for any wing at any T PC = No. of the Employees in L2/No. of employees in L1 L ower the TPC, higher is the chances of getting promoted. W hat is the ratio of highest TPC of post graduate to the highest TPC of a graduate? 1.  1 : 5 4.  25 : 7

2.  5 : 1 5.  none of these

3.  7 : 3

Exports in Rs. million

level is calculated as follows:

7 6 5 4 3 2 1 0

2006-07

2007-08 Apple

Mango

2008-09 Citrus

2009-10

Practice Exercise 1  17. For how many years are the combined exports of mangoes and citrus greater than the exports of apples by at least 150%? 1.  0 4.  3

2.  1 5.  none of these

19. Combined export value of which fruit from India is the maximum in the given years? 1.  Apple 2.  Mango 4.  cannot be determined

3.  2

ANSWER KEYS

2.  2 5.  none of these

3.  Citrus 5.  none of these

20. Out of the given four years, in which year the export value of the fruits given is the maximum?

18. In how many years the average exports of all the three fruits in a given year are greater than the average yearly exports for all four years? 1.  1 4.  4

  1.257

1.  2006-07 4.  2009-10

2.  2007-08 5.  none of these

3.  3

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

4

4.

1

5.

3

6. 11.

2 3

7. 12.

3 4

8. 13.

2 1

9. 14.

1 4

10. 15.

2 2

16.

2

17.

1

18.

2

19.

4

20.

3

3.  2008-09

1.258 

  Quantitative Aptitude and Data Interpretation

HINTS AND EXPLANATIONS Goals Goals For Against

Won

Drawn

Lost

Bihar

2

0

1

1

2

4

Cost of 2000 kg of B in 2006 = Rs 7000 and

Punjab

2

0

1

1

3

7

Cost of 3000 kg of C in 2006 = Rs 10500.

Haryana

2

2

0

0

7

1

So, Cost of 6000 kg of D in 2006 is Rs 25500. So [3] 12. Minimum time will be if he earns maximum salary. This is possible if he works at the top level of Marketing Wing. He saves Rs 7225. Hence time taken to save Rs 200000 is 28 months. Hence option [4] is the answer.

Score Card: Bihar – (2–2), (0–2) Punjab – (2–2), (1–5) Haryana – (5–1), (2–0) 4. (1)  Computer sales = 0.17 1200 = Rs 204 crore Dealer sales = 0.21 1200 = Rs 252 crore Hence, dealers sales by other products = Rs 48 crore 5. (3) In 2008-09, computer’s sales = 1.5 204 = Rs 306 crore Dealer sales = 1.3 252 = Rs 327.6 cross 2008-09 sales by dealers of other products = 327.6 – 306 = Rs 21.6 crore From 48 to 21.6, change is negative and exceeds 50%. 336 6. (2) 0.28 × 1200 = ≈ 10.45% 3215 3215

9. (3500-1750)/1750 = 100%. So [1]

Match Played

For 2005: 2500 × 3 – (3000 + 2500) = Rs 2000

For 2006: 7500 – 5750 = Rs 1750 For 2007: 9000 – 5500 = Rs 3500 For 2008: 6000 – 5500 = Rs 500 8. 2000 : 1750 = 8 : 7. So [2]

11. Cost of 1000 kg of A in 2006 = Rs 8000

13. At the middle level, finance wing gives highest salaries. Hence he is bound to save most in this wing. Hence [1] 15. Highest TPC for a post-graduate is from entry level to middle level in finance wing (50%). Highest TPC for graduate is also from entry level to middle level in finance wing (10%). Hence ratio = 5 : 1. Hence [2] 16. Option 2, from middle level to top level in HRD. 17. Total combined exports of mango and citrus should be at least 2.5 times exports of apples. This is the case in none of the options. Hence option (1) is the answer. 19. It is not given that only these fruits are exported from India in the given years. Hence cannot be determined. 20. Looking upon the bars, 2008-09 is the maximum. Exercise 1

Attempts

Right

RoI/minute = Marks/50 mins

Wrong Marks

% Accuracy

PRACTICE EXERCISE  2

1.  1991 4.  1996

2.  48% 5.  58%

3.  50%

2. Lockouts in which of the following years represent the mean of lockouts over the period? 2.  1971 5.  1994

1.  1961 4.  1991

3.  1981

3. Lockout/strike ratio is maximum in which of the following years? 1.  1961% 4.  1991

2.  1971 5.  1994

3.  1981

Direction for questions 4 to 7:  The following graph shows industrial disputes. Study the graph and answer the questions that follow it. The following chart gives the exports by EoUs from 1991 to 1997.

0 18

160

0 170

0 18

20

140

0 17

150

0 15

140

0 12

0 16

130

Export by EOUs (in tons)

1991

1992

1993

1994

Production

1995 Export

1.  120% 4.  150%

2.  130% 5.  160%

1996

1997

3.  140%

Direction for questions 8 to 12:  The following graph shows the price (Rs Per kg) of different commodities during the last 6 months. 45 40 35 30 25 20 15 10 5 0

Mar

Apr Potato

May Onion

Jun

Jul

Aug

Tomato

8. In the month of July, a person purchased 20 kg potatoes, 5 kg onions and 3.5 kg tomatoes. How much money did he spend to buy these things? 1.  Rs 351.7 4.  Rs 550

100

225 200 175 150 125 100 75 50 25 0

7. The sum of exports in 1991 and 1993 was approximately what per cent of the exports in 1996?

40

1.  44% 4.  55%

3.  1994

35

1. What approximate percentage of growth has taken place in lockouts in 1991 over 1981?

2.  1993 5.  1997

38

Lockouts

Strikes

14.5

1994

32

1991

3.  24.3 LT

6. In which of the following years, export as a percentage of production was maximum?

13 16.85 22.5

1981

2.  23.6 LT 5.  26.8 LT

12.5 10 18

1971

1.  22.8 LT 4.  25.7 LT

5.25 6.25 10

1961

100 0

5. The average production per year was approximately how much more than the average exports?

23.75

117

2.  1993 and 1995 4.  1994 and 1996

14

422

Lockouts

274

500 400 300 200

880

344

1278

1500 1000 500 0

600

532

2245

2478

2000

1240

Strikes

3000 2500

1.  1992 and 1993 3.  1992 and 1994 5. None of these

20

Industrial Disputes

4. The exports in which of the following pair of years were the same?

13.5

Direction for questions 1 to 3:  The following graph shows industrial disputes. Study the graph and answer the questions that follow.

2.  Rs 531.75 5.  Rs 451.25

3.  Rs 5531.75

9. Price of which commodity shows the highest percentage increase in a month? 1.  Onion in August 2.  Potato in April 3.  Tomato in July 4.  Tomato in April 5.  Onion in April

  Quantitative Aptitude and Data Interpretation

1.260 

10. What is the percentage increase in the price of onions from April to August? 1.  50 4.  350

2.  150 5.  None of these

3.  250

11. Price of which month is closest to the average price of six months in the case of tomatoes? 1.  April 4.  July

2.  May 5.  August

3.  June

12. Which of the following statements is not correct? 1. Percentage increase in price from March to August is the highest in case of onions. 2. In the month of August onions registered the highest price rise compared to July. 3. The price of onions always lies between the price of tomatoes and the price of potatoes across all the months. 4. If a person had hundred rupees he could have purchased one kg of each of the three commodities in August. 5.  None of these Direction for questions 13 to 17:  The following table shows number of applicants for different groups and those selected. Study the table carefully and answer the questions that follow. Year 1990 91 92 93 94 95 96 97

Group A Appl. Sel. 245 187 296 162 306 236 252 201 324 306 384 286 312 209 436 148

Group B Appl. Sel. 346 312 389 267 412 317 416 329 438 282 482 295 486 306 543 274

Group C Group D Appl. Sel. Appl. Sel. 412 367 244 162 402 262 287 212 414 376 356 266 367 198 469 197 427 304 673 202 562 215 439 207 386 259 487 223 468 227 639 236

Appl. = Applicants; Sel.= Selected All those who are not selected are rejected. 13. In which of the following years, the percentage of selected persons for group C the was minimum? 1.  1991 4.  1997

2.  1993 5.  1996

3.  1995

14. In which of the following groups has there been a continuous increase in the number of applications? 1.  Group A 4.  Group D

2.  Group B 3.  Group C 5.  None of these

15. In which of the following years is the total number of selected candidates the minimum? 1.  1990 4.  1994

2.  1992 5.  1997

3.  1993

16. The number of candidates selected in 1994 in Group B is approximately what percentage of candidates applied for Group D in 1996? 1.  48% 4.  58%

2.  52% 5.  62%

3.  55%

17. In which of the following years was the percentage of selected candidates for group D the maximum? 1.  1990 4.  1993

2.  1991 5.  1995

3.  1992

Direction for questions 18 to 21:  Go through the data given below and solve the questions based on it. The following is a table describing garments manufactured based upon the colour and size for each lay. There are four sizes: M-Medium, L-Large, XL-Extra large and XXL-Extra-Extra Large. There are three colours: Yellow, Red and White.

Number of Garments

Lay

Yellow

Red

White

LayNo.

M

L

XL

XXL

M

L

XL

XXL

M

L

XL

XXL

1

14

14

7

0

0

0

0

0

0

0

0

0

2

0

0

0

0

0

0

0

0

42

42

21

0

3

20

20

10

0

18

18

9

0

0

0

0

0

4

20

20

10

0

0

0

0

0

30

30

15

0

Practice Exercise 2 

  1.261

5

0

0

0

0

24

24

12

0

30

30

15

0

6

22

22

11

0

24

24

12

0

32

32

16

0

7

0

24

24

12

0

0

0

0

0

0

0

0

8

0

20

20

10

0

2

2

1

0

0

0

0

9

0

20

20

10

0

0

0

0

0

22

22

11

10

0

0

0

0

0

26

26

13

0

20

20

10

11

0

22

22

11

0

26

26

13

0

22

22

11

12

0

0

2

2

0

0

0

0

0

0

0

0

13

0

0

0

0

0

0

0

0

0

0

20

20

14

0

0

0

0

0

0

0

0

0

0

22

22

15

0

0

10

10

0

0

2

2

0

0

22

22

16

0

0

0

0

1

0

0

0

1

0

0

0

17

0

0

0

0

0

5

0

0

0

0

0

0

18

0

0

0

0

0

32

0

0

0

0

0

0

19

0

0

0

0

0

32

0

0

0

0

0

0

20

0

0

0

0

0

5

0

0

0

0

0

0

21

0

0

0

18

0

0

0

0

0

0

0

0

22

0

0

0

0

0

0

0

26

0

0

0

0

23

0

0

0

0

0

0

0

0

0

0

0

22

24

0

0

0

8

0

0

0

1

0

0

0

0

25

0

0

0

8

0

0

0

0

0

0

0

12

26

0

0

0

0

0

0

0

1

0

0

0

14

27

0

0

0

8

0

0

0

2

0

0

0

12

Production

76

162

136

97

67

194

89

59

135

198

195

156

Order

75

162

135

97

67

194

89

59

135

197

195

155

Surplus

1

0

1

0

0

0

0

0

0

1

0

1

18. How many varieties of fabrics, which exceed the order, have been produced ? 1.  3 4.  6

2.  4 5.  None of these

3.  5

19. How many lays are used to produce Extra-Extra Large fabrics? 1.  15 4.  18

2.  16 5.  None of these

3.  17

20. How many lays are used to produce Extra-Extra Large Yellow or Extra-Extra Large White fabrics? 1.  8 2.  9 3.  10 4.  15 5.  None of these 21. How many lays are used to produce Yellow colour fabrics? 1.  10

4.  14

2.  11

5.  None of these

3.  12

1.262 

  Quantitative Aptitude and Data Interpretation

No.

Name

International Airport Type

Code

Location

1

Hartsfield

A

ATL

Atlanta, Georgia, USA

77939536

2

Chicago-O/hare

A

ORD

Chicago, Illinois, USA

72568076

3

Los Angles

A

LAX

Los Angeles, California, USA

63876561

4

Heathrow Airport

E

LHR

London, United Kingdom

62263710

5

DFW

A

DFW

6

F

HND

E

FRA

Frankfurt, Germany

45858315

8

Hancda Airport Frankfurt Airport Roissy-Charles de Gaulle

Dallas/Ft.Worth, Texas, USA Tokyo, Japan

E

CDG

Paris, France

43596943

9

San Francisco

A

SPO

10

Denver Amsterdam Schiphol Minneapolis-St Paul Detroit Metropolitan Miami Newark McCarran Phoenix Sky Harbor Kimpo George Bush John F.Kennedy

A

7

11 12 13 14 15 16 17 18 19 20

Passengers

60000125 54338212

DIA

San Francisco, California, USA Denver, Colorado, USA

38034231

E

AMS

Amsterdam, Netherlands

36781015

A

MSP

Minneapolis-St Paul,USA

34216331

A

DTW

Detroit, Michigan, USA

34038381

A A A

MIA EWR LAS

Miami, Florida, USA Newark, New Jersy, USA Las Vegas, Nevada, USA

33899246 33814000 33669185

A

PHX

Phoenix, Arizona, USA

33533353

FE A A

SEL IAH JFK

Seoul, Korea Houston, Texas, USA New York, New York USA

33371074 33089333 32003000

Direction for questions 22 to 25:  Go through the data given below and solve the questions based on it.

1.  4 4.  7

Answer these questions based on the table given below concerning the busiest twenty International Airports in the world.

24. How many international airports not located in the USA handle more than 30 million passengers?

22. What percentage of the top ten busiest airports is in the United States of America?

1.  5 4.  14

1.  60 4.  90

2 5. Of the five busiest airports, roughly what percentage of passengers is handled by Heathrow airport?

2.  80 5.  None of these

3.  70

23. How many international airports of type ‘A’ account for more than 40 million passengers?

1.  30 4.  50

2.  5 5.  None of these

40387422

2.  6 5.  None of these

2.  40 5.  None of these

3.  6

3.  10

3.  20

ANSWER KEYS

Practice Exercise 2  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

3

3.

5

4.

2

5.

3

6. 11.

2 2

7. 12.

3 3

8. 13.

2 3

9. 14.

2 2

10. 15.

3 5

16. 21.

4 4

17. 22.

3 1

18. 23.

2 2

19. 24.

2 2

20. 25.

4 3

  1.263

HINTS AND EXPLANATIONS 1. (4)  Percentage growth in lockout in ‘91 = 532–344 × 100 ≈ 55% 344 1689 2. (3)  Mean of lockouts = = 337.8 ≈ 344 5 344 3. (5)  422 > 532 > 2245 880 1278

18. Total varieties for which there is surplus is our answer in this question. We can see there are 4 such varieties.

5. (3) Difference of average production and average export = 1160 – 990 = 170 ≈ 24.3 LT. 7 7 6. (2)  Percentage of export to production. 1991

1993

1994

1996

1997

83%

93%

88%

85%

89%

19. Again we would count those lays for which extra-extra large fabric is produced of any colour. So we would count lays for which at least one of XXL from 3 colours is non-zero. The following are the lay numbers—7,8,9,10,11,12,13,1 4,15,21,22,23,24,25,26,27. Hence, 16 lays is the number. 20. Now count lay numbers for which at least one of the XXL from yellow and white are non-zero. Lay number 7,8,9,10,11,12,13,14,15,21,23,24,25,26,27. Hence, 15 lays is the answer. 21. We have to count only those lays that produces any size of yellow coloured fabric.

7. (3)  8. (2)  (20×14) + (23.75×5) + (38×3.5) = Rs 531.75 9. (2) The price of potato in April rose from Rs 5.25 to Rs 12.5 per kg. 12.5 – 5.25 Therefore % increase = × 100 ≈138% 5.25 In no other case, the price increase is more than 100%. 10. (3)  % increase in price = 25 × 100 =250% 10 11. (2) Average price = Rs 26.75, which is closest to the price of May (Rs 22.5). 13. (3)  1991

‘93

‘95

‘95

‘97

65%

53.9%

38.2%

67%

48.5%

 he following are the lay numbers—1,3,4,6,7,8,9,11,12, T 15,21,24,25,27 Hence, 14 lays is the answer. 22. There are only six airports of USA among the top 10 busiest airports. Hence 60% is the answer. 23. In that case we have only five International Airports of type A having more than 40 million passengers. They are—S. No. 1.2.3, 5, 9. Rest all ‘A’ type is below 40 million. 24. All the International Airports handle more than 30 million passengers. Among these, only 6 airports are not located in USA. Hence, (2) is the answer. 25. The percentage of passengers handled at Heathrow airport is to be calculated (which is 62 millions)

16. (4)  Percentage = 282 × 100 = 58% 487 17. (3)

 ow total number of passengers in the 5 busiest airN port is approximately = 77 + 72 + 63 + 62 + 60 million

1990

‘91

‘92

‘93

‘95

= 334 million. At Heathrow airport, it is 62 million.

66.3%

73.8%

74.7%

42%

47%

The approximate percentage = 20%

PRACTICE EXERCISE  3 Direction for questions 1 to 7:  Go through the data set given below and solve the questions based on it. The following table gives the marks obtained by 6 students A, B, C, D, E and F in 6 subjects—History, Science, Geography, English, Hindi and Math. Marks in bracket show total marks in that subject. For example—History (150) shows that total marks in History = 150. Marks obtained by 6 students in 6 subjects History Science Geography English Hindi Maths Total (150) (200) (150) (200) (100) (200) (1000)

A

75

110

90

140

75

170

660

B

105

130

75

130

80

140

660

C

95

105

80

150

90

160

680

D

85

115

95

125

65

135

620

E

115

135

110

145

70

125

700

F

120

160

96

110

55

145

686

1. How many students have got more than 50% marks in each of the subjects and more than 65% marks in total? 1.  0 4.  3

2.  1 5.  None of these

3.  2

2. What is the difference between the percentage marks obtained by the student B in History and percentage marks obtained by C in Hindi? 1. 25 4.  30

2.  20 5.  None of these

3.  35

3. For C, what is the difference between the percentage of marks in English and the percentage of marks obtained in total? 1.  82 4.  14

2.  38 1

3

3.  7

5.  None of these

4. Distinction is awarded if marks obtained is more than or equal to 75% in any subject. What is the sum total of number of distinctions awarded to all the students in all the subjects? 1.  7 4.  10

2.  8 5.  None of these

3.  9

5. In how many subjects did D get more than 70% marks? 1.  0 4.  3

2.  1 5.  None of these

3.  2

6. For English, what is the approximate average percentage of marks obtained by the all the six students? 1.  67 2.  72 4.  Cannot be determined

3.  80 5.  None of these

7. Pass marks = 40%. If a student fails in any subject, s/he is supposed to appear in that subject once again. Who among the following will have to appear in maximum number of subjects? 1.  A 4.  D

2.  B 5. None of these

3.  C

Direction for questions 8 to 12:  Go through the data set given below and solve the questions based on it. Study the tables the Indian foreign trade given below to answer the questions. Principal Commodities’ Export Commod ities

Weight (%) 2003-04

2004-05

2005-06

Plantations

0.92

0.78

0.71

Agri and allied prdts

8.39

7.61

7.21

Marine products

2.08

1.60

1.40

Ores and minerals

3.69

5.29

6.02

Leather and mfrs

3.19

2.89

2.56

Gems and jewellery

16.56

17.29

15.13

Sports goods

0.15

0.12

0.13

Chemicals and related products

15.43

16.00

15.10

Engineering goods

16.41

18.41

18.66

Electronic goods

2.74

2.28

2.18

Project goods

0.09

0.06

0.13

  1.265

Practice Exercise 3 

0.43 0.75

0.40 0.81

0.28

0.10

0.61

5.54

8.57

11.21

4.07

2.66

2.94

100.00

100.00

100.00

44.2735

1.  1.36 4.  1.48

2003-04

2004-05

2005-06

Bulk imports

37.87

39.09

42.56

 earls, precious P and semi-precious stones

9.25

8.80

6.42

Machinery

10.63

10.00

10.94

Project Goods

0.49

0.54

0.57

Others

41.76

41.57

39.51

100.00

100.00

100.00

TOTAL IMPORTS Total Imports (in Crore of Rupees)

359107.66 501064.54 630526.77

8. The three commodities which had highest export growth rate in the year 2004-05 as compared to the previous year, arranged in descending order of growth rates are:

1.  39.77 4.  95.98

12. In the two year period from 2004-05 to 2005-06, the average growth in import (in Indian Rupees) of which commodity to India was maximum? 1.  bulk imports 2.  pearls, precious and semi-precious stones 3.  machinery 4.  project goods 5.  others Direction for questions 13 to 17: Go through the data set given below and solve the questions based on it. Following graph shows the price (Rs Per kg) of different commodities during the last 6 months. 45 40 35

1. petroleum products, ores and minerals, engineering goods.

30

2. ores and minerals, gems and jewellery, chemicals and related products.

20

3. gems and jewellery, chemicals and related products agriculture and allied products.

10

4. ores and minerals, chemicals and related products, agriculture and allied products. 5. ores and minerals, engineering goods, chemicals and related products.

2.  41.85 3.  91.24 5.  None of the above

35

Commodities

11. Growth of trade imbalance (exports minus import) in dollar terms in the year 2005-06 as compared to the previous year was

38

Weight (%)

2.  1.38 3.  1.46 5.  None of the above

32

Principal Commodities’ Import

44.9315

25 15 5 0

Mar

Apr Potato

16.85 22.5

45.9513

454799.97

13

293366.75 375339.53

18

Total Exports in Rupees Crore US Dollar Exchange Rate

10. Given that the weight (%) of Petroleum crude and products in the total imports of India is 26.70, 27.87, and 30.87 in the years 2003-04, 2004-05, and 200506 respectively. What is the ratio of yearly difference in the export of Petroleum products and import of Petroleum crude and products, in dollar terms, in the year 2005-06 versus 2004-05?

12.5 10

Unclassified exports GRAND TOTAL

5.25 6.25 10

Petroleum products

40

0.70 0.90

May Onion

Jun

Jul Tomato

14.5

Handicrafts Carpets Cotton raw incl. waste

9. In the year 2005-06 the commodity which witnessed maximum growth in exports (in Indian Rupees) as compared to the year 2004-05 is 1.  petroleum products 2.  projects goods 3.  ores and minerals 4.  sports goods 5.  None of the above

23.75

14.80

14

15.16

20

18.86

13.5

Textiles

Aug

  Quantitative Aptitude and Data Interpretation

1.266 

13. In the month of July, a person purchased 20 kg potatoes, 5 kg onions and 3.5 kg tomatoes. How much money did he spend to buy these things? 1.  Rs 351.7 2.  Rs 531.75 3.  Rs 5531.75 4.  Rs 550 5.  Rs 451.25 14. What is the percentage increase in the price of onions from April to August? 1.  50 2.  150 3.  250 4.  350 5.  None of these 15. Price of which month is closest to the average price of six months in case of tomatoes? 1.  April 4.  July

2.  May 5.  August

3.  June

16. Which of the following statements is not correct? 1. Percentage increase in price from March to August is the highest in case of onions. 2. In the month of August onions registered the highest price rise compared to July. 3. The price of onions always lies between the price of tomatoes and the price of potatoes across all the months. 4. If a person had hundred rupees he could have purchased one kg of each of the three commodities in August. 5.  None of these 17. Price of which commodity shows the highest percentage increase in a month? 1.  Onion in August 2.  Potoato in April 3.  Tomato in July 4.  Tomato in April 5.  Onion in April Direction for questions 18 to 21:  Go through the data set given below and solve the questions based on it. Sick industrial units (in thousands) and outstanding bank credit (in Rs hundred crore). 70 60

60

40

35 28

30 20 10 0

40

15

20

45

2.  1994 5.  1997

3.  1995

19. For how many years there is an increase in bank credit per sick unit over the previous year? 1.  0 4.  3

2.  1 5.  None of these

3.  2

20. What was the percentage increase in number of sick units from 1996 to 1997? 1.  50% 4.  200%

2.  25½% 5.  None of these

3.  20%

21. Which year witnessed the maximum percentage increase in the bank credit over the previous year? 1.  1994 4.  1997

2.  1995 3.  1996 5.  Cannot be determined

Direction for questions 22 to 24:  Go through the data set given below and solve the questions based on it. There are three counters A1, A2 and A3 for handling transaction, enquiry and admission procedures at an office. Time and day of their being opened are given below: ▪ A1 is open between 9 am to 1 pm on Tuesday, Thursday and Friday and between 2 pm to 4 pm on Monday, Wednesday and Saturday. ▪ A2 is open between 10 am to 1 pm on Monday, Wednesday and Thursday and between 2 pm to 3 pm on Tuesday, Friday and Saturday. ▪ A3 is open between 8 am to 11 am on Wednesday, Friday and Saturday and 12 noon to 2 pm on Monday, Tuesday and Thursday. 22. On which day before noon, all three counters are simultaneously open at least for some time? 2.  Thursday 3.  Wednesday 5.  None of these

23. On which day, more than one counters are not open simultaneously at any given time? 1.  Tuesday 4.  Saturday

25

10

1993

1.  1993 4.  1996

1.  Saturday 4.  Monday

50

50

18. In which year was the bank credit per sick unit the maximum?

2.  Wednesday 5.  None of these

3.  Friday

24. On which day’s afternoon, only A1 and A2 are open simultaneously for some time? 1994 Sick Units

1995

1996 Bank Credit

1997

1.  Saturday 4.  Tuesday

2.  Thursday 5.  None of these

3.  Monday

  1.267

ANSWER KEYS

Practice Exercise 3  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1. 6. 11. 16. 21.

4 1 2 3 1

2. 7. 12. 17. 22.

2 5 1 2 5

3. 8. 13. 18. 23.

3 1 2 4 5

4. 9. 14. 19. 24.

3 1 3 3 1

5. 10. 15. 20.

1 1 2 3

HINTS AND EXPLANATIONS 1. (4) C, E and F are the students. [We have to consider more than 50%] 105 × 100 = 70% 150

2. (2)  C

12. (1)  Bulk imports register the highest growth. 13. (2)  (20 × 14 + (23.75×5) + (38 × 3.5) = Rs 531.75 14. (3)  % increase in price = 35 – 10 × 100

= 90%

10

= 25 × 100 = 250% 10

∴ Reqd. difference = 90 – 70 = 20

15. (2) Average price = Rs 26.75, which is closest to the price of May (Rs 22.5).

3. (3)  Percentage of marks of English 150 = × 100% = 75% 200 Average percentage of marks 680 = × 100% = 68% 1000 Therefore required = 75 – 68 = 7

17. (2) The price of potato in April rose from Rs 5.25 to Rs 12.5 per kg. Therefore % increase = 12.5 – 5.25 × 100 ≈ 138%

5.25

In no other case, the price increase is more than 100%.

4. (3)  Look at the table given below:

18. (4) Bank Credit per sick unit Total marks History Science Geography English Hindi Math

Distinction marks

Total distinctions

112.5 150 112.5 150 75 150 Total

2 1 0 1 3 2 9

150 200 150 200 100 200

8. (1) As seen from the table, petroleum products register highest growth followed by ores and minerals and engineering goods. 9. (1)  Growth in petroleum products is highest 10. (1)  Ratio =

30.87 × 6.30 – 11.21 ×4.54 × 100 = 1.36 27.87 × 5.01 – 8.57 × 3.75

11. (2) Growth= (630526 – 454799)

(630526 – 454799) – (501064 – 375339) × 100 (501064 – 375339)

Percentage =

175727 – 125725 50,000 × 100 = × 125725 125725 100 = 41.85%

Year

1993

1994

1995

1996

1997

Credit (in Rs Lakh)

6.66

7.14

7.14

8

7.5

1993 0.66

1994 0.714

1995 0.714

1996 0.8

1997 0.75

It can be clearly seen that the rise is in two years. 20. (3)  Required percentage =

10 × 100 = 20% 50

Counter

Ist Session/Days

IInd Session/Days

A1

(9-1) Tue, Thu, Fri

(2-4) Mon, Wed, Sat

A2

(10-1) Mon, Wed, Thu

(2-3) Tue, Fri, Sat

A3

(8-11) Wed, Fri, Sat

(12-2) Mon, Tue, Thu

22. (5)  There is no such day. 24. (1)  Sat (2 pm–3 pm) Exercise 3 Attempts Right Wrong Marks % Accuracy

PRACTICE EXERCISE  4 Direction for questions 1 to 5:  Go through the data set given below and solve the questions based on it.

Direction for questions 6 to 7: Go through the data set given below and solve the questions based on it.

Household expense: All the values are percentage figures for different heads.

The following bar diagram gives the domestic production and domestic consumption of Steel (in Lakh tonnes) during 2003-04 to 2006-07.

16

Education Travelling

5

21

12

8

10

13 11 13 11

Entertainment Health

39 41

Food

6

11 11

Savings 0

10

4.75

5.07

4.5

4.86

5.25

5.62

2003–04

2004–05

2005–06

2006–07

4.35

4

20 1997

30

40

50

2

1996 

1. If the total expenses for 1996 = Rs 12,000, total expenses for 1997 = Rs 15,000 then what is the difference between the expenses on food and travelling for 1997 and the expenses on food and education for 1996? 1.  Rs 600 4.  Rs 900

5.49

8

2.  Rs 1200 5.  None of these

3.  Rs 390

2. What is the percentage change in the expenses on food for 96 over 97? 1.  6 2 % increase 2.  9.375% increase 3 3.  9 41 % increase 4.  6 3 % increase 8 5.  Cannot be determined 3. Which item shows the maximum percentage increase from 1996 to 1997?

0 Production

Consumption

6. Ratio of consumption to production is highest in the year 1.  2003-04 2.  2004-05 3.  2005-06 4.  2006-07 5.  None of these 7. Which of the following statements is wrong? 1.  Consumption is always more than production. 2.  Production increases continuously over the period. 3.  Consumption increases continuously over the period. 4. India needs to import steel every year assuming that any deficit is fulfilled by imports. 5.  None of these

5. If percentage share of the expenses for any head for each of the years is more than 15%, then that head is known as alarming. How many expense heads are in an alarming condition?

Direction for questions 8 to 13: Go through the data set given below and solve the questions based on it. Seven film buffs G, I, L, M, R, V, and Y–attend a showing of classic films. Three films are shown: one each directed by Guru Dutt, Satyajit Ray, and Ritwik Ghatak. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions apply: Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film. G and R do not see the same film as each other. I and M do not see the same film as each other. V and Y see the same film as each other. L sees the Satyajit Ray film. G sees either the Guru Dutt film or the Ritwik Ghatak film.

1.  0 4.  3

8. If exactly one film buff sees the Ritwik Ghatak film, then which one of the following must be true?

1.  Health 3.  Entertainment

2.  Travelling 4.  Saving 5.  None of these

4. What is the maximum difference between the sum of any two items of 1996 and the sum of any two items of 1997? 1.  Rs 6300 2.  Rs 1200 3.  Rs 1050 4.  Rs 900 5.  Cannot be determined

2.  1 5.  None of these

3.  2

Practice Exercise 4  1.  V sees the Satyajit Ray film.

  1.269

2.  G sees the Guru Dutt film.

Year/ Types

2003

2004

2005

2006

2007

2008

3.  M sees the Guru Dutt film.

A

36

34

40

35

37.5

40

4.  I sees the Guru Dutt film.

B

20

22

25

23

19.5

18

5.  R sees the Satyajit Ray film.

C

14

22

16

25

29

35

D

60

62

67.5

75

76

80

E

40

45

48

50

80

105

F

45

52

55

60

57.5

56

Total

215

237

251.5

268

299.5

334

9. Each of the following must be false except: 1.  Exactly three people see Satyajit Ray film. 2.  R is the only film buff to see the Satyajit Ray film. 3.  Y is the only film buff to see the Ritwik Ghatak film. 4.  Exactly two film buffs see the Ritwik Ghatak film. 5.  None of these 10. Which one of the following could be a complete and accurate list of the film buffs who do not see the Satyajit Ray film? 1.  G, M 4.  G, M, Y

2.  G, R 5.  G, V, Y

3.  G, I, R

11. Which one of the following could be an accurate matching of film buffs to films? 1 G: the Satyajit Ray film; I: the Ritwik Ghatak film; M: the Satyajit Ray film 2. G: the Ritwik Ghatak film;I: the Guru Dutt film; V: the Guru Dutt film 3. I: the Satyajit Ray film; R: the Ritwik Ghatak film; V: the Guru Dutt film 4. M: the Ritwik Ghatak film; R: the Ritwik Ghatak film; V: the Ritwik Ghatak film 5. M: the Satyajit Ray film; R: the Satyajit Ray film; Y: the Satyajit Ray film

14. In which year was the total production of A and D together equal to the total production of E and F together? 1.  2007 2.  2003 3.  2005 4.  2004 5.  None of these 15. In which year was the total production of all types of cars taken together equal to the approximate average of the total production of cars during the given period? 1.  2006 4.  2004

2.  2007 5.  None of these

3.  2005

16. How many types of cars have shown a continuous growth in the production for the given period? 1.  2 4.  1

2.  3 5.  None of these

3.  4

17. The approximate percentage increase in the total production of all types of cars in 2007 over 2005 was 1.  16% 4.  25%

2.  20% 5.  28%

3.  23%

18. f(t) = maximum difference possible in between any two types of cars for the year. Find the value of f(t) for 2008.

12. If V and G see the same film, then which one of the following could be true? 1.  G sees the Guru Dutt film. 2.  I sees the Satyajit Ray film. 3.  R sees the Ritwik Ghatak film. 4.  V sees the Satyajit Ray film. 5.  Y sees the Guru Dutt film.

1.  14750 4.  87000

13. Each of the following could be a complete and accurate list of the film buffs who see the Guru Dutt film except

Direction for questions 20 to 24: Go through the table given below and solve the questions based on it.

1.  G, I 4.  M, R

2.  G, M 5.  V, Y

3.  I, R

Direction for questions 14 to 19:  Go through the data set given below and solve the questions based on it. Following table gives the production of different types of cars from 2003 to 2008. Answer the questions based on the data given (All values in ‘000s).

2.  75000 5.  56000

3.  57500

19. What is the maximum difference in the production of any two types of two cars for the years 2007 and 2008? 1.  14750 4.  147500

2.  87500 5.  None of these

3.  157500

The following is the final results of standard X. The subjects in which students are tested are—English, Hindi, Science, Maths, Social service, Drawing, PT, Craft, Social science and scout-guide. To have a better presentation of the mark sheet, the scores in first four subjects are consolidated into A-1, the next three into A-2 and last three into A-3. The final score is the total of these three scores A1, A2 and A3. On the basis of the final score, students get their ranks. The table below gives the scores of top eighteen students of the class.

1.270 

  Quantitative Aptitude and Data Interpretation Social Science

Grade

Final Score

A1

A2

A3 Drawing PT

Anana

A

725

282

217

226

80

81

69

Pankaj

B

864

310

87

267

85

86

92

Vamshi

C

812

300 290

222

70

91

74

Ram

C

805

270

262

273

65

79

97

Shann

D

900

391

292

217

96

86

81

Saket

D

876

301 297 278

65

87

93

Mini

C

825

296 296 233

50

89

91

Rashi Singh

E

905

320 290 295

72

99

99

Parul

B

895

310 290 295

72

99

98

22. What is the least that Kush Verma must get in A2 that would ensure him 5th rank?

Rakesh Rathi

B

870

276 296 298

63

99

99

1.  289 4.  299

Gauri

C

888

361 270 257

82

78

92

Kush Verma

23. Who has scored maximum marks in Scout-guide provided the maximum marks in any subject = 100?

A

-

315

296

62

99

99

Pragya

A

897

312 299 286

69

97

92

Shipra Gupta

D

907

319 289 299

71

100

100

Sachin

E

910

387 290 233

86

69

79

Sarita

A

901

389 270 242

87

79

86

ANSWER KEYS

Name

-

Mahavir Sherawat

C

897

388 297 212

83

69

89

Ritu Sehgal

D

898

299 300 299

73

100

99

20. How many students have got grade A and more than 250 marks in all the group scores (A1, A2 and A3)? 1.  0 4.  3

2.  1 5.  None of these

21. What is the difference between total marks in drawing of grade A students and grade C students? 1.  50 4.  62

2.  52 5.  None of these

1.  Rakesh Rathi 2.  Ritu Sehgal 4.  Rakesh Rathi and Ritu Sehgal 5.  None of these

1.  214 4.  196

2.  208 5. None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

5

3.

2

4.

5

5.

3

6. 11.

3 5

7. 12.

4 2

8. 13.

1 5

9. 14.

5 5

10. 15.

3 1

16. 21.

1 2

17. 22.

2 1

18. 23.

4 2

19. 24.

4 5

20.

3

HINTS AND EXPLANATIONS

3. (2)  Visual inspection 4. (5)  We don’t have the actual figure.

3.  Saket

24. What is the difference between the sum of final scores of top five scorers and sum of final scores of bottom five scorers?

Ans.

2. (5) Since total expenses are not given, we cannot calculate this.

3.  48

2.  288 3.  290 5.  Cannot be determined

Q.

1. (3) Required difference =(0.47 × 15000) – (0.62 × 12000) = –390

3.  2

6. (3)  The ratio in 2003-04 =

4.5 4.35 =1.034

The ratio in 2004 –04 = 1.023 The ratio in 2005 – 06 = 1.0355 The ratio in 2006 – 07 = 1.0236

3.  174

Practice Exercise 4  8. (1) If exactly one film buff sees the Ritwik Ghatak film, then four film buffs see the Satyajit Ray film and two film buffs see the Guru Dutt film. Now G can’t see the Satyajit Ray film and out of I and M only one can see the Satyajit Ray film. So V and Y must see the Satyajit Ray film. 9. (5) Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film. Hence options (2), (4) and (1) are ruled out. V and Y see the same film as each other. Hence option (3) is ruled out.

  1.271

15. (1) Approximate average of the total production

215 + 237 + 251.5 + 268 + 299.5 + 334 6 1605 =267.5 ≈ 268 which is equal to production in 2006 = 6 =

16. (1) D and E have shown continuous increase in the production.

299.5 –251.5 = 48 = 50 = 1 = 20% 251.5 251.5 250 5

10. (3) Exactly four film buffs see the Satyajit Ray film and three don’t see the Satyajit Ray film. Hence options (1) and (2) are ruled out. Now, V and Y along with L must see the Satyajit Ray film. Hence options (4) and (5) are ruled out.

17. (2) 

11. (5) G sees either the Guru Dutt film or the Ritwik Ghatak film. Hence option (1) is ruled out. If V sees the Guru Dutt film, Y also must see the Guru Dutt film. So along with I, three film buffs see the Guru Dutt film which is not possible. Hence option (2) is ruled out. If R sees the Ritwik Ghatak film, G must see the Guru Dutt film. So again G, V and Y see the Guru Dutt film. Hence option (3) is ruled out. Three film buffs can’t see the Ritwik Ghatak film. Hence option (4) is ruled out. So, option 5 is the answer.

19. (4) For the maximum no. of difference of the production of two types of for 2007 and 2008, we need to have a two step process:

12. (2) If V and G see the same film, they must see the Ritwik Ghatak film. Hence options (1) and (4) are ruled out. V and Y see the same film. Hence option (5) is ruled out. G and R do not see the same film. Hence option (3) is ruled out. Hence option 2 is the answer.

E → 80 + 105 = 185 ⇒ 185000

13. (5) lf V and Y see the Guru Dutt film, then exactly four film buffs see the Satyajit Ray film. Now G does not see the Satyajit Ray film. It means remaining four must see the Satyajit Ray film. But I and M do not see the same film. Hence Y and V can’t see the Guru Dutt film. 14. (5)  2006 is such year. Visual inspection.

18. (4) Production of E is maximum and production of B is minimum.

Step 1:  Select the types one having the highest production for 2007 and 2008 and Step 2:  Select the types having the lowest production for 2007 and 2008.

B → 19.5 + 18 = 37.5 ⇒ 37500 20. Pragya and Kush Verma are the only two students.

Attempts Right Wrong Marks % Exercise 4 Accuracy

PRACTICE EXERCISE  5 Household expense: All the values are percentage figures for different heads.

Direction for questions 1 to 5:  Go through the data set given below and solve the questions based on it.

16

Education Travelling

5

21

8 13 11 13 11

Entertainment Health

1997 1996 39 41

Food 11 11

Savings 0

10

20

30

40

50 

1. If the total expenses for 1996 = Rs 12,000, total expenses for 1997 = Rs 15,000 then what is the difference between the expenses on food and travelling for 1997 and the expenses on food and education for 1996? 1.  Rs 600 3.  Rs 390

2.  Rs 1200 4.  Rs 900

2. What is the percentage change in the expenses on food for 96 over 97? 2 1.  6 % increase 2.  9.375% increase 3 1 3.  9 % increase 4.  cannot be determined 4 3. Which item shows the maximum percentage increase from 1996 to 1997? 1.  Health 2.  Travelling 3.  Entertainment 4.  Saving 4. What is the maximum difference between the sum of any two items of 1996 and the sum of any two items of 1997? 1.  Rs 6300 3.  Rs 1050

2.  Rs 1200 4.  Cannot be determined

5. If percentage share of the expenses for any head for each of the years is more than 15%, then that head is known as alarming. How many expenses head are in alarming condition?

1.  0 3.  2

2.  1 4.  3

Direction for questions 6 to 7:  Go through the data set given below and solve the questions based on it. The following bar diagram gives the domestic production and domestic consumption of Steel (in Lakh tonnes) during 2003-04 to 2006-07 12 10 5.49

8 6

4.35

4.75

5.07

4 2

4.5

4.86

2003–04

2004–05

5.25

5.62

2005–06

2006–07

0

Production

Consumption

6. Ratio of consumption to production is highest in the year

Practice Exercise 5  1.  2003-04 3.  2005-06

2.  2004-05 4.  2006-07

  1.273

Direction for questions 8 to 10:  Go through the data set given below and solve the questions based on it.

7. Which of the following statements is wrong? 1.  Consumption is always more than production. 2.  Production increases continuously over the period. 3.  Consumption increases continuously over the period. 4.  India needs to import steel every year assuming that any deficit is fulfilled by imports.

There are six companies 1 through 6. Each of these companies uses six operations A through F. The following bar chart shows the distribution of efforts put by each company in these six operations (All figures in percentage and lowest bar shows for company 1 and so on):

160 140

23.6

120 100

28.6 15.6

80

15.1

17.6

60

18.5

40

16.4

16.1 10.3 16.4

18.5

16.7

20 0

17.7

17.6

13.8 13 8.2 10.9 9.3 9.8

A

B

C

2.  3 4.  5

9. If it is possible that the companies can remove outright the operations B, C, and D and redistribute the spared effort equally among all operations, then which operation will show maximum across all companies and all operations? 1.  The company one in operation E 2.  The company four in operation E 3.  The company two in operation E 4.  The company five in operation E 10. A new technology is introduced in company 4 such that the efforts allocated to operations B, C, D, E and F gets equally divided among these. What is the change in percentage effort of E? 1  Reduce by 12.3 2.  Reduce by 5.6 3.  Increase by 12.3 4.  Increase by 5.6

11.8 7.7 11.2 16.3 7.4 15.7

D

6 5 4 3 2 1

19.7

28.6

8. If the effort allocated to various operations is changed in the sequence: B and C are interchanged, then C and D are interchanged and finally D and E are interchanged. If the companies are now ranked in ascending order of the percentage effort allocated to operation E, then the rank of the company three is:   1.  2 3.  4

17.6

23.4

21.8

18.2 25.9 22.2 23.5

15.7

E

F

Direction or questions 11 to 14:  Go through the chart given below and solve the questions based on it. Diagram given ahead presents the domestic consumption and import of oil for the given period: 70 60 50 40 30 20 10

Oil imports & Self-sufficiency (in million tonnes) 64 55 23

19

Domestic Consumption Net import

16

0

38

26

32

1970

1980

1990

1994

11. The percentage growth of domestic consumption over the period was approximately: 1.  273% 3.  237%

2.  245% 4.  187%

12. The average of imports of which of the following pair of years was approximately equal to the average of imports over the period?

1.274 

  Quantitative Aptitude and Data Interpretation

1.  1970 and 1994

2.  1990 and 1994

1.  14750

2.  75000

3.  1980 and 1994

4.  1980 and 1990

3.  57500

4.  87000

13. The ratio of net imports to domestic consumption is the maximum in the year. 1.  1970 2.  1980

19. What is the maximum difference in the production of any two types of two cars for the years 2007 and 2008?

3.  1990

4.  1994

1.  14750

2.  87500

14. Domestic consumption = Net imports + domestic production. If net imports is 50% more than domestic production for any particular year, then country is said to be Non-self-sufficient. For how many years given as the data points, the country is Non-self sufficient? 1.  0 2.  1

3.  157500

4.  147500

3.  2

4.  3

Direction for questions 15 to 20:  Go through the data set given below and solve the questions based on it. Following table gives the production of different types of cars from 2003 to 2008. Answer the questions based on the data given (All values in ‘000s) Year/Types A B C D E F Total

2003 36 20 14 60 40 45 215

2004 34 22 22 62 45 52 237

2005 2006 2007 2008 40 35 37.5 40 25 23 19.5 18 16 25 29 35 67.5 75 76 80 48 50 80 105 55 60 57.5 56 251.5 268 299.5 334

15. In which year was the total production of all types of cars taken together equal to the approximate average of the total production of cars during the given period?

20. In which year was the total production of A and D together equal to the total production of E and F together? 1.  2007

2.  2003

3.  2004

4.  2006

Direction for questions 21–25: Read the information given below and answer the questions that follow: Seven representatives of a company – Samir, Nita, Richa, Shweta, Gifty, Paul and Mohit – traveled to three different countries i.e. South Africa, Australia and France. Each of them traveled on different days of the week (no two persons traveled on the same day), starting on Monday and ending on Sunday. Minimum two people traveled to each country and South Africa is the only country to which three people traveled.    Samir traveled to South Africa on Monday. Paul traveled to Australia but neither on Tuesday nor on Saturday. Mohit traveled on Sunday but not to France. The one who traveled to Australia traveled on Tuesday and the one who traveled to France traveled on Saturday. Gifty traveled on Wednesday. Richa traveled to South Africa but not on Thursday. Nita did not travel to France.

1.  2006

2.  2007

21. If everyone’s trip is postponed by one day, who will be traveling on Wednesday?

3.  2005

4.  2004

1.  Paul

2.  Richa

16. How many types of cars have shows a continuous growth in the production for the given period?

3.  Nita

4.  Gifty

1.  2

2.  3

22. Who amongst the seven representatives traveled on Saturday?

3.  4

4.  1

1.  Nita

2.  Shweta

3.  Richa

4.  Cannot be determined

17. The approximate percentage increase in the total production of all types of cars in 2007 over 2005 was 1.  16%

2.  20%

3.  23%

4.  25%

18. f(t) = maximum difference possible in between any two types of cars for the year t. Find the value of f(t) for 2008.

23. To which country and on which day did Nita travel? 1.  Tuesday, Australia 2.  Friday, Australia 3.  Thursday, Australia 4.  Wednesday, South Africa

Practice Exercise 5  25. Who was the last one to travel?

24. Which one of the following combinations is true according to the given information?

1.  Samir

1.  Paul – Thursday – South Africa

2.  Richa

2.  Shweta – Wednesday – France

3.  Shweta

3.  Mohit – Monday – South Africa

4.  Mohit

4.  None of these

ANSWER KEYS

  1.275

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

4

3.

2

4.

4

5.

3

6.

3

7.

4

8.

2

9.

4

10.

1

11.

3

12.

4

13.

1

14.

3

15.

1

16.

1

17.

2

18.

4

19.

4

20.

4

21.

3

22.

2

23.

1

24.

4

25.

4

HINTS AND EXPLANATIONS 1. Required difference = (0.47 × 15000) – (0.62 × 12000) = –390 2. Since total expenses are not given, we cannot calculate this. 3. Visual inspection 4. We don’t have the actual figure. 6. Ratio in 2003–04 = 4.5 =1.034 4.35 Ratio in 2004–04 = 1.023 Ratio in 2005–06 = 1.0355 Ratio in 2006–07 = 1.0236 8. After interchanging the effort allocation between operations B and C, then C and D, and then D and E we find that B takes the E’s position. Looking at the effort in B and then ranking in ascending order, company 3 ranks third. 9. Looking at the options, we are given about company 1,4,5 in options. Hence we will look for change in these companies only. Allocation of effort in B,C,D in companies 1 = 43.1

So, change is E = 28.6 – 16.3 = 12.3% 11. % growth in domestic consumption =

64 − 19 × 100 ≈ 237% 19

12. Average imports over the period = 16 + 23 + 26 + 38 = 103 = 25.75 4 4 13. Ratio of imports to consumption in 1970

1980

1990

1994

0.84

0.71

0.47

0.59

14. Following table gives the data:  

1970

1980

1990

1994

Domestic consumption

19

32

55

64

Net imports

16

23

26

38

Domestic production

3

9

29

26

50% more: Yes or no

Yes

Yes

No

No

So, remaining operations gets 43.1/3 = 14.4% each

15. Approximate average of the total production

Allocation of effort in B,C,D operations of company 4 = 29.7

= 215 + 237 + 251.5 + 268 + 299.5 + 334 6 1605 = = 267.5 ≈ 268 which is equal to production in 2006 6

Remaining operation is allocated extra = 9.9% each. Allocation of effort in B,C,D operation of company 5 = 36.8 Remaining operation is allocated = 12.3% each We see that operation E in company 5 will show the maximum in that case.

16. D and E have shown continuous increase in the production.

10. Total effort for operation B through F is 81.5%.

17. 299.5 − 251.5 = 48 ≈ 50 = 1 = 20% 251.5 251.5 250 5

Even distribution will give effort allocation in each operation =16.3%

18. Production of E is maximum and production of B is minimum.

1.276 

  Quantitative Aptitude and Data Interpretation

19. For the maximum no. of difference of the production of two types of for 2007 and 2008, we need to have a two step process:

Days

Person

Country

Step 1 - Select the types one having the highest production for 2007 and 2008 and

Wednesday

Gifty

France

Thursday

Paul

Australia

Friday

Richa

South Africa

Saturday

Shweta

France

Sunday

Mohit

South Africa

Step 2 - Select the types having the lowest production for 2007 and 2008. E → 80 + 105 = 185 ⇒ 185000 B → 19.5 + 18 = 37.5 ⇒ 37500 Following is the solution:

Exercise 5 

Days

Person

Country

Monday

Samir

South Africa

Tuesday

Nita

Australia

Attempts Right

Wrong

Marks % Accuracy

 

 

 

 

 

PRACTICE EXERCISE  6 Direction for questions 1 to 3:  Go through the table and information given below and solve the questions based on it. Results of a General Studies Paper (GSP) administered to candidates appearing in the Civil Services Examination are given in the Table below. The GSP has four sections Section

Range of Marks 0 – 10

Range of Range of Range of Range of Range of Range of Marks Marks Marks Marks Marks Marks 11 – 25 26 – 40 41 – 55 56 – 70 71 – 85 86 – 100

History Sciences Political Science Current Affairs

1520 3320 5175

9150 6950 6500

9210 8910 8625

13135 12150 14215

10785 10125 9590

8210 9750 5750

2990 3815 5145

2750

8185

9190

16250

10140

6200

2285

1. The total number of candidates who appeared for the Civil Services Examination, assuming that all the candidates wrote all the four sections, is 1.  50000 2.  60000

3.  55000 4.  65000

2. If the minimum marks for qualifying in the Civil Services Examination is more than 40% in each section, the ratio of the number qualifying in History to the number qualifying in Political Science is 1.  1.112

2.  1.012

4.  0.912

3.  0.812

3. Comparing the modal ranges of all the subjects, it is seen that the largest number of candidates got marks in the range of 1.  11 – 25 3.  41 – 55

of 100 marks each. These sections are History, Sciences, Political Science, and Current Affairs. The numbers in the Table below represent the number of candidates securing the respective range of marks, given in discrete numbers, wherein all the candidates wrote all the four sections.

2.  56 – 70 4.  26 – 40

Direction for questions 4 to 7:  Go through the table and information given below and solve the questions based on it. The table below gives the state-wise cumulative utilization of funds available under the Members of Parliament – Local Area Development Scheme (MP-LADS), by the Lok Sabha MPs, for the fiscal years 2005-06 and 200607.

States having Fiscal Year 2005-06 Fiscal Year 2006-07 MP-LADS Amount % Funds Amount % Funds Available Utilized Available Utilized Andhra 888 95 974 93 Pradesh Bihar 812 70 880 78 Gujarat 542 95 586 90 Karnataka 578 93 628 89 Madhya 611 75 667 82 Pradesh Maharashtra 977 89 1080 85 Rajasthan 530 82 587 88 Uttar 1700 78 1843 87 Pradesh Total 6638 83.65 7245 86.4 (8 States)

4. The percentage of funds utilized by Andhra Pradesh, Gujarat, Karnataka, and Maharashtra has changed in the following way from fiscal year 2005-06 to 2006-07 1.  Increased by around 10% 2.  Remained the same 3.  Decreased by around 10% 4.  Decreased by around 5% 5. The ratio of the funds utilized by Bihar, as the percentage of the funds utilized by all the states in fiscal year 2005-06 to 2006-07 has

1.278 

  Quantitative Aptitude and Data Interpretation

1.  Decreased by around 1% 2.  Decreased by around 5% 3.  Increased by around 5% 4.  Increased by around 1%

1.  was larger 3.  was equal

6. The ratio of the funds available to Uttar Pradesh against those available to all other states in fiscal years 2005-06 and 2006-07 has

An industry comprises of four firms (A, B, C, and D). Financial details of these firms and of the industry as a whole for a particular year are given below. Profitability of a firm is defined as profit as a percentage of sales.

Direction for questions 11 to 12:  Answer the questions on the basis of the information given below.

1.  Decreased by around 1% 2.  Decreased by around 5% 3.  Increased by around 5% 4.  Increased by around 1%

Figures in Rs Sales

7. Out of the given states, for how many states, funds used in 2006-07 is more than the funds used in previous year? 1.  5 3.  7

2.  6 4.  8

Direction for questions 8 to 10:  Answer the questions on the basis of the information given below. Spam that enters our electronic mailboxes can be classified under several spam heads. The following table shows the distribution (out of 100%) of such spam worldwide over time. The total number of spam emails received during December 2002 was larger than the number received in June 2003. The total number of spam emails received during September 2002 was larger than the number received in March 2003. The figures in the table represent the percentage of all spam emails received during that period, falling into those respective categories. Category Adult Health Financial Internet Products Scams Others

Sep-02 38 25 11 5 3 5 13

Dec-02 33 30 19 3 7 6 2

Mar-03 19 37 5 10 10 11 8

Jun-03 17 45 18 6 11 2 1

1.  A 3.  C

1.  55% 3.  35%

10. In the financial category, the number of spam emails received in September 2002 as compared to March 2003.

62708 9177 17684

2.  B 4.  D

2.  45% 4.  50%

Direction for questions 13 to 15: Answer the questions on the basis of the information given below. Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW, WHITE, ORANGE, and PINK paints. ORANGE paint can also be produced by maxing RED and YELLOW paints in equal proportions. Similarly, PINK paint can also produced by mixing equal amounts of RED and WHITE paints. Among other paints, RBPC sells CREAM paint, (formed by mixing WHITE and YELLOW in the ratio of 70:30) AVOCADO paint (formed by mixing equal amounts of ORANGE and PINK paint) and WASHEDORANGE paint (formed by mixing equal amounts of ORANGE and WHITE paint). The following table provides the price at which RBPC buys paints.

YELLOW WHITE ORANGE PINK

2.  was smaller 4.  Cannot be determined

16151 10258 2850 1578 4750 3946

12. If firm A acquires firm B, approximately what percentage of the total market (total sales) will they corner together?

1.  Financial 3.  Products

9. In the health category, the number of spam emails received in December 2002 as compared to June 2003 is

19101 2292 4075

Total 89570

11. Which firm has the highest profitability?

Color RED

2.  Scams 4.  None of the above

A B C D 24568 25468 23752 15782

Operating costs 17198 Interest costs 2457 Profit 4914

8. In which category was the percentage of spam emails increasing but at a decreasing rate?

1.  was larger 3.  was equal

2.  was smaller 4.  cannot be determined

Rs,/Litre 20 25 15 22 18

13. The cheapest way to manufacture AVOCADO paint would cost 1.  Rs 19.50 per litre 2.  Rs 19.75 per litre

Practice Exercise 6 

  1.279

3.  Rs 20.00 per litre

1.  AVOCADO

4.  Rs 20.25 per litre

2.  CREAM

14. WASHEDORANGE can be manufactured by mixing

3.  WASHERDORANGE

1.  CREAM and RED in the ratio 14:10

4.  Sufficient data is not available

2.  CREAM and RED in the ratio 3:1

Direction for questions 16 to 19:  Study the following chart carefully and answer the questions based on it.

3.  YELLOW and PINK in the ratio 1:1 4.  RED, YELLOW and WHITE in the ratio 1:1:2 15. Assume that AVOCADO, CREAM and WASHEDORANGE each sells for the same price. Which of the three is the most profitable to manufacture? 30%

Following bar chart shows the sales of Cars in USA in 2008 in preference to different colors of the car:

26%

25% 19% 20% 13%

15%

10%

9%

10%

10%

6%

5%

5% 0%

2%

Green

Blue

Yellow

White

Golden

Black

Brown

Silver

Others

16. Which of the following colour of cars combined consist 50% of the total cars sold?

1.  0 3.  6

1.  Black, Golden, Blue, Silver 2.  Blue, Black, Green, Silver 3.  White, Golden, Blue, Black 4.  White,Blue,Green, Black

19. To increase the percentage share of all color cars under 10% of total sales, a new exchange policy has been brought under practice. Following are the terms and conditions of this exchange policy: i. Only those colour cars can be exchanged (to obtain a new colour car under 10% market share) which have a percentage share of more than 15%. ii. No colour car whose market share is in between 10% - 15% can be used in exchange. How many different combinations are possible under this exchange scheme?

17. Number of cars sold is directly proportional to the color of car. Cars of how many colours are at least 20% more popular than green coloured cars? 1.  0 3.  3

2.  2 4.  cannot be determined

18. Brown coloured car is the least number of cars sold, and no other colour car’s percentage share in total sale of cars is less than 4%. Now the sales figure of different coloured cars are arranged in ascending order. For how many colours’ sales figure, we can definitely determine its rank?

2.  1 4.  cannot be determined

(A combination is defined as a set of a new car, which a person obtains after exchanging, and an old car defined as a car with the person before this exchange.) 1.  6 3.  12

2.  8 4.  Cannot be determined

1.280 

  Quantitative Aptitude and Data Interpretation

Direction for questions 20 to 24:  Go through the table below and answer the questions based on it.

Month/Items A B C D E F G H I J K L M N O

Jan 98 91 106 109 95 86 88 98 100 97 98 103 83 104 94

The table given below represents the Supply to demand ratio per 100 units of 15 items from the period Jan to Oct. For example, supply of item A in Jan was only 98 units where as the demand is of 100 units.

Feb March April May June July August Sep 99 98 98 96 99 97 97 96 91 89 87 88 87 86 90 91 105 102 99 102 100 105 96 92 110 112 108 108 112 85 101 86 94 94 96 101 102 96 97 96 83 84 96 94 87 93 99 101 88 89 94 86 97 93 101 92 89 89 96 94 91 86 102 94 98 96 101 104 98 104 99 111 100 101 99 96 94 100 97 101 96 95 97 98 94 93 98 96 97 96 96 95 92 91 99 101 105 100 103 100 99 98 104 107 78 80 82 86 92 91 100 98 91 95 96 99 92 93 92 97

Oct 95 92 90 99 92 105 89 84 100 92 100 104 102 87 100

20. Which of the following items show the maximum increase in the supply to demand ratio from Feb to August?

23. How many items are constantly under supply throughout the given period (under supply means demand is more than the supply)?

1.  F 3.  G

1.  1 3.  3

2.  N 4.  H

21. For which item does supply exceed demand the maximum number of times? 1.  C 3.  D

24. How many items are constantly under demand throughout the given period (An item is under demand if supply exceeds the demand in all the months during the given period)?

2.  M 4.  J

1.  1 3.  3

22. For the item with the least supply to demand ratio, what is the percentage increase in that ratio in the next month? 2.  3% 4.  2%

ANSWER KEYS

1.  2.5% 3.  4%

2.  2 4.  4

2.  2 4.  0

Exercise 6 

Attempts Right

Wrong

Marks % Accuracy

 

 

 

 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

3

4.

4

5.

3

6.

1

7.

4

8.

3

9.

4

10.

1

11.

4

12.

1

13.

2

14.

4

15.

2

16.

3

17.

4

18.

2

19.

4

20.

2

21.

3

22.

1

23.

2

24.

4

 

Practice Exercise 6 

  1.281

HINTS AND EXPLANATIONS 8. In case of products, percentage of spam e-mails is increasing but at decreasing rate, from Sept 2002 to Dec 2002 products increased by [(7–3)/3] × 100 = 133.33% and in march 2003 about [(7 – 4)/7] × 100 = 43% and in June 2003, [(11 – 10)/10] × 100 = 10%. 9. Since percentage of spam in Dec 2002 is LOWER than June 2003, and the number of total e-mails received is higher, hence cannot be determined.

And cost of WASHERDORANGE is Rs.18.50. Hence CREAM is most profitable. 16. (3) This question can be done by simple calculation using the options. 17. (4) Since we do not know the colours of cars contained in ‘Others’ category, we cannot answer this question.

10. In September 2002, percentage is higher as compared to March 2003, however the total number of e-mails received in Sept 2002 is lower than that in March 2003. Hence obviously larger .

18. (2) We can determine the ranks of only those colour cars which are having a share less than 4%. Reason being unavailability of the data pertaining to the colours contained in ‘others’ category.

11. Profitability is defined as percentage of sales. Approximately Firm A has 25% profit, B has 16.66%, C has 20% and D has approximately 30% profit.

19. (4) We do not know the colors in ‘Others’ category. It might be a possibility that ‘Others’ category is containing 4-5 different colours and each one being around 4% - 5%.

13. Paint AVOCADO is made by mixing ORANGE and PINK in equal quantities. If ORANGE is made using RED and YELLOW, then the cost of ORANGE would be (20 + 25)/2 = 22.5 which is greater than the cost of the ORANGE. If we make PINK by RED and WHITE, the cost of PINK would be (20 + 15)/2 = 17.5 and it is less than the cost of the PINK paint. Hence, the cost of the paint AVOCADO is (22 + 17.5)/2 = 19.75 14. The ratio of RED, YELLOW and WHITE is 1:1:2. 15. If cost of AVOCADO paint is Rs 19.75. The cost of the CREAM is (7 × 15 + 3 × 75)/10 = Rs 18

Hence cannot be determined. 20. By observation we can say that ‘N’ shows maximum increase in supply to demand ratio. 21. For D, supply exceeds demand the maximum number of times. 22. N has least supply to demand ratio in February % increase =

2 × 100 = 2.5%. 78

23. Only items A and B are in under supply. You are required to see that even for atleast one month, it is more than 100, then it cannot be the answer.

PRACTICE EXERCISE  7 Direction for questions 1 to 5:  Go through the chart below and answer the questions based on it. Given four currencies represents the following: US Dollar, Singapore Dollar, UK Pound and Euro. Following is the order of their valuations: UK pound > US Dollar > Euro > Singapore Dollar.

Value in Rs.

Valuation of currencies in Indian Rupees 80 60 40 20 0

74.8

40%

45.94 30.27

33.35

30% 20%

Foreign Currencies 

1. A person wants to buy an article worth 65 Singapore Dollars. If Singapore Dollar loses 2% with respect to the above given exchange rates, then how many US dollars must be spend? 1.  42.1 3.  44.9

2.  41.9 4.  43.6

2. A person wants to buy 800 barrels of oil. The payment can be made either in US dollars or in Euros. If the payment is made in Euros, then it would be 47 Euros per barrel while if one pays in US dollars, the rate would be 29 US dollars per barrel. How much money will he save if he goes for the cheaper deal? 1.  29200 US dollars 2.  34100 US dollars 3.  37600 Euros 4.  None of these 3. In the above question, if there is a discount of 16% on paying in Euros and if the person goes for paying in Euros, how much does a person stand to gain or lose? 1.  Rs 12482 gain 3.  Rs 3987 loss

Direction for questions 6 to 10:  Go through the charts below and answer the questions based on it. The bar charts shown here represent the earning of a Sales executive Mohit. Bar-chart (1) gives us the details of his earnings in the four quarters of the year across the five regions—West, North, South, East and Central. Bar chart (2) gives the details of his total earning in the four quarters in three different years. Bar-chart (1) is applicable for bar chart (2) and vice-versa.

2.  Rs 12482 loss 4.  Rs 3987 gain

4. US bonds give 9% return on investment. Which of the following when invested in US bonds gives maximum returns? 1.  4000 US dollars 2.  2500 UK Pounds 3.  5300 Euros 4.  7000 Singapore Dollars

10% 0%

1st Qtr

2nd Qtr

3rd Qtr

West

South

North

East

4th Qtr

Central

 

4WU 4WU

 





4WU



4WU

 



























6. Across the given years, which quarter has given the maximum earning to Mohit? 1.  Qtr 1 3.  Qtr 3

2.  Qtr 2 4.  Qtr 4

7. Which Region has brought maximum earning for Mohit in the year 2000? 1.  South 3.  East

2.  West 4.  Central

5. Value of Rs depreciates against US Dollar by 10%. What will be the new value of US Dollar in Rs?

8. During which year and quarter the earnings from the north Region have shown maximum change over the previous quarter in that year?

1.  Rs 41.34 3.  Rs 50.53

1.  Quarter III, year 2000 2.  Quarter II, year 2002

2.  Rs 51.04 4.  Rs 40.83

Practice Exercise 7  3.  Quarter II, year 2001

1.  14400 3.  8000

4.  Quarter IV, year 2002. 9. What is the maximum difference between any two regional earnings in any quarter? 1.  Rs 15500

2.  Rs 13000

3.  Rs 14500

4.  None of these

10. Find the percentage change in Mohit’s earning due to the south zone during 2001 over the previous year. 1.  14%

2.  20%

3.  25%

4.  33%

Direction for questions 11 to 15:  Study the following chart carefully and answer the questions based on it. Following table shows the percentage population of six states below poverty line and the proportion of male and female. State

Percentage Population Below poverty Line

A

12

B C D E F

15 25 26 10 32

Proportion of male and female Below Above Poverty line poverty line M:F M:F 3:2 4:3 5:7 4:5 1:2 6:5 2:3

3:4 2:3 5:6 3:2 4:5

11. The total population of State A is 3200, then what is the approximate number of females above poverty line in state A? 1.  1200

2.  2112

3.  1800

4.  1950

12. If the total population of C and D together is 18000, then what is the total number of females below poverty line in these two states? 1.  5000

2.  5500

3.  4800

4.  cannot be determined

13. If the population of males below poverty line in state A is 3000 and that in state E is 6000, then what is the ratio of the total population of state A and E? 1.  3:4

2.  4:5

3.  1:2

4.  None of these

14. If the population of males below poverty line in state B is 500 then what is the total population of B?

  1.283

2.  6000 4.  7600

15. If in state E population of females above poverty line is 19800 then what is the population of males below poverty line in that state? 1.  5500 3.  2970

2.  3000 4.  None of these.

Direction for question 16 to 18:  Go through the information given below and solve the questions based on it. A young girl Roopa leaves home with x flowers, goes to the bank of a nearby river. On the bank of the river, there are four places of worship, standing in a row. She dips all the x flowers into the river. The number of flowers doubles. Then she enters the first place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the second place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flower doubles. She goes to the third place of worship, offers y flowers to the deity. She dips the remaining flowers into the river, and again the number of flowers doubles. She goes to the fourth place of worship, offers y flowers to the deity. Now she is left with no flowers in hand. 16. If Roopa leaves home with 30 flowers, the number of flowers she offers to each deity is 1.  30 3.  32

2.  31 4.  33

17. The minimum number of flowers that could be offered to each deity is 1.  0 3.  16

2.  15 4.  Cannot be determined

18. The minimum number of flowers with which Roopa leaves home is 1.  16 3.  0

2.  15 4.  Cannot be determined

Direction for questions 19 to 21:  Read the information below and solve the questions based on it. ABC is a firm that deals with furniture. Manufacturing of table requires three levels of assembly. The finished table is at first level. The leg assembly and tabletop are second level. The pieces that go into the leg assembly are at the third level which consists of shortrails, longrails and legs. One unit of table requires one unit of tabletop and one unit of leg assembly. One unit of leg assembly requires 2 units of shortrails, 2 units of longrails and 4 units of legs. Orders are placed just in time to minimize storage.

1.284 

  Quantitative Aptitude and Data Interpretation

The lead time for activities are (Lead time is waiting time required to complete one activity) Parts Assemble table Finished leg assembly Purchase legs Purchase shortrails Purchase longrails Purchase table top

1.  100 units in week 1

Weeks 1 1 1 1 1 2

2.  200 units in week 3 3.  300 units in week 6 4.  None of these Direction for question 22 to 24:  Answer the questions on the basis of the information given below.

The availability of parts at present time: Parts Table Leg assembly Legs Shortrails Longrails Table top

A, B, C, D, E, and F are a group of friends. There are two housewives, one professor, one engineer, one accountant and one lawyer in the group. There are two married couples in the group. The lawyer is married to D, who is housewife. No woman in the group is either an engineer or an accountant. C, the accountant, is married to F, who is a professor. A is married to a housewife. E is not a housewife.

Units 50 100 150 50 0 50

22. Which of the following is one of the married couples?

Demand of finished tables Details Demand (units)

Week 4 200

Week 5 150

Week 6 100

19. For meeting the demand of 200 units of finished table of week 4, when would the first order of tabletops be placed? 1.  Week 1 3.  Week 5

2.  Week 3 4.  None of these

2.  50 4.  800

ANSWER KEYS

1.  A and B

2.  B and E

3.  D and E

4.  A and D

23. What is E’s profession? 1.  Engineer

2.  lawyers

3.  Professor

4.  accountant

24. How many members of the group are males?

20. How many legs should be ordered for meeting the demand of week 4 finished tables? 1.  200 3.  400

21. When and how many units of shortrail would be placed for meeting the demand of finished table of week 6?

1.  2

2.  3

3.  4

4.  Cannot be determined

Exercise 7

Attempts Right

Wrong

Marks % Accuracy

 

 

 

 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

4

3.

1

4.

4

5.

2

6.

3

7.

4

8.

4

9.

4

10.

1

11.

1

12.

4

13.

4

14.

3

15.

2

16.

3

17.

3

18.

2

19.

1

20.

2

21.

2

22.

4

23.

1

24.

2

 

  1.285

Practice Exercise 7 

HINTS AND EXPLANATIONS 1. Taking into consideration above rates: 1 US $ = Rs 45.94 1Singapore $ = Rs 30.27 Hence, 1 US $ = 1.52 Sing. $ Singapore $ has lost 2% with respect to the above given exchange rates So, 1 US $ = 1.52 × 1.02 = 1.55 Sing. $ Hence, 65 Sing. $ = 41.9 USD Thus, the person should give 41.9 US $ to get 65 Singapore Dollars. 2. Price for 800 barrels = 37600 Euros = Rs 1253960. However, if we are paying in US $, we will be paying $23200 = Rs. 1065808.

10. Let us tabulate the information given: Region

Annual earnings for the region

West

0.4 x Q1 +0.3 x Q11 + 0.3x QIV

North

0.1 x Q1 + 0.4 x Q11 +0.1x Q111 + 0.2x QIV

South

0.2 x Q1 + 0.2 xQ11 + 0.3 x Q111

East

0.1 x Q11 + 0.2 x Q111 + 0.3x QIV

Central

0.3 x Q1 + 0.4 x QIII + 0.2 x QIV

Earning in south Region in 2001 = 20000 × 0.2 + 10000 × 0.2 + 20000 × 0.3 = 12000 Earning in south Region in 2000 = 10000 × 0.2 + 5000 × 0.2 + 25000 × 0.3 = Rs 10500

Thus, we are paying 188152 Rupees less = 4096 US dollars.

Therefore, percentage change = 14.28%

3. If there is a discount of 16% on paying in Euros, then a person will have to pay 31584 Euros instead of earlier 37,600 dollars. To buy this much Euros, we will have to spend Rs 12482 less than the earlier case.

11. No. of females above poverty line in state A 3 = 3200 × (100 – 12)% × ≈ 1200 7

So, if we are paying in Euros we will be gaining Rs 12482. 4. Larger the amount larger the returns as rate is constant. We are just supposed to find out that which amount given in the options is largest. It can be seen that 7000 Singapore Dollars (4666.7 US dollars) is the largest investment and so it would give the maximum returns. 5. It should be understood that if Rupee is depreciating by 10%, then dollar is appreciating by 11.11%. 6. Use the second bar chart. It is a visual inspection solution. 7. Region

Annual earnings for the region (in thousands)

West

0.4 × 10 + 0.3 × 5 + 0.3 × 15 = 10

North

0.1 × 10 + 0.4 × 5 + 0.1 × 25 + 0.2 × 15 = 8.5

South

0.2 × 10 + 0.2 × 5 + 0.3 × 25=10.5

East

0.1 × 5 + 0.2 × 25 + 0.3 × 15 =10

Central

0.3 × 10 + 0.4 × 25 + 0.2 × 15 = 16

However we could have done this question without using the actual calculation method too. Just see the major contributing quarters and major contributing Region in it. Major contributing quarters are quarter III and IV while central Region is main contributor in those quarters. 8. It can be seen that whenever percentage share of north Region in any quarter decreases, the total earning during that quarter increases and vice versa with the only exception being quarter IV, year 2002. So, the maximum change over the previous quarter must be during quarter IV, year 2002 when it’s percentage share and total earnings both have increased. 9. Maximum quarterly zonal earnings are for central Region during quarter III, 2002 = Rs 18000 Minimum quarterly zonal earnings are East Region during quarter II, 2000 = Rs 500 Hence, Maximum difference= 18000 – 500 = Rs 17500

12. From the given information, we cannot find the population of states C and D individually; so we can’t find the required value. 13. Population of State A below poverty line 5 = 3000 × = 5000 3

5000 × 100 12 And the population of state E below poverty line = 11000 11000 Therefore, total population of state E = × 100 10 5 10 25 Therefore, Required ratio = × = 12 11 66

Therefore, total population of state A =

14. Total population of state B = 500 (0.15) (0.4166) = 8000 Place of worship

Number of flowers before offering

Number of flowers offered

Number of flowers left

1

(15/8)y

Y

(7/8)y

2

(7/4)y

Y

(3/4)y

3

(3/2)y

Y

y/2

4

Y

Y

0

Number of flower before entering first place of worship is 15 y , 8 15 y hence, number of flowers before doubling = 16 This is equal to 30. Hence, y = 32 16. Answer is option (c). 15 y is a whole number is 16. 16 Therefore, 16 is the minimum number of flowers that can be offered. Hence option (3) is the answer.

17. The minimum value of y so that

18. For y to be 16, value of 15 y = 15. 16 Hence, the minimum number of flowers with which Roopa leaves home is 15. Hence option (2) is the answer.

1.286 

  Quantitative Aptitude and Data Interpretation

21. (+) is Male

(B)(Housewife)(–)

(-) is Female

(E)(Engineer)(+)

A(Lawyer)(+)------Couple-------D(Housewife)(–) C(Accountant)(+)--------Couple--------F(Professor)(–) accountant is a female]

[As

no

22. (4) 23. (1) 24. (2)

r e v i e w

t e s t

 5

Data Interpretation This review test is based on the following chapter   Data Interpretation

Direction for questions 1 to 4:  Read the passage below and solve the questions based on it.

3. If the total number of copies made is 45,000, then which copier should be chosen?

dueNorth Academics is evaluating new copying machines to replace the current copier of the company. Three machines are available with the following estimates of operating costs. The labour costs on the copying operation is payable in proportion to the number of copies actually made:

1. A 3.  C

Particulars

Copier A Copier B Copier C

Material cost per copy

0.15

0.12

0.06

Labour cost per copy

0.21

0.12

0.06

Annual lease rental

9000

17400

30000

(All figures are in Rs.) 1. Which of the copiers should be chosen by the company? Would your answer change for the different number of copies made per year? 1.  A 3.  C

2.  B 4.  cannot be determined

2. At what number of copies made per annum will be total cost of copier A and total cost of copier B per annum be same? 1.  45000 3.  90000

2.  70000 4.  7000

2.  B 4.  either A or B

4. Company estimates that the copying volume will be 80,000 per annum. However, the actual number of copies made is only 60,000. Company has already opted for copier B. What is the resultant loss (if any) with respect to the most efficient copier for this volume category?

1.  Rs 1200 2.  Rs 12000 3.  Rs 2400 4.  None of these

Direction for question 5 to 9:  Go through the data set given below and solve the questions based on it. The table below presents data on percentage data on percentage covered by drinking water and sanitation facilities in selected Asian countries. Population covered by drinking water and sanitation facilities (Percentage Coverage) Drinking water

Sanitation Facilities

Urban Rural Total Urban Rural Total India

85

79

81

70

14

29

Bangladesh

99

96

97

79

44

48

1.288 

  Quantitative Aptitude and Data Interpretation

China

97

56

67

74

7

24

Pakistan

82

69

74

77

22

47

Philippines

92

80

86

88

66

77

Indonesia

79

54

62

73

40

51

Sri Lanka

88

52

57

68

62

63

Nepal

88

60

63

58

12

1

1.  76 3.  73

2.  70 4.  Cannot be determined

8. Again, using only the data presented under ‘Sanitation facilities’ columns, sequence China, Indonesia and Philippines in ascending order of rural population as a percentage of their respective total population. The correct order is

Country A is said to dominate B or A>B if A has higher percentage in total coverage for both drinking water and sanitation facilities, and, B is said to be dominated by A, or BPakistan and India>Indonesia B.  India>China and India> Nepal C.  Sri Lanka>China D.  China>Nepal

Direction for question 10 to 11:  Go through the data set given below and solve the questions based on it.

1.  A and C 2.  B and D 3.  A, B and C 4.  B, C and D

The figure below represents states sales and net profit in Rs crore of dueNorth Academics. For five years from 1994-95 to 1998-99. During this period the sales increased from Rs 100 crore to Rs 680 crore. Correspondingly, the net profit increased from Rs 2.5 crore to Rs 12 crore. Net profit is defined as the excess of sales over total costs.

7. Using only the data presented under ‘sanitation facilities’ columns, it can be concluded that rural population in India, as a percentage of its total population is approximately

15

800 600

8.5

400 200 0

2.5

12

680

6

4.5 250

300

5

290

100 1994-95

10

0 1995-96

1996-97 Sales

1997-98

Net profit

1998-99

Review Test 5  10. The highest percentage of growth in sales, relative to the previous year occurred in 1.  1995-96 3.  1997-98

2.  1996-97 4.  1998-99

1.  1998-99 3.  1994-95

mum possible average of section A is still more than maximum possible average of section C? 1.  20 3.  24

11. Defining the profitability as the ratio of net profit to sales, IVP Ltd, recorded the highest profitabil- ity in 2.  1997-98 4.  1996-97

Direction for question 12:  Read the passage below and solve the questions based on it. Ten different samples of milk solution—A, B, C, D, E, F, G, H, I and J are taken and the concentration of each sample (total quantity of milk as a percentage of total quantity of solution) was found out and the results were tabulated as follows: Sample A B C D E F G H I J Concentration (%) 78 57 82 84 98 66 34 87 79 71

  1.289

2.  22 4.  None of these

Direction for questions 15 to 18:  Read the information given below and solve the questions based on it. There is a carpenter who sells only tables (with two legs only) or chairs (with four legs only). The top part of table and top part of chair (the wooden plank) are same and one wooden plank is required to configure one chair or one table. Carpenter gets the legs and top wooden plank separately and then assembles it to make either chair or table. It is also given that Profit per table = Rs 1000/unit and profit per chair = Rs 1500/unit. 15. If there is limited supply of 1200 legs and top wooden plank, which is more profitable to produce – table or chair to maximize the overall profit? 1.  Table 2.  Chair 3.  Either will give same profit 4.  Cannot be determined

12. If two samples of milk are taken and it is required to form a sample whose concentration is more than 80%, then a maximum of how many distinct pairs of samples are there, which will never give the desired result for any ratio of their volumes?



1.  30 3.  12

16. Carpenter takes 4 hours to assemble a table and 3 hours to assemble a chair. If there is limited supply of 1000 man-hour labor, which is more profitable to produce – table or chair to maximize the overall profit?

2.  48 4.  15

Direction for questions 13 to 14:  Read the passage below and solve the questions based on it. There are three sections in class X at A R Academy. Below is the table indicating the number of students, and range of marks obtained by the students of that particular section. Section A No. of students 25 Minimum marks 22 Maximum marks 30

Section B 30 24 28

Section C 20 20 26

Minimum and maximum marks are providing us only the range of marks which can be obtained by the students of that particular section. 13. What is the average marks obtained by all the students of class X together? 1.  24.25 3.  26.75

2.  26.33 4.  cannot be determined

14. What is the maximum no. of students which can be transferred from section A to section C, so that maxi-



1.  Table 2.  Chair 3.  Either will give same profit 4.  Cannot be determined

17. If we club the information given in Q15 and Q16, then how many tables should be produced to maximize the overall profit? 1.  40 3.  0

2.  280 4.  60

18. In the above question, what is the total maximum profit? 1.  240000 3.  460000

2.  280000 4.  None of these

Direction for questions 19 to 20:  Go through the data set given below and solve the questions based on it. Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum

1.290 

  Quantitative Aptitude and Data Interpretation

returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others.

19. The maximum guaranteed return to Shabnam is 1.  0.20% 3.  0.30%

Option A: Invest in a public sector bank. It promises a return of +0.10%

20. What strategy will maximize the guaranteed return to Shabnam?

Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3%.

1.  64% in option B and 36% in option C 2.  1/3 in each of the three options 3.  3 0% in option A, 32% in option B and 38% in option C 4.  36% in option B and 64% in option C

Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail of +2%.

ANSWER KEYS

2.  0.15% 4.  0.1%

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

2

3.

1

4.

1

5.

3

6.

2

7.

3

8.

1

9.

4

10.

1

11.

2

12.

4

13.

4

14.

3

15.

1

16.

2

17.

1

18.

3

19.

1

20.

4

HINTS AND EXPLANATIONS

Variable cost/copy = Material cost/copy + labour cost/copy



Annual lease rental is fixed cost.

1. It can be seen that if dueNorth has to make only one copy, copier A is the best option (we would be concerned with fixed cost only), though if the number of copies to be made is 1 crore copies, then copier C is the best option (we would be more concerned with the variable cost per copy and not with fixed cost).

Hence answer depends upon the volume. Hence option (4) is the answer.

2. Let us assume that for x number of copies, costs will be same.

Cost of copier A = 9000 + 0.36x



Cost of copier B = 17400 + 0.24x



Since costs are same, hence 9000 + 0.36x = 17400 + 0.24x



Hence x = 70,000. Hence option (2) is the answer.

3. Taking a cue from the above question, we can say that in the limit 0-70000, copier A is the best copier. Hence option (1) is the answer. 4. Since the estimate was of 80,000, copier B must would be chosen by the management. Since the actual number of copies = 60,000, hence company will lose some amount because for this quantity, best copier is copier A.

Loss = Cost of 60,000 copies by copier B – Cost of 60,000 copies by copier A = Rs. 1200.



Hence option (1) is the answer.

5. Bangladesh > Philippines (97>86) for drinking water. And Philippines > any other countries for sanitation facilities. Thus, these two countries are on the coverage frontier for two facilities.

6. Statement A > Statement B only if statement A has higher percentage in total coverage for both drinking water and sanitation facilities taken independently and not as a total of the two facilities.

Thus, only statement B and statement D are true



India > China

(81>67 and 29>24)



India > Nepal

(81>63 and 29>18)



Also China > Nepal

(67>63 and 24>18)

7. Let the urban population be x and rural population be y.

From the sanitation column, we have 0.7x + 0.14y = 0.29(x+y), OR, 0.41x = 0.15y 15y Therefore x = 41 Therefore percentage of rural population y y 41 × 100 = × 100 = × 100 = 73.2% 15y x+y 56 +y 41

8. In the same way as the previous questions, we can find percentage of rural population for Philippines, Indonesia and China.



P

50%

I

66.66%

C

79.8%

Thus, Philippines < Indonesia < China.

9. India is not on coverage frontier because

a. It is below Bangladesh and Philippines for drinking water.



b. For sanitation facilities it is below Philippines inter alia.

Review Test 5  15. In this situation, for any limited supply of legs, it is more profitable to make table (if at all production to be made). We can simply see it through the concepts of average that in case of table, profit per leg = Rs 500, and for chair profit per leg = Rs 375/leg. We are not considering the top wooden plank because no. of unit required for each of table and chair is same = 1 top wooden plank. 16. Calculating again the per unit time profit of table and chair,

Profit per hour for table = Rs 250 and



Profit per hour for chair = Rs 500. Hence it is more profitable to produce chair.



Equation for legs ⇒ 2x + 4y ≤ 1200 (we are taking ‘≤’ and not ‘=’ sign because we may not be using all the units supplied)



Equation for man-hour labor ⇒ 4x + 3y ≤ 1000 (we are taking ‘≤’ and not ‘=’ sign because we may not be using all the units supplied)



Total profit = 1000x + 1500y



Objective is to maximize total profit ⇒ maximize (1000x + 1500 y)



In this question, we have only one pair of equation formed from the constraints viz. of legs and man-hour labor.



2x + 4y = 1200

----------------------------(1)



4x + 3y = 1000

----------------------------(2)

Solving these two equations, we get y = 280, x = 40

Hence carpenter should make 40 tables and 280 chairs to maximize his profit.

18. Using the data from previous solution, Total profit = 1000x + 1500y = 1000 × 40 + 1500 × 280 = 460,000 19. 60. Let the amount invested in option B and C be in the ratio 1: K

17. Assume that ‘x’ table and ‘y’ chairs are to be made.





  1.291

So, depending on whether there is a rise or fall in the stock market, The amount earned will be 5 −

5k or2k − 3. 2

{

}

5 − 5k , 2k − 3 2



Therefore guaranteed return = min



Therefore the maximum guaranteed return will be earned when 5 − 5k 16 = 2k − 3. i.e., 9k = 16, i.e., k = . 2 9



Therefore the maximum guaranteed return is when, the amounts invested are in the ratio 9 : 16 i.e., 36% and 64% respectively. Now, the guaranteed return for this distribution is 0.2% (see Q.11). Since option A gives a return of 0.1% which is lesser than this, no amount should be invested in option A.



Hence maximum guaranteed return = 0.20%.



Hence, option [1] is the answer.

section test

1

Quantitative Aptitude and Data Interpretation

1. Find the last two digits of the expression 3245461. 1.  24

2.  76

1.  210 3.  410

3.  36

4.  74

6. What is the remainder when 22010 is divided by 13?

2. A, B and C can complete a piece of work in 15, 30 and 40 days respectively. They started the work together. A left the work 2 days before the completion and B left 4 days before the completion of work. In how many days was the total work completed? 1.  73/10 days

2.  152/15 days

3.  307/30 days

4.  None of these

3. At what time after 3 : 10 AM, the acute angle made by the minute hand and hour hand is double to that of 3 : 10 AM, for the first time? 1.  4 h 43 min

2.  3h 48 min

3.  3 h 320/11 min 4.  None of these 4. In a triangle ABC, sides AB = 20.5 cm and AC = 12 cm. Let D be the point on the side BC such that AD is perpendicular to BC. If AD = 5 cm, what is the radius of the circum-circle of triangle ABC? 1.  25.25 cm

2.  26.75 cm

3.  24.60 cm

4.  25.20 cm

5. Find the number of positive integral solution of a + b + c + 4d = 23.

1.  12 3.  6

2.  305 4.  405 2.  1 4.  4

7. An odd number n has 23 factors, what is the difference in the number of factors of numbers n2 and 2n? 1.  1 3.  3n

2.  45 4.  44

8. S is the set of 2n consecutive natural numbers. If A is the average of even numbers and B is the average of odd numbers, then find the value of A – B? 1.  n/2

2.  1 or -1 n2 − n 3.  (n/2) or (-n/2) 4.  2 9. Consider obtuse angled triangle with sides 10 cm, 24 cm and x cm. If x is an integer, then how many such triangles exist? 1.  14 3.  21

2.  16 4.  18

10. A man leaves home at 5:00 pm to pick up his son from school and return home at 7:00 pm. One day the school was over at 5:00 pm and the son instead of waiting for his father as usual, started walking towards home. Father

Section Test 1  as usual started from home and met his son on the way and returned home with him 12 minutes earlier than usual. If the speed of the Father’s bike is 40 kmph, find the speed of son. 1.  40/9 kmph 3.  39/7 kmph

11. Find the value of 0.16 1.  1 3.  Log 2

6%

. 25%

2.  2 4.  4

5%

2.  r = 2p3 + pq 4.  None of these

2.  1 4.  None of these

1.  24

2.  18

4.  24 3 + 8

3.  24 3



999999998000000001 = ?

1.  999999999 2.  99999999 3.  9999999999 4.  999999991

16. Find the number of terms in the expansion of (a + b + c + d)20. 1.  1771 3.  1001

2.  7117 4.  1971

Rent Telephone & electricity bill Transport Salaries Raw material Others

PamTech (TOTAL EXPENDITURE IN 2008 = Rs 80000) 15%

Rent

20%

35%

Telephone & electricity bill Transport Salaries

5%

14. If a, b, c are positive numbers and abc = 9, then find the minimum value of (1 + a)(1 + b)(1 + c)?

15.

10%

45%

13. If a and b are the roots of the equation x2 + ab = (a + 1)x, then a is equal to which of the following? 1.  –1 3.  2

4%

10% 10%

12. Two roots of the equation t3 – pt2 + qt – r = 0 are equal and opposite in sign. Then, which of the following is true? 1.  pq = r 3.  r = p2q

RamTech (TOTAL EXPENDITURE IN 2008 = Rs 100000)

2.  29/8 kmph 4.  35/8 kmph 1 1 1  log 2.5I + + + ...... ∞ I   3 9 27 

  1.293

20%

Raw material Others

18. The amount spent on transport by PamTech is what percentage of the amount spent by RamTech on transport? 1.  30%

2.  35%

3  40%

4  45%

19. The expenditure on raw material for both companies taken together, is what fraction of the total expenditure in 2008? 1.  0.2

2.  0.25

3.  0.3

4.  0.4

20. Both RamTech and PamTech spend the same amount on which category?

17. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper?

1.  Rent

2.  Transport

3.  Salaries

4.  Others

1.  140 cm2 3.  560 cm2

21. For which category the difference in expenditure is maximum?

2.  240 cm2 4.  None of these

Direction for questions 18 to 21:  Go through the data set given below and solve the questions based on it. The following pie charts show the break-up of the annual expenditures of two private sector companies:

1.  Telephone & Electricity Bill 2.  Transport 3.  Salaries 4.  Raw Material

1.294 

  Quantitative Aptitude and Data Interpretation

Direction for questions 22 to 24:  Go through the table given below and solve the questions based on it.

% of total FDI % of total outflows inflows in inflows of of that Year Country India India country 2000 Mauritius 20103 44% 56% 3% 2001 US 4070 12% 2002 UK 3460 6% 9% 2003 Singapore 2694 4% 3% 2004 Netherlands 2435 9% 14% 5% 2005 Japan 3856 11%

of TV ads are summarized in table 1. The figures in the first row are annual sales of the small cars when the company uses a high profile individual as its brand ambassador in its TV ads and the ones in the second row are that when the company does not use any brand ambassador in TV ads, for different states of the economy. Without knowing what exactly will be the state of the company in the coming one year, the company will either have to sign a TV ad contract with some high profile individual, who will be the company’s brand ambassador for its small car for the next one year, or go for a TV ad without featuring any high profile individual. It incurs a cost of Rs 3.45 lakh (excluding the payment to the brand ambassador) to put a car on the road. When the company’s profit is ascertain, the company makes decisions on basis of its expected profit. If the company can earn a profit xi with probability pi (the probability depends on the state of economy), then the expected profit of the company is ∑ pixi .

22. UK’s total outflow in 2002 is what percentage of India’s total inflow of 2002?

25. The maximum that the company can afford to pay its brand ambassador is

1.  66.66% 3.  133.33%

1.  Rs 10.0 crore 3.  Rs 10.8 crore

Following table and line chart gives the FDI inflows (USD million) in India for the six years from 2000-2005 for six different countries, its percentage share in the total inflows of India in that particular year and percentage of total outflows from that country in that particular year across the globe.

2.  33.33% 4.  166.66%

23. For how many years, India’s total FDI inflow in any particular year is more than the FDI outflow of the country given in that particular year? 1.  0 3.  2

2.  1 4.  3

24. In the year 2006, India stops FDI inflows from Mauritius and it is observed that for each of the remaining five countries, increase in FDI outflow to India in 2006 is exactly equal to the 1/5th of Mauritius’s FDI outflow in 2000. For which country the percentage increase in the FDI outflow is maximum over the data given for that country? 1.  US 3.  Netherlands

2.  UK 4.  Singapore

Direction for questions 25 to 27:  Go through the data set given below and solve the questions based on it. An automobiles company’s annual sales of its small cars depends on the state of the economy as well as on whether the company uses some high profile individual as its brand ambassador in advertisements of its product. The state of the economy is “good”, “okay” and “bad” with probabilities 0.3, 0.4 and 0.3 respectively. The company may choose a high profile individual as its brand ambassador in TV ads or may go for the TV ads without a high profile brand ambassador. If the company fixes price at Rs 3.5 lakh, the annual sales of its small cars for different states of the economy and for different kinds

2.  Rs 10.6 crore 4.  Rs 12.0 crore

26. Mr. Khan a popular film actor, agrees to sign the contract to become the company’s brand ambassador for Rs 9 crore. The cost to the company of putting a car on the road also got escalated. The maximum escalation in cost of putting a car on the road, for which the company can afford to sign the contract with Mr Khan is 1.  Rs 900 3.  Rs 1250

2.  Rs 967 4.  Rs 1267

27. Mr Khan a popular film actor, agrees to sign the contract to become the company’s brand ambassador for Rs 9 crore. The cost to the company of putting a car on the road also got escalated by Rs 1000. If the company signs the contract with Mr Khan, its profit will

1.  increase by Rs 40 lakh 2.  increase by Rs 60 lakh 3.  decrease by Rs 20 lakh 4.  decrease by Rs 40 lakh

28. If x satisfies | x-1 | + | x-2 | + | x-3 | ³ 6, then

1.  0 ≤ x ≤ 4 3.  x ≤ 0 or x ≤ 4

2.  x ≤ –2 or x ≤ 4 4.  none of these

29. Sterling Silver is 92.5% pure silver. In what ratio should pure silver and sterling silver be mixed to obtain a 94% Silver alloy?

  1.295

Section Test 1  1.  1:4 3.  1:3

and the remaining audience heard 2/3rd of the talk. The average number of minutes of the talk hard be by the audience are:

2.  4 :1 4.  3:1

ANSWER KEYS

30. At a Business seminar, chairman addressed the audience for an hour. 20% of the audience heard the entire talk and 10% slept through the entire talk. Half of the remainder heard only 1/3rd of the talk

1.  30 3.  24

2.  45 4.  33

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

2

3.

3

4.

3

5.

2

6.

1

7.

1

8.

2

9.

1

10.

1

11.

4

12.

1

13.

4

14.

1

15.

1

16.

1

17.

1

18.

3

19.

4

20.

4

21.

4

22.

1

23.

4

24.

3

25.

4

26.

3

27.

2

28.

3

29.

1

30.

4

HINTS AND EXPLANATIONS 1. For the last two digits of any expression we have to check last two digits of the expression



In the last 4 days, work completed is 22 + 6 = 28 units



Rest of work = 120 – 28 = 92 was completed by A, B and C in 92/15) days



3245461 = 245461



When 24 raised to some power, last two digits follows a second order cyclicity i.e.



Therefore total days taken to complete the work = 4 + 92/15 = 152/15 days



241 has last two digits 24



Hence option (2) is the answer.



242 has last two digits 76 243 has last two digits 24 × 76 = 24

3. Angle between two hands at 3 : 10 AM = (90 + 5 ) – 60 = 350







So, required angle = 700, after 3 : 10 AM

24 has last two digits 76



Generalizing the above calculation, whenever 24 has odd power, last two digits = 24 and whenever 24 has even powers, last two digits = 76.

Total time required to make 700 angle when minute hand is ahead of hour hand = 20/11



So, at 3 h 320/11 min the required angle will be formed.



Hence option (3) is the answer.

4

In this question, 24 has odd power. So the last two digits of the expression is 24.



Hence option (1) is the answer.



[For more details on Cyclicity, Go through Cyclicity chapter in the book Demystifying Number System].

4.

A

2. Let the total work be LCM (15, 30, 40) = 120 units

Work Done of A = 8 unit per day



Work Done of B = 4 unit per day



Work Done of C = 3 unit per day



B left 4 days before the completion of work means last 4 days work was done by A & C



A left 2 days before the completion of work means last 2 days work was done by C



C can complete 2 × 3 = 6 unit of work in last 2 days



A & C can complete 2 × 11 = 22 unit of work in second last 2 days

B

D

C







As given in the statement, AB = 20.5 cm and AC = 12 cm Let BC = k



Radius of the circum-circle of the triangle abc 20.5 × 12 × (k ) = R= = 4(area) 4(area) Area of the triangle 1/2 × k × 5



  Quantitative Aptitude and Data Interpretation

1.296 

20.5 × 12 × (k ) = 24.60cm 4( 1 2 × 5 × 5)



Therefore, R =



Hence option (3) is the answer.

5. In this question we have to focus only d, except d all other variables have co-efficient unity.

At d = 1, given equation becomes a + b + c = 19



No. of positive integral solution = 18C2 = 153



(As No. of positive integral solution of a1 + a2 +….. + ar = n – 1Cr – 1)



At d = 2, given equation becomes a + b + c = 15



No. of positive integral solution = 14C2 = 91



At d = 3, given equation becomes a + b + c = 11



No. of positive integral solution = 10C2 = 45



At d = 4, given equation becomes a + b + c = 7



No. of positive integral solution = 6C2 = 15



At d = 5, given equation becomes a + b + c = 3



10. Clearly, Distance from home to school is 40 x 1 = 40 kmph

Time saved = 12 minutes



Distance covered by Ram in 12 minutes = (12/60) × 40 = 8km



It includes onward and return journey distance both.



So, distance covered by his son = (1/2) x 8 = 4 km



Distance covered by Ram =n 40 – 4 = 36 km



Time taken by Ram = 36/40 hr 4 Therefore, speed of son = 9 = 40/9 kmph 10



Hence option (1) is the answer.



Let y = 0.16

No. of positive integral solution = 2C2 = 1



Taking log on both sides,



Therefore, total number of positive integral solution of the given equation is



Log(y) = log ↓ 2.5(1/2) ) × log(0.16) =



153 + 91 + 45 +15 + 1 = 305



Hence option (2) is the answer.

6. 212 leave the remainder 1 when divided by 13.

2



Hence option (1) is the answer.

2010

= (2 ) . 2 leaves remainder 12 when divided by 13. 6 167

6

7. As given in the statement, odd number n has 23 factors, then odd number is of the form

n = (odd prime)22 implies that 2n = 2 (odd prime)22 has factors = 46



n2 = (odd prime)44 has factors = 45



Therefore, the required difference is 46 – 45 = 1



Hence answer option is (1)

1 1 1 1 11. It is known that + + + ..... ∞ = 3 = ½ 1 3 9 27 1− 3 1   log 2.5 I I  2 

−log 2 × 2(log(0.4)) = 2 log(2) = log 4 − log 0.4



Therefore, y = 4



Hence option (4) is the answer.

−log 2 × 2(log(0.4)) = log 2.5

12. Let a, –a and b are the roots of the equation.

Sum of the roots is b = p



As p is one root of the equation, it will satisfy the equation



p3 – p3 + qp – r = 0  implies that  pq = r

13. Sum of the roots of the given equation is a + b = a + 1 implies that b = 1 a can be arbitrary any complex number.

Therefore, there is no unique value of a.

14. As 1, a are positive numbers, then 8. If S starts with even numbers then A – B =



1+ a ≥ a 2 (1 + a) ≥ 2 a 

……………. (i)



(1 + b) ≥ 2 b 

……………. (ii)



A – B = (1) + (1) + ..... + (1)(n times) = 1 n Therefore, A – B is either –1 or +1



(1 + c) ≥ 2 c 

……………. (iii)



Hence answer option is (2)



Multiplying (i), (ii) and (iii)

9. Using triangle inequality,



(1 + a)(1 + b)(1 + c) ≥ 8 abc = 24



(24 – 10) < x < (24 + 10)  implies that  14 < x < 34



Therefore, the minimum value of the required expression is 24.



Case I: Let x is the greatest possible side



X2 > 242 + 102







i.e. 27, 28, 29, 30, 31, 32, 33



i.e. 7 cases



Case II: Let 24 is the greatest possible side



242 > x2 + 102







i.e. 15, 16, 17, 18, 19, 20, 21



i.e. 7 cases



Therefore, total number of triangles is 7 + 7 = 14 Hence answer option is (1)



( −1) + ( −1) + ..... + ( −1)(n times) = –1 n If S starts with odd numbers, then

X > 26

X < = 21



15. 92 = 81

992 = 9801



9992 = 998001



99992 = 99980001



…………………………….



………………………………….



9999999992 = 999999998000000001



Alternatively, this question can be done by generating a small pattern also.

16. Number of terms = n + r – 1Cr – 1



Therefore, required number of terms is 20 + 4 – 1C4 – 1 = 1771

Section Test 1  17. When folded along breadth, we have: 2(1/2 + b) = 34 or 1 + 2b = 34

When folded along length, we have: 2(1 + b/2) = 38 or 2i + b = 38

Year

Solving (i) and (ii), we get: 1 = 14 and b = 10.

2000

Area of the paper = (14 × 10) cm2 = 140 cm2 .

2001 2002

18. Amount spent by PamTech on transport = 5% of Rs 80000 = Rs 4000

Amount spent by RamTech on transport = 10% of Rs 100000 = Rs 10000



Hence, (4000 × 100)/10000 = 40%.



20. Others for both the companies = Rs. 4000. 21. For the category, raw material the difference is maximum = 45000 – 28000 = Rs. 17000. 22. Understand that 9% of UK’s outflow is 6% of India’s inflow  a higher percentage of UK’s value = a lower percentage of India’s value. Hence we can conclude that UK’s outflow is less than India’s inflow. Hence multiplier should be less than 1. So UK’s outflow is 6/9 = 2/3 of India’s inflow = 66.66% of India’s inflow. Hence option (A) is the answer

US UK

Total FDI outflow for that country

20103 4070

3%

135667

3460

9%

38444 89800

35898

2003

Singapore

2694

2004

Netherlands

2435

14%

17393

3856

5%

77120

Japan

Since FDI outflow for Netherlands is the lowest, hence a change of USD 4020 million will reflect maximum percentage change. Hence option (C) is the answer.

29. The amounts of the two input mixtures are unknown; the amount of the output mixture is 100 g (Assume). Let x = grams of 92.5% silver alloy Then, since the total weight is 100g, we have (100 – x) = grams of 100% silver We now write an equation relating the amounts of pure silver in the two “input” mixtures and in the “output” mixture: “x” grams at 92.5% silver + (100 – x) grams at 100% = 100g at 94% (x)(0.925) + (100 – x)(1.0) = (100)(0.94) 0.925x + 100 – x = 94 6 = 0.075x 6000 = 75x 6000/75 = x 80 = x So to make 100 g of an alloy of 94% silver, you need to mix 80 g of 92.5% alloy and 20 g of pure silver. Hence option (A) is the answer 30.

23. Reflect the following statement upon yourself: If % of total inflows of India < % of total outflows of that country, then India’s FDI inflows will be more than the FDI outflow of that country in that particular year. Hence three years is the answer. Hence option (D) is the answer. 24. This question expects us to explore the future scenario. Average of Mauritius FDI inflow in 2000 = 20103/5 = 4020.6 Now let us see the solution:

Mauritius

% of total outflows of that country 56%

3%

2005

19. (45+35)/200 = 0.4.

Country

FDI inflows in India

  1.297

% Audience

Minutes Heard

Total

20 10 35 35  

60 0 20 40  

1200 0 700 1400 3300



Total time heard = 3300 minutes



Hence average time spent hearing = 3300/100 = 33 minutes. Hence option (D) is the answer.

section test

2

Quantitative Aptitude and Data Interpretation

1. For how many natural number values of N, N4 + 4 will be a prime number?

1.  900 3.  1800

1.  0 3.  2

5. How many values of x will satisfy the following equation:

2.  1 4.  None of these

2. In the figure given, ABCD is a cyclic quadrilateral and AB = 25 cm, BC = 39 cm, CD = 52 cm and AD = 60 cm. What is the diameter of the circle?

A

D

C 2.  65 cm 4.  178 cm

3. How many natural numbers are there which give a remainder of 41 after dividing 1997? 1.  2 3.  6

x + x + x ...............∞ = x. x. x ..........∞

1.  0

2.  1

3.  2

4.  None of these

6. ABC is an equilateral triangle with side length 1 unit. P is any point on the circumcircle of this triangle. What is the value of AP2 + BP2 + CP2? _ 1.  Ö2 _ 3.  2Ö2

B

1.  60 cm 3.  72 cm



2.  4 4.  None of these

4. You are selecting 10 numbers randomly out of the first 100 odd numbers. Sum of these 10 odd numbers is N. How many different values of N are possible?

2.  1801 4.  901

2.  2 4.  3

7. How many integral points are contained inside a triangle with the vertices (0, 0), (21, 0) and (0, 21)? 1.  190 3.  210

2.  231 4.  171

8. In a race on a circular track, A, B and C start from the same point N in the same direction. Their speeds are n m/s, (n+1) m/s and (n+2) m/s respectively where n is a natural number. How many times will they meet before they meet for the first time at point N(n>0, N>0)? 1.  1 3.  2

2.  1 4.  None of these

Section Test 2  9. There are a certain number of students in a class and each of them have at most 4 books. The number of students who have at most 1, 2, 3 and 4 books is 11, 18, 19 and 21 respectively. What is the number of students with at least 3 books?

1.  0

2.  1

3.  2

4.  3



  1.299

Direction for questions 10 to 12:  Go through the information given below and solve the questions based on it.

Table 1 – Mode of travel between two cities Patna Bus Train Air plane Train

Patna Mumbai Calcutta Chennai Bangalore

Mumbai Bus Train Train Air plane

Calcutta Train Train Air plane Bus

Chennai Air plane Train Air plane Bus

Bangalore Train Air plane Bus Bus -

Table 2 – Distance between two cities (In kms) Patna Patna Mumbai 100 Calcutta 150 Chennai 150 Bangalore 300

Mumbai 100 200 300 500

Calcutta Chennai Bangalore 150 150 300 200 300 500 500 300 500 100 300 100 -

Speed (in kmph) Airplane Train Bus 0

5

10

15

20

25

30

35

40

45 

10. Which city can be reached from Patna in the least time? 1.  Mumbai 3.  Chennai

2.  Calcutta 4.  Bangalore

11. For which of the following options, travel time is the least?

1.  Mumbai-Chennai 2.  Patna-Bangalore 3.  Bangalore-Chennai 4.  Mumbai-Calcutta

12. If one can travel by bus or train only, then which two cities will have the least travel time?

1.  Patna-Mumbai 2.  Bangalore-Calcutta 3.  Chennai - Mumbai 4.  None of these

13. In a town 25% families own a phone and 15% own a car. 65% families own neither a phone nor a car. 2000 families own both a phone and a car. Consider the following statements in this regard: 1.  10% families own both a car and a phone 2.  35% families own either a car or a phone 3.  40,000 families live in the town Which of the above statements are correct? 1.  1 and 2 3.  2 and 3

2.  1 and 3 4.  1, 2 and 3

14. The function f(x) = |x–2| + |2.5 – x| + |3.6 – x|, where x is any real number, attains a minimum     value at 1.  x = 2.3 3.  x = 2.7

2.  x = 2.5 4.  None of these

1.300 

  Quantitative Aptitude and Data Interpretation

15. Find the number of natural numbers which are smaller than 2.108 written by means of the digits 1 and 2. 2.  766 4.  782

1.  760 3.  754

16. The quadratic equation g(x) = (px2 + qx + r), p ≠ 0, attains its maximum value at x = 7/2. Product of the roots of the equation g(x) = 0 is equal to 10. What is the value of p × q × r? 2.  –70 4.  Cannot be determined

1.  70 3.  0

17. In the given figure, ABCD and BDQP are two rectangles, in which AB = 12 units and AD = 5 units. Find the area of the rectangle BDQP. A

B

C

D



1.  36 3.  5

2.  30 4.  40

22. If the sum of five consecutive positive integers is A, then the sum of the next five consecutive integers in terms of A is (a)  A+1 (c)  A+25

(b)  A+5 (d)  2A

Direction for questions 23 to 26:  Go through the table given below and solve the questions based on it. The following table gives the tariff (in paisa per kilo–watt– hour) levied by the NTPC in 2004–05, in the four sectors and the regions within them. The table also gives the percentage change in the tariff as compared to 2001–02.

P

Region 1 Region 2 Region 3 Region 4 Region 5 Sector 1 425 +15 472 +5 420 –4 415 +8 440 +10 Sector 2 430 +12 468 +8 448 +7 423 –3 427 +11

Q

1.  78 sq. units 3.  65 sq. units

21. Rs 180 is divided among 66 boys and girls of a class. The sum of the boy’s share and girl’s share are in ratio 5:4 but their individual shares are 3 : 2 respectively. The number of boys in the class is



2.  60 sq. units 4.  52 sq. units

Direction for questions 18 to 20:  Read the following instructions and solve the questions based on it.

Sector 3 428 +8 478 –4 432 +6 441 +10 439 +8 Sector 4 434 –5 470 +15 456 +10 451 +12 446 –12

23. If the amount of power consumed by the various Regions in Sector 1 is the same, then, as compared to 2001–02, the net tariff in 2004–05 1.  Increased by 9.5% 2.  Decrease by 1.5% 3.  Decrease by 13.3% 4.  None of these

Choose A If the question can be answered by one of the statements alone and not by the other. Choose B If the question can be answered by using either statement alone. Choose C If the question can be answered by using both the statements together, but cannot be using either statement alone. Choose D If the question cannot be answered even by using both the statements together.



1 8. Is x > 2? Statement A: |2x − 19| < 7 Statement B: x2 – 4x = 0

25. Which of the following has got a maximum percentage increase for the given period?

19. Is x > y? Statement A: 3x + 5y = 11 where x and y are integers Statement B: x5 > y5 20. If both m and n are positive integers less than 100 and greater than 10, is the sum m + n a multiple of 11? Statement A: m – n is a multiple of 22 Statement B: The tens digit and the units digit of m are the same; the tens digit and the units digit of n are the same

24. What approximately was the average tariff per sector in Region 3 in 2001–02? 1.  402 3.  433



2.  424 4.  None of these

1.  Region 1 – Sector 1 2.  Region 1 – Sector 2 3.  Region 5 – Sector 2 4.  None of these

26. There are a total of 20 units of NTPC divided into regions and then subdivided into sectors, as given in the above table. For how many units of NTPC in 04-05, there is a net increase in the tariff ? 1.  15 3.  8

2.  5 4.  None of these

Section Test 2  Direction for questions 27 to 29:  Go through the table given below and solve the questions based on it.

this value, better is the forecasting. Which year’s forecasting is best?

Table given below gives the Estimated and Actual Sales revenue and cost figures for three years. Answer the questions based on it.

1.  2007 3.  2009

1.  340 3.  428

Estimated Profit = Estimated Revenue – Estimated Cost Actual Profit = Actual Revenue – Actual Cost

2.  401 4.  None of these

30. In a geometric progression, product of 11th term, 18th term and 20th term is equal to the product of 28th term and 5th term. Which of the following is necessarily true about that GP?

27. For how many years, actual profit is more than estimated profit? 2.  1 4.  3



28. A measure of forecasting done by marketing team is the ratio of Estimated Sales to actual sales. Lower is

ANSWER KEYS

2.  2008 4.  cannot be determined

29. Company plans to use a different mechanism for forecasting of its maximum possible profit = Max(Estimate, Actual(Sales Revenue)) – Min(Estimate, Actual(Cost)). What is the maximum possible profit derived this way?

Sales   Revenue 2007 2008 2009 Cost 2007 2008 2009 Estimated 1281 1452 1228 Estimated 986 1051 1024 Actual 1326 1286 1452 Actual 988 1076 1068

1.  0 3.  2

  1.301

1.  One of terms of this GP has to be equal to zero. 2.  One of the terms of this GP has to be equal to one. 3.  This GP will have infinite terms. 4.  Common ratio of this GP will be less than 1.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

2

3.

3

4.

4

5.

3

6.

2

7.

1

8.

4

9.

4

10.

3

11.

3

12.

1

13.

3

14.

2

15.

2

16.

4

17.

2

18.

4

19.

2

20.

1

21.

2

22.

3

23.

4

24.

4

25.

1

26.

1

27.

3

28.

3

29.

3

30.

2

HINTS AND EXPLANATIONS 1. 1st of all we should understand that we cannot solve this question by taking different values of N and checking if its prime or not. We need to devise some alternative method.

N4 + 4 = (N2 + 2)2 – (2N)2 = (N2 + 2 + 2N) (N2 + 2 – 2N)



Since N is a natural number, each of the above factors will also be a natural number.



We can conclude that N4 + 4 = (N2 + 2 + 2N) (N2 + 2 – 2N) is product of two natural numbers. Hence it cannot be a prime number except for the value N = 1 for which the values are as follows:



(N2 + 2 + 2N) = 5 and (N2 + 2 – 2N) = 1, So (N2 + 2 + 2N) (N2 + 2 – 2N) = 5 × 1 = 5



(For N = 1, value can be obtained using N4 + 4. Though for higher values of N, calculating the value and checking if its prime of not is difficult).

2. BC, CD and BD constitute a right-angled triangle (13 × 3, 13 × 4 and 13 × 5). If BD = 65, then it satisfies the other set of values of AB and AD also. 3. Let us assume that the quotient is Q and divisor is D. Using the condition given in question, 1997 = QD + 41 Þ QD = 1956. Now we will factorize 1956 in two parts such that D (divisor) is more than 41. 4. The minimum possible value of first 10 consecutive odd numbers = 100 and next value of sum would be obtained as 102 (by replacing 19 by 21). And so on all the other even values from 100 to 1900 will be a value of sum. There are 901 even numbers from 100 to 1900. 5. Go through hit and trial.

1.302 

  Quantitative Aptitude and Data Interpretation

6. Assume any one vertex of the triangle to be the point of the circum-circle and then solve.

19. Statement (A): 3x + 5y = 11

We will assume some values of x to check the inequality.

7. Here we need to find out the solution of 2 ≤ x + y ≤ 20



If x = 2; y = 1 implies that x > y



If x = -2; y = 7 implies that x > y



If x = 3; y = 4 implies that x < y



Statement (A) alone is not sufficient to give the answer of the question.



Statement (B): x5 > y5 implies that x > y (as from the xn > yn implies that x > y if n is odd)



Therefore, Statement (B) alone is sufficient.



We know that the integral solutions possible of x + y = n, where zero solutions are not possible is n-1Cr-1.

So, total points = 19 ´ 20 /2 = 190 8. Since their speeds are consecutive natural numbers, there will be just one meeting point and that is the starting point. So, answer = 0. Hence option (4) is the answer.

Let us make a table for the time taken: Patna Mumbai Calcutta Chennai Bangalore Patna Mumbai

4

5

3.75

10

4

-

6.666667

10

12.5

12.5

12

Calcutta

5

6.666667

Chennai

3.75

10

12.5

Bangalore

10

12.5

12

4 4

-

14. Minima of f(x) = |x–2| + |2.5 – x| + |3.6 – x| at one of the critical points.

F(x)x = 2 = 0 + 0.5 + 1.6 = 2.1

F(x)x = 2.5 = 0.5 + 0 + 1.1 = 1.6 F(x)x = 3.6 = 1.6 + 1.1 + 0 = 2.7

Obviously minima is obtained at x = 2.5. Hence option (B) is the answer.

15. 2.108 is a nine-digit number. So, all the numbers which are of less than 9 digits will be smaller than 2.108.

Total number of numbers of 1 digit = 2



Total number of numbers of 2 digit = 22



Total number of numbers of 3 digit = 23



Total number of numbers of 4 digit = 24



Total number of numbers of 5 digit = 25



Total number of numbers of 6 digit = 26



Total number of numbers of 7 digit = 27



Total number of numbers of 8 digit = 28



Total number of numbers of less than 9 digits = 510



Total number of numbers of 9 digits less than 2.108 = 28







Hence option (B) is the answer.

Total number of numbers of less than 2 × 108 = 510 + 256 = 766

16. Value of p cannot be calculated, so p × q × r cannot be determined. 17. Ar(DBCD ) = ½ ar(ABCD) = ½ ar (BDQP)

So, ar(ABCD) = ½ ar (BDQP) = 60 sq. units



Hence option (B) is the answer.

18. Statement (A): |2x − 19| < 7, implies that -7 < |2x − 19| < 7

20. Using statement (A) alone: Since m-n is a multiple of 22, m-n is a multiple of 11 and of 2 because 22 = 11 × 2 If both m and n are multiples of 11, the sum m + n will also be a multiple of 11. Consider the following examples: 44 – 22 = 22 {which is a multiple of 11 and of 22} 44 + 22 = 66 {which is a multiple of 11 and of 22} 88 – 66 = 22 {which is a multiple of 11 and of 22} 88 + 66 = 154 {which is a multiple of 11 and of 22} However, if m and y are not individually divisible by 11, it is possible that m – n is a multiple of 22 (and 11) while m + n is not a multiple of 11. For example: 78 – 56 = 22 but 78 + 56 = 134 is not a multiple of 11. Hence statement (A) alone is not sufficient to answer the question. Using statement (B) alone: Since the tens digit and the units digit of m are the same, the range of possible values for m includes: 11, 22, 33, 44, 55, 66, 77, 88, 99 Since each of these values is a multiple of 11, m must be a multiple of 11. Since the tens digit and the units digit of n are the same, the range of possible values for n includes: 11, 22, 33, 44, 55, 66, 77, 88, 99 Since each of these values is a multiple of 11, n must be a multiple of 11. Now if both m and n are multiples of 11, (m + n) and (m – n) will be a multiple of 11. Statement (B) alone is sufficient. Hence option (A) is the answer. 21. Boy’s share = 180(5/9) = Rs 100

Girl’s share = 180(4/9) = Rs 80



Given that (100/3x) + (80/2x) = 66 implies that x = 10/9



Therefore, number of boys in the class = (100 × 9)/30 = 30



Hence option (B) is the answer.

22. Best way of solving this question is - Assume values. Assume 1, 2, 3, 4 and 5. Sum of these five numbers = 15 = A. Now next five numbers are 6, 7, 8, 9, 10. Sum of these five numbers = 40. 40 = A + 25. Hence option (C) is the answer.



Implies that x > 13 or x < 13





Hence statement (A) alone is not sufficient.

27. Following is the profit figure:



Statement (B): x – 4x = 0 implies that x = 0 or x = 4



Statement (B) alone is also not sufficient.



Even by using both the statements together, no definite conclusion can be drawn.



Hence option (D) is the answer.

2

2007



2008

2009

Estimated Profit

295

401

204

Actual Profit

338

210

384

Hence option (C) is the answer.

Section Test 2  28. Following is the ratio:





Min(Estimate, Actual(Cost))

2007

2008

2009

2007

2008

2009

0.966063

1.129082

0.84573

986

1051

1024

Hence option (C) is the answer.

29. Max(Estimate, Actual(Sales Revenue)) 2007

2008

2009

1326

1452

1452



Maximum possible profit = 428 crores (in 2009)



Hence option (C) is the answer.

  1.303

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PART

2

VERBAL AND LOGICAL REASONING

This page is intentionally left blank.

c h a p t e r

 1

Reading Comprehension   WHAT IS READING COMPREHENSION? Reading comprehension section in the CAT is the advanced version of the reading comprehension asked back school. Historically, the passages in the CAT have ranged from 350-1300 words, followed by a set of few questions. The passages are drawn from areas like pure sciences, social sciences, medicine, art, literature, technology etc. A student is supposed to answer the questions in light of the information given in the passage within the stipulated time. The ability of the student to make sense of the information and ideas presented in the passage is put to test through questions with multiple choice answers. More specifically, a person’s ability to understand standard written English, analyse complex ideas, and ability to draw inferences from the written material is put to test. The significance of Reading Comprehension, commonly known as RC can be gauged from the fact that almost half the questions in the Verbal Section are based on Reading Comprehension. Many students find RC to be tough and challenging, but with consistent practice, and patience, the art of Reading Comprehension can be mastered.

 WHY IS READING COMPREHENSION ASKED? RC is the most important and wide question type of the English section of the CAT and other B-School entrance test. RC section helps examiners in assessing the expertise

of one in understanding the language. Besides, RC also checks how well a person understands someone else’s (the author’s) view point his preferences and prejudices. 1. Reading Comprehension is integral to success in the CAT Reading is important not only for RC, but also for English Usage area (especially in the Critical Reasoning or FIJ or Sentence arrangement questions), and LR/DI section. Having a good reading habit will make more time available for solving the problem. 2. Reading is essential to do well in a B-school. Life in a B-school demands extensive reading and research for case studies, presentations, and business projects. Today’s global manager has to keep pace with the latest happenings in the corporate world, political changes in the country and the world, changing preferences of the customer. Therefore, newspapers, journals and business magazines form the staple diet of a wannabe professional. 3. Reading helps in getting ahead in career Recent researchers have tried to analyse the reading habits of adults working in different organizations at different levels of management hierarchy. One such research finds that people at the higher levels have more positive attitudes toward reading and spend more time in reading. It gives us an idea that reading helps probably because a well read person will have viewpoints and knowledge about diversified fields in his/her occupation, that may lead to faster growth.

2.4 

  Verbal and Logical Reasoning

Source: http://www.eric.ed.gov (sponsored by US Dept of Education) Let us now go through a sample RC passage:

Breaking the ice with RC and English Usage Read the passage carefully and answer the questions on the basis of the information supplied by the passage. With Barack Obama taking oath yesterday as America’s 44th and first African-American president, the United States turned a page and closed a chapter. Obama’s spectacular success story is packed with poignant, and powerful, symbolism. If he accepted the Democratic nomination last August on the anniversary of Martin Luther King Jr’s ‘I Have a Dream’ speech, his inauguration follows the American holiday in memory of King. It is the culmination of an extraordinary story and a new beginning. Obama rode on a ticket for change. A country left bitter, fearful and divided by eight years of George W Bush’s presidency, welcomed him with relief and expectation. The world, which had viewed America with growing alarm during these years, tuned in to Obama as well. He represented hope that America would manage its own house responsibly and favour consensus and cooperation while dealing with the world. But as enormous as his moment in history are the challenges Obama will face from day one. Undoubtedly, the gloomy economy will consume much of the new president’s energies and he has so far shown signs of clear thinking on how to get America up on its feet again. Equally tough are the assortment of challenges that will present themselves on Obama’s foreign policy plate. One war needs to be wound down responsibly while America’s attention has to shift to the real battleground in Afghanistan and Pakistan. Obama cannot afford to engage Pakistan only to tackle al-Qaeda and the Taliban. To continue the world’s war against terror, he will have to pursue the other extremist outfits like Lashkar-e-Taiba and its front organizations which export violence from that country. They have had a generally free run despite Pakistan’s claims to the contrary. For the sake of the world’s security, Obama must press Islamabad to clamp down on these groups and close down their bases, something that the Bush administration failed to do for most of its run. And then there is the Middle East mess. Trying to achieve a degree of resolution there will require fresh commitment and thinking from Washington. It is evident that Obama will have to hit the ground running. There are soaring expectations which cannot be all fulfilled. But he has a good base of credibility to start from. Opinion polls show he enjoys close to 80 per cent approval ratings as he picks up the keys to the White House and that the American people across political divides, are willing to give him a chance and their time. His commitment to consultative governance while being firmly in charge, and the A-list team he has picked, would hopefully serve America and the world well. Obama’s inauguration party which has seen millions of Americans pour onto the streets to have a blast is a

fine celebration of democratic ideals and values. Democracy’s enabling promises are why Americans and those who share similar values elsewhere are raising a toast as they welcome President Barack Hussein Obama. 1. What does the author want to convey from the statement ‘But as enormous as his moment in history are the challenges Obama will face from day one’ 1. His ascent heralds a significant change but it also poses many daunting tasks ahead. 2. The challenges in front of Obama are insignificant in comparison to his heroic stature. 3. This the biggest moment in the history of the US, but also marks the beginning of Osama’s onerous journey. 4. Obama shall face the toughest challenges in the first phase of his presidency. 5. Obama’s historical win guarantees that he will be able to sail through the tough times easily. 2. What can be inferred about the policies of Obama’s predecessor? 1. His policies had less room for consensus and cooperation in world affairs. 2. His policies lacked clear thinking on how to get America upon its feet. 3. Pakistan was not engaged to tackle al-Qaeda and the Taliban. 4. He showed lack of commitment to tackle the Middle East crisis. 5. His policies were largely responsible for the looming financial crisis. 3. According to the passage, Obama is likely to face all the following major challenges except: 1.  To wind up the unresolved war. 2.  To improve the gloomy economic situation. 3.  To find a solution to the Middle East crisis. 4.  To put a curb on terrorism and terrorist organizations. 5. To get the complete support of the White House and the American people push his plans ahead.

Answers and Explanation 1. The passage conveys that the change is remarkable but also throws new challenges ahead, hence option 1. The other options talk about something which is nowhere given or indicated in the passage. 2. It can be inferred from the second paragraph fourth line ‘He represented hope that …. dealing with the world,’ hence option 1.

Reading Comprehension 

3. The passage talks about 80 per cent approval ratings as he picks up the keys to the White House and that the American people across political divides’, therefore ‘to get the support of people’ is not a challenge for him, so option 5.

How to acquire mastery over Reading Comprehension?

  2.5

after a long tiring day, and it may just be reading with the eyes …… But for the competitive exams we need to read with our brain because the purpose is different. And there comes the comprehension part. We read to find out the main idea of the passage and be accurate in answering the question, which even drains the physical energy. We read with sole objective to maximize our score, within a limited framework of time.

Knowing the weightage given to RC in the verbal section across the range of B school entrance tests, a student is hardly left with any choice but to attempt at least a few passages. In order to master the RC section, there are facts that a test-taker needs to know, prior to taking a test. These include:

A practical suggestion can be given as to develop the habit of reading books of different genre, and developing a taste for intellectual debate and exploration. This can go a long way to develop the complete personality of the reader besides increasing the level of comfort in the RC section.

1.  Does speed matter? Looking at the pattern of last few CAT papers, average length of a passage have hovered around 900-1000 words per passage including questions. Assuming that a student solves 3 passages in 25 minutes time, this leads to going through 3000 words in 25 minutes ⇒ 120 words per minute. However, if a student goes through only two passages, then s/he will be going through only 2000 words in 25 minutes ⇒ 80 words per minute. Let us do a scenario analysis (considering CAT 2008 to be the base) to understand it better:

3.  Practice is the key Solving RC practice exercises regularly helps develop confidence and gives an exposure to the nuances of RC. An aspirant is suggested to find out the main-idea of the articles in the editorial section of the news-papers, so that identifying the main-idea comes naturally to a student as it is integral to answering questions in CAT especially inferential ones.

No. of Words Read- No. of Accu- Net pasto be ing questions racy marks sages read Speed attempted

Scenario 1

3

3000

120

15

80%

45

Scenario 2

2

2000

80

10

90%

35

Scenario 3

1

1000

40

5

100%

20

Obviously, this scenario analysis assumes many ifs and buts like there is no regression or there is 100 per cent comprehension etc., however, it clearly drives home a basic point that with a speed of 80 words per minute and 90 per cent accuracy (at 80 words per minute, 90 per cent accuracy is not too high to expect), one can fetch 35 marks. Even if accuracy drops to 80 per cent, marks obtained in this section will be 30 marks under scenario 2. Having said this, I strongly suggest pushing the limits and increasing the comprehension speed as much as possible, however not at the cost of accuracy. 2.  Its more about comprehension than reading: There are two types of reading—reading with the eyes and reading with the brain. Reading for RC is different from general reading where we read either to get some specific piece of information or we read at ease to relax or unwind ourselves

So, now what we focus upon is not reading speed but Comprehension speed.

4.  And finally, analyse the exercises done The work doesn’t finish after solving the exercise. Analysing a test after solving is more important than students generally may think it to be. Analysis not only tells us where we went wrong and why we went wrong but also how those mistakes are to be avoided thence.

How to increase your reading speed? We have already discussed that with a decent speed of 80-100 words per minute only, RC can be managed for CAT, although importance of improving the reading speed (or for that matter improving anything else too) cannot be denied. Generally, we read slowly because we believe that if we read slowly we will understand the things better. On the other hand, reading slowly leads to loss of concentration as our mind gets easily distracted, which leads to loss of interest, which further lowers down the reading speed. It is important to understand how we read. Generally we read one to two words at a glance, pause for a fraction of a second and move to the other chunk of words. If we can train our eyes to read more number of words in a glance, our reading speed can increase manifold. With consistent practice, it may be possible to read the lines of a newspaper column in a single glance. While reading a piece of text, we have tendency to move back, cross check and re-read the things which we have already read. Generally, this happens because of lack

2.6 

  Verbal and Logical Reasoning

of interest, complex vocabulary, or poor retention of the reader. This is known as regression or skip back. The habit of regression has to be minimized if not eliminated. Pausing once in a while to figure out the contextual meaning of words, however, is not regression. Regression is a big time killer. It breaks the flow of thought, and leads to poor concentration, which leads to more regressions, which further lowers down the reading speed. Thus regression makes reading a slow and tiresome process. The best way to eliminate regression is to move a pen or pencil smoothly under the text and make your eyes follow the text. This is a great way to train oneself to read faster. Some of us move our lips while reading. We tend to mumble the words audibly or inaudibly. The habit of sounding out words while reading is known as vocalization. The habit has its roots in our childhood when we were asked by our teachers in school to read aloud. Even at our homes, our mother would ask us to read aloud, when she used to be busy with the house chores. You could focus on the text (as there was no choice!), but how much of that could you understand? The problem with vocalization is it limits our reading speed, although it may help the reader to fix his mind on the subject matter. Please note that as you experiment with these speed enhancement techniques, your comprehension will dip initially. Your mind may revolt, as many of us have been regressing and vocalizing throughout our school and college life. With a firm faith to improve reading effectiveness, coupled with consistent practice you can increase your reading speed manifold.

Instructions Move your pen/pencil under the line of text uniformly and let your eyes follow the movement of the pacer (pen/pencil) and answer the following questions with Yes or No. Is Muntazer al-Zaidi, the Iraqi who hurled his Number 10 footwear at George W Bush during a press conference in Baghdad, a hero or a heel, in more ways than one? Opinion is sharply divided on this. On the one hand or rather, foot there are those who feel that al-Zaidi’s behaviour was totally unacceptable, breaching as it did the code of conduct for journalists who as opinion formers must stick to rules of parliamentary conduct in their professional lives. Conversely, the footloose, or shoe-loose, journo has been hailed as a champion by all those and there are many of them who feel that his was a robust and deserved retort-in-kind to Bush’s jackbooted militarist policy in Afghanistan, Iraq itself, and elsewhere. The Baghdad authorities have taken a dim view of the episode and al-Zaidi who has in a letter to the Iraqi prime minister pleading for clemency described his no-soles-barred attack as an “ugly act” could face two years imprisonment for his outburst. However, an enthralled Egyptian father

has offered his daughter’s hand in marriage to the feisty al-Zaidi, saying that he had nothing more valuable than his girl child to offer the barefoot guerrilla. Another admirer, a Saudi tycoon, had offered to buy the famous footwear for $10 million. Unfortunately, the sale could not take place as an embarrassed Iraqi officialdom had consigned the items in question to an incinerator. While the jury remains out on whether al-Zaidi should eventually end up in the hall of fame or that of infamy, protocol officers and event managers of politicians and other public figures should put on their thinking caps to figure out ways and means to avoid or at least to minimize the impact of such incidents in future. All public rites and rituals marriages, funerals, birthday parties, press conferences are organized according to commonly accepted codes of behaviour. It is high time that the ritual of public protest so vital to democracy and the concept of a free society should have its own guide book of dos and don’ts; we need an etiquette of demonstrative dissent. In this exercise, we might like to take a tip from the would-be novelist who, before a public reading of his latest work, went to the market and bought quantities of eggs and tomatoes which he distributed among the audience, explaining that if he were to be pelted for deficiencies in his prose he would prefer the missiles to be fresh and not old and foul-smelling. This would appear to be an eminently civilized way of ordering such encounters: the protester would have the satisfaction of lodging, or lobbing, his protest, and the protestee the person being protested against would have the option of choosing the ammunition of the protester. In this way, both parties could claim satisfaction. In the al-Zaidi-Bush case, such mutual gratification cannot be ruled out. While in the Arab world, and indeed in the Indian subcontinent, footwear with its unclean, animal skin associations is considered a particularly offensive projectile to have hurled at oneself, in the rawhide Texan context of 10-gallon hats and cowboy boots that the exiting US president hails from, similar qualms of ritual pollution need not apply. In Islamic and Indic traditions, footwear is removed before entering places of worship or even private houses. No such practice applies in the West, particularly in the fabled Wild West of which Dubya is in some ways an embodiment in which it was deemed an honour to have ‘died with one’s boots on’. Indeed, having ducked in time, the president didn’t seem particularly fazed by being targeted by jootis, and later remarked that he must think up some good shoe jokes for future reference. Sound advice to all those who need to go public. Think of some good shoe jokes. Or good whatever-it-is-youwould-like-thrown-at-you jokes. And lay in stocks of your preferred tokens of protest to give to those who would protest against you. Eggs, tomatoes, chappals; the choice is yours.

Reading Comprehension 

1. Baghdad authorities have welcomed al-Zaidi’s act. Yes/No 2. The shoe which was hurled was 9 in number. Yes/No 3. In Texas footwear is considered an offensive projectile. Yes/No 4. In Islamic tradition, footwear is removed before entering private houses. Yes/No 5. A Saudi tycoon bought the famous footwear for $10 million. Yes/No

Answers and Explanation 1. No, The passage authorities have taken a dim view of the episode. 2. No, it was 10 in number. 3. No, the passage says that it’s a part of the Texan culture where cowboys don leather apparel. 4. Yes, given in the second last paragraph. 5. No, Saudi tycoon had only offered to buy the famous footwear, and the sale did not take place.

 DIFFERENT CATEGORIES OF RC PASSAGES The reading passages in CAT and other B school entrance tests are different subject areas like History, Philosophy, Literature, Economics etc. On the basis of the subject matter, viz., RCs can be broadly classified into different genre viz., Literature, Religion and Philosophy, Economics and business, Psychology, Life Sciences, Physical Sciences etc. A passage from sociology, arts, or philosophy can discombobulate a student from science background, and disturb the momentum of the entire paper. Although the average length of passages has gone down significantly over the years to as low as 500-600 words, the subject matter can be quite unfamiliar and unfriendly to an average test taker. The primary reason behind this discomfiture is that students are seldom comfortable with the vocabulary and concepts used in these subject areas. Therefore a serious aspirant must thoroughly read newspapers editorials, magazine articles and books from different areas which offer new ideas and challenging vocabulary. Expose yourself to new concepts and ideas through online glossaries and encyclopedia. The idea is to develop a basic framework of knowledge so that the reader becomes comfortable with different branches of knowledge. This can greatly reduce the shock factor one faces while confronting the abstract passages in the test paper.

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Let’s take a few sample passages from different disciplines. Be patient and keep your mind open to learning. Try to make sense of what the passage talks about, what the author is trying to convey.

PASSAGE  1 Physical Science A large part of the North Polar Region the Arctic, Alaska and Greenland has lost over two trillion tonnes of ice over the last five years, according to scientists interpreting new data obtained from a NASA satellite. What is alarming is that the melt figure refers to depletion of landlocked ice, and more than half the loss is in Greenland, contributing to half a millimeter of sea level rise annually. The total ice melt from the entire region has led to sea levels rising by one-fifth of an inch in five years. Add to this the Arctic Amplification Effect. The increase in the volume of Arctic waters absorbs more heat in the absence of sunlight-reflecting white ice which warms the oceans even more in summer. In autumn, the heat is released into the air, leading to rise in air temperatures, up to 10 degrees warmer now than recorded in the 1980s. The Intergovernmental Panel on Climate Change’s fourth assessment report warned last year that if the current rate of emissions continues unabated, the world could reach a tipping point by 2050. Among other dire consequences, this would seriously impact the availability of drinking water, especially in Asia, Africa and Small Island Developing States. James Hansen, director of NASA’s Goddard Institute of Space Studies, says that the IPCC’s estimates are conservative and the information outdated. New data reveal a situation that is far worse, calling for a `Climate Code Red’. In other words, it’s a planetary emergency. The December 2008 UN climate change conference in Poznan, Poland, did not reflect this urgency. Neither specifics nor timelines for curbing emissions were agreed upon that would help formulate a global plan of action at the Copenhagen December 2009 summit to firefight climate change. The year 2008 could be the tenth warmest year on record, according to the UN Meteorological Agency. Tackling the problem together ought to get top priority rather than assignment of blame, since emissions and their effects know no borders. The answer lies in sharing of clean technology and stepping up research and development efforts in alternative and renewable energy options despite cheaper oil. Industrialized countries should release the promised 2 per cent from carbon trade profits to the UN Adaptation Fund to help developing countries cope with the effects of climate change. India is among the hot spots identified by the UN for extreme weather events. Its National Action Plan on Climate Change

2.8 

  Verbal and Logical Reasoning

shows India is taking the problem seriously. But this might be insufficient without a global plan.

  EXPLANATION The passage begins with the alarming fact that the North Polar Region has lost over two trillion tonnes of ice over the last five years. The melting ice leads to rising sea levels. The increased water volumes absorb more heat and release it into the air, leading to rise in air temperature, which causes global warming. The recent IPCC report says that if the current rate of emissions goes unchecked the world could reach a tipping point by 2050. James Hansen, director of NASA’s Goddard Institute of Space Studies believes that the situation is even bleaker. The answer lies in sharing of clean technology and stepping up research and development efforts in alternative and renewable energy options. Industrialized countries should part with some of their carbon trade profits to help the developing countries cope with the effects of climate change.

PASSAGE  2 Politics/Government The closing decades of the last century saw substantial offloading of responsibilities by national governments to those below both in the US and Canada. It would appear there is, what Kincaid (2002) calls a “federalist ferment” across the world. The ferment notwithstanding, federalism is facing challenges from several directions. First of all, the intellectual case for de­centralization and federalism has come under some critical reappraisal. Even some of the key assertions regarding the virtues of decentralization and the assumptions underlying them have been challenged. Attention has been drawn to the possibility of decentralization failures and the merits of strong nationhood as a check against centrifugal forces gaining ascendancy and subverting the integrity of nations. What is more, the very forces that led to the fall of oppressive statism and provided the impetus for decentralization, viz., globalization and the demise of statism, are now posing a threat to the sovereignty of nation states–their life blood–and along with them that of their constituent units with implications that are yet to unfold. Despite the moves towards decentralization and more room for junior governments in established federations, viz., the US, Canada and Australia, the signals are mixed. Federal government still accounts for 60 per cent of government expenditure in the US. Things have not changed much in Canada either. In Australia, the trend, if any, is towards even more centralization. Some of the decentralized federal countries like Brazil are “recentralizing”. Globalization has generated

pressures for reform in the economic and political organisation and thereby intergovernmental relations of all developing countries. There are forces pulling in opposite directions, tend­ing to centralize functions envisaged by second tier govern­ments, like states in India, and decentralize some to tiers fur­ther down citing “subsidiarity”. The choice of the federal form for the US constitution that pres­aged the emergence of the federal idea across the world was motivated largely by the anxiety to have a central government that can act decisively when required unlike in a confederation, but with effective checks and balances by dividing powers be­ tween the federal government and the states. What accounts for the current federalist ferment despite warnings about its risks and inefficiencies are basically two fold. One is the economic ben­efits of efficiency in the organisation and functioning of the pub­lic sector from decentralization1–now encapsulated by the prin­ciple of “subsidiarity” in the EU’s Maastricht treaty–combined with the gains from the operation of a large common market. The other is commitment to diversity rather than homogeneity. And this is particularly relevant for a diverse country like India. There is also the strength that comes from unity, the ability to face calamities like the tsunami and threats to security like ex­ternal aggression or terrorism.

Explanation Federalism faces difficult challenges in the era of globalization, since the latter has generated pressures for reform in economic and political organizations and thereby in inter-governmental relations of all developing countries as well. There are forces in inter-governmental relations pulling in opposite directions, some tending to centralize functions of second tier governments, such as of the states in India, and others moving to decentralise to tiers further down, citing “subsidiarity”.

PASSAGE  3 Philosophy/Religion When I was a fairly precocious young man, I became thoroughly impressed with the futility of the hopes and strivings that chase most men restlessly through life. Moreover, I soon discovered the cruelty of that chase, which in those years was much more carefully covered up by hypocrisy and glittering words than is the case today. By the mere existence of his stomach everyone was condemned to participate in that chase. The stomach might well be satisfied by such participation, but not man insofar as he is a thinking and feeling being. As the first way out there was religion, which is implanted into every child by way of the traditional education-machine. Thus I came—though the child of entirely irreligious (Jewish) parents—to a deep religiousness, which, however, reached an abrupt end at the age of twelve. Through the reading of

Reading Comprehension 

popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression. Mistrust of every kind of authority grew out of this experience, a skeptical attitude toward the convictions that were alive in any specific social environment-an attitude that has never again left me, even though, later on, it has been tempered by a better insight into the causal connections. It is quite clear to me that the religious paradise of youth, which was thus lost, was a first attempt to free myself from the chains of the “merely personal,” from an existence dominated by wishes, hopes, and primitive feelings. Out yonder there was this huge world, which exists independently of us human beings and which stands before us like a great, eternal riddle, at least partially accessible to our inspection and thinking. The contemplation of this world beckoned as a liberation, and I soon noticed that many a man whom I had learned to esteem and to admire had found inner freedom and security in its pursuit. The mental grasp of this extra-personal world within the frame of our capabilities presented itself to my mind, half consciously, half unconsciously, as a supreme goal. Similarly motivated men of the present and of the past, as well as the insights they had achieved, were the friends who could not be lost. The road to this paradise was not as comfortable and alluring as the road to the religious paradise; but it has shown itself reliable, and I have never regretted having chosen it.

Explanation This is a selection from an essay written by the great scientist Albert Einstein. The author says that most people chase material comforts throughout their lives, but it doesn’t satisfy the thinking and feeling people like him. He believes that the traditional education ‘machine’ is rigid and mechanical. It dumbs down a person and limits one’s freethinking. The author wants to free himself from the chain of merely personal to something bigger and universal, something which can give inner freedom and security. He sums up his argument by saying that path of religion offers many shortcuts and comfortable solutions but the quest for truth is riddled with many challenges.

PASSAGE  4 Economics China’s lunar New Year sees the world’s largest migration, as tens of millions of workers flock home. Deserting for a few days the factories that make the goods that fill the world’s shops, they surge back to their native villages. This

  2.9

week, however, as they feasted to the deafening rattle of the firecrackers lit to greet the Year of the Ox, their celebrations had an anxious tinge. Many will not have jobs to go back to. China’s breakneck growth has stalled. The rest of East Asia, too, which had hoped that it was somehow “decoupled” from the economic trauma of the West, has found itself hit as hard as anywhere in the world—and in some cases harder. The temptation is to see this as a plague visited on the region from outside, which its governments are powerless to resist or cure. In truth, their policy errors have played their part in the downturn, so the remedies are partly in their hands. The scale and speed of that downturn is breathtaking and broader in scope than in the financial crisis of 1997-98. China’s GDP, which expanded by 13 per cent in 2007, scarcely grew at all in the last quarter of 2008 on a seasonally adjusted basis. In the same quarter, Japan’s GDP is estimated to have fallen at an annualized rate of 10 per cent, Singapore’s at 17 per cent and South Korea’s at 21 per cent. Industrial-production numbers have fallen even more dramatically, plummeting in Taiwan, for example, by 32 per cent in the year to December. The immediate causes are plain enough: destocking on a huge scale and a collapse in exports. Even in China, exports are spluttering, down by 2.8 per cent in December compared with the previous year. That month Japan’s fell by 35 per cent and Singapore’s by 20 per cent. Falls in imports are often even starker: China’s were down by 21 per cent in December; Vietnam’s by 45 per cent in January. Some had suggested that soaring intra-regional trade would protect Asia against a downturn in the West. But that’s not happening, because trade within Asia is part of a globalized supply chain which is ultimately linked to demand in the rich world. Some Asians are blaming the West. The Western consensus in favour of globalization lured them, they say, into opening their economies and pursuing export-led growth to satisfy the bottomless pit of Western consumer demand. They have been betrayed. Western financial incompetence has trashed the value of their investments and consumer demand has dried up. This explanation, which absolves Asian governments of responsibility for economic suffering, has an obvious appeal across the region. Awkwardly, however, it tells only one part of the story. Most of the slowdown in regional economic growth so far stems not from a fall in net exports but from weaker domestic demand. Even in China, the region’s top exporter, imports are falling faster than exports. Domestic demand has been weak not just because of the gloomy global outlook, but also because of government policies. After the crisis a decade ago, many countries fixed their broken financial systems, but left their economies skewed towards exports. Savings remained high and domestic consumption was suppressed. Partly out of fright at the balance-of-payments pressures faced then, countries

2.10 

  Verbal and Logical Reasoning

have run large trade surpluses and built up huge foreignexchange reserves. Thus the savings of poor Asian farmers have financed the habits of spendthrift Westerners. That’s not at all bad. One consequence is that Asian governments have plenty of scope for boosting domestic demand and thus spurring economic recovery. China, in particular, has the wherewithal to make good on its promises of massive economic stimulus. A big public-works programme is the way to go, because it needs the investment anyway. When Japan spent heavily on infrastructure to boost its economy in the early 1990s, much of the money was wasted, because it was not short of the stuff. China, by contrast, could still do with more and better bridges, roads and railways. Yet, infrastructure spending alone is not a long-term solution. This sort of stimulus will sooner or later become unaffordable, and growth based on it will run out of steam. To get onto a sustainable long-term growth path—and to help pull the rest of the world out of recession—Asia’s economies need to become less dependent on exports in other ways. Asian governments must introduce structural reforms that encourage people to spend and reduce the need for them to save. In China, farmers must be given reliable title to their land so that they can borrow money against it or sell it. In many countries, including China, governments need to establish safety-nets that ease worries about the cost of children’s education and of health care. And across Asia, economies need to shift away from increasingly capital-intensive manufacturing towards labour-intensive services, so that a bigger share of national income goes to households. For Asian governments trying to fix their countries’ problems, the temptation is to reach for familiar tools—mercantilist currency policies to boost exports. But the region’s leaders seem to realise that a round of competitive devaluation will help no one. China has responded to American accusations of currency “manipulation” by denying it has any intention of devaluing the Yuan to boost exports. Structural reforms to boost demand would not only help cushion the blow to Asia’s poor and thus help avert an explosion of social unrest that governments such as China’s fear; they would also help counter the relentless rise in protectionist pressure in the West. If emerging Asia needs a warning of the dangers of relying on exports, it need look no further than Japan. Japan’s decade-long stagnation ended in 2002, thanks to a boom in exports, especially to China. Now, largely because of its failure to tackle the root causes of weak domestic demand, it is taking more of an economic hiding than any other rich country. Japan used to see itself as the lead goose in a regional flight formation, showing the way to export-led prosperity. It is time for the other geese to break ranks.

Explanation The article begins with a hint of irony that tens of millions of Chinese workers have been rendered jobless due to

the economic recession amidst the backdrop of New Year celebrations. Many people believe that the economic crisis occurred because the Western countries lured the Asian countries into opening their economies and pursuing export-led growth. However, most of the slowdown in regional economic growth so far stems not from a fall in net exports but from weaker domestic demand. The domestic demand has been weak not just because of the gloomy global outlook, but also because of government policies, which left their economies skewed towards exports; The Savings remained high and domestic consumption was suppressed. But there is a silver lining too. There is a scope for boosting domestic demand and spend heavily on infrastructure. Asia’s economies need to become less dependent on exports by introducing structural reforms that encourage people to spend and reduce the need for them to save. Moreover, the Asian economies need to shift away from increasingly capital-intensive manufacturing towards labour-intensive services.

PASSAGE  5 Literature He that hath wife and children hath given hostages to fortune; for they are impediments to great enterprises, either of virtue or mischief. Certainly the best works, and of greatest merit for the public, have proceeded from the unmarried or childless men; which both in affection and means, have married and endowed the public. Yet it were great reason that those that have children, should have greatest care of future times; unto which they know they must transmit their dearest pledges. Some there are, who though they lead a single life, yet their thoughts do end with themselves, and account future times impertinences. Nay, there are some other, that account wife and children, but as bills of charges. Nay more, there are some foolish rich covetous men that take a pride, in having no children, because they may be thought so much the richer. For perhaps they have heard some talk, Such an one is a great rich man, and another except to it, Yea, but he hath a great charge of children; as if it were an abatement to his riches. But the most ordinary cause of a single life, is liberty, especially in certain self-pleasing and humorous minds, which are so sensible of every restraint, as they will go near to think their girdles and garters, to be bonds and shackles. Unmarried men are best friends, best masters, best servants; but not always best subjects; for they are light to run away; and almost all fugitives, are of that condition. A single life doth well with churchmen; for charity will hardly water the ground, where it must first fill a pool. It is indifferent for judges and magistrates; for if they be facile and corrupt, you shall have a servant, five times worse than a wife. For soldiers, I find the generals commonly in their hortatives, put men in mind of their wives and children; and I think the

Reading Comprehension 

despising of marriage amongst the Turks, maketh the vulgar soldier more base. Certainly, wife and children are a kind of discipline of humanity; and single men, though they may be many times more charitable, because their means are less exhaust, yet, on the other side, they are more cruel and hardhearted (good to make severe inquisitors), because their tenderness is not so oft called upon. Grave natures, led by custom, and therefore constant, are commonly loving husbands, as was said of Ulysses, vetulam suam praetulit immortalitati. Chaste women are often proud and forward, as presuming upon the merit of their chastity. It is one of the best bonds, both of chastity and obedience, in the wife, if she think her husband wise; which she will never do, if she find him jealous. Wives are young men’s mistresses; companions for middle age; and old men’s nurses. So as a man may have a quarrel to marry, when he will. But yet he was reputed one of the wise men, that made answer to the question, when a man should marry, —A young man not yet, an elder man not at all. It is often seen that bad husbands, have very good wives; whether it be, that it raiseth the price of their husband’s kindness, when it comes; or that the wives take a pride in their patience. But this never fails, if the bad husbands were of their own choosing, against their friends’ consent; for then they will be sure to make good their own folly.

Explanation This is one of the most famous essays written by Francis Bacon, noted English philosopher, statesman, scientist, lawyer, jurist, and author titled ‘Marriage and Single Life’. In this essay, he uses witty language to compare the merits and demerits of married life with that of single life. It begins on a cynical note that marrying is a hindrance to any great enterprise. The unmarried or childless people have done the greatest things. The essence of single life is liberty, especially for self-pleasing and humorous minds. Marriage makes a person more disciplined and humane. Although single men are quite charitable they are more cruel and hardhearted. It includes one of the most popular quotes of Bacon, ‘Wives are young men’s mistresses; companions for middle age; and old men’s nurses.

 UNDERSTANDING THE STYLE AND TONE OF THE PASSAGE Different writers adopt different ways to present their ideas, and even while using the similar writing techniques the author may reflect a different outlook, his way of looking at things. Therefore, to develop a better understanding of the text that is critical to answering questions in the CAT, it is important to understand the style and tone of the passage. The style of the passage refers to how the ideas have been presented. It is the technique used by the author to

  2.11

convey his/her ideas. The style of writing depends on a variety of factors like the choice of words, clarity and accuracy of expression, sentence length, variety and structure, lucidity or complexity of language used.

Writing Styles 1. The author could use a narrative style in which things move like a story; with a definite beginning, middle and end. It is characterized by a personal touch to the description of events. 2. Descriptive style of writing reports the details of a person, place, thing or event. It is more like a news report you see in the front page of a daily newspaper. The writer begins in a general manner, and then offers a detailed description of the subject. 3. Analytical style of writing, as the name suggests, involves a detailed treatment of an issue or situation. The author dives deep and tries to follow the chain of reasoning and draw inferences. The author weighs the different points of view in favour of or against his argument before arriving at any conclusion. 4. When the author uses the argumentative style of writing, he analyses the topic after taking a stand. He tries to persuade the reader using a chain of reasoning,evidence or suggestions. It is a variant of the analytical style of writing.

Tone of Writing The word tone generally refers to the quality of sound. But, when we refer to the tone of the passage, it refers to the predominant emotion or absence of it displayed by the author. The tone also reflects the attitude of the author towards a subject or character. Any predominant emotion may, thus become the author’s tone. Broadly, the tones can be classified as subjective or objective in nature. An objective tone is used when the author does not choose any side, and remains a neutral and detached observer. On the contrary a subjective tone reflects the emotion displayed by the author. Some of the common tones used by the authors are listed as follows: Critical:  Denotes negative or fault finding attitude of the author. Sometimes, the word critical is also used to denote deep analysis of the issue with a neutral outlook. Laudatory/Eulogistic:  To shower high praise on somebody or something. Cynical:  A higher degree of pessimism coupled with a sense of scepticism and helplessness. Satirical:  To use humour as a tool for healthy criticism.

2.12 

  Verbal and Logical Reasoning

Sarcastic:  To use the words opposite to what you mean to taunt or make fun of somebody. Didactic:  When the author tries to teach or instruct through his writing. Nostalgic:  Conveys a sense of longing for the past.

Explanation Identify the tone of the passages given below.

PASSAGE  1 ­ lants are not the only organisms that can be cloned natP urally. The unfer­t ilized eggs of some animals (small invertebrates, worms, and some species of fish, lizards and frogs) can develop into full-grown adults under certain environmental conditions—usually a chemical stimulus of some kind. This process is called parthenogenesis, and the offspring are clones of the females that laid the eggs. Another example of natural cloning is identical twins. Although they are genetically different from their parents, identical twins are naturally occurring clones of each other. Scientists have experimented with animal cloning, but have never been able to stimulate a specialized (differentiated) cell to produce a new organism directly. Instead, they rely on transplanting the genetic information from a specialized cell into an unfertilized egg cell whose genetic information has been destroyed or physically removed. In the 1970s, a scientist named John Gurdon successfully cloned tadpoles. He transplanted the nucleus from a specialized cell of one frog (B) into an unfertilized egg of another frog (A) in which the nucleus had been destroyed by ultraviolet light. The egg with the transplanted nucleus developed into a tadpole that was genetically identical to frog B. While Gurdon’s tadpoles did not survive to grow into adult frogs, his experiment showed that the process of specialization in animal cells was reversible, and his technique of nuclear transfer paved the way for later cloning successes.

Explanation The passage describes the process of cloning in animals. He describes the early experiments of animal cloning objectively; without taking any stand or position. Therefore, the tone of the passage is Objective or Scientific.

PASSAGE  2 Everyone agrees that President George Bush’s lobotomy has been a tremendous success.

Dick Cheney, the vice-president, declared that he was fully satisfied with it from his point of view. “Without the lobotomy,” Mr Cheney told the American Academy of Neurology, “it might have proved difficult to persuade the president to start wars all around the world without any good pretext. But the removal of those parts of the brain associated with understanding the outcome of one’s actions has enabled the president to function fully and without hesitation. Even when it is clear that disaster is around the corner, as it is currently in Iraq, the chief executive is able to go on TV and announce that everything is on course and that he has no intention of changing tactics that have already proved disastrous. “I would like to commend the surgeons, nurses and all involved with the operation,” said Mr Cheney. Similarly, Donald Rumsfeld regards the surgery as an unqualified success. He writes in this month’s American Medical Association Journal: “The president’s prefrontal leucotomy has successfully removed all neural reflexes resistant to warprofiteering. It is a tribute to the medical team who undertook this delicate operation that, no matter how close the connection between those instigating military action and the companies who benefit from it, the president is able to carry on as if he were morally in the right.” Paul Wolfowitz, the deputy secretary of defence, is also delighted at the beneficial effect that medical intervention has had on the president. “Just imagine how the president might have responded to Ariel Sharon’s crazy schemes if we hadn’t had the foresight to take out the neural pathways normally connected with perception and understanding,” Mr Wolfowitz told a meeting of the Association of Muslim Neurosurgeons For An All-Jewish Israel. “The president is now capable of treating the man responsible for the massacres at Shatila and Sabra as a decent human being, whose advice on how to deal with the problems of Israel is worth not only listening to, but also taking.” With all this acclaim for the US president’s lobotomy, it is scarcely surprising that Tony Blair, should have decided to follow suit and undergo similar psychosurgery. Thanks to the inhibition of specific presynaptic terminals, Mr Blair now appears to feel totally comfortable giving his support to the US massacre in Falluja and to the activities of US snipers who have been so busy in that city shooting women, children and ambulance drivers in revenge for the murder of four mercenaries. It is also believed that intervention in the motor speech area of his cortex now enables Mr Blair to describe Iraqis who respond negatively to having their houses blown up as “fanatics, extremists and terrorists”. Similarly, ablation of the oculomotor nerve means that Mr Blair is now able to see Israeli plans to retain Jewish settlements in the West Bank as a big step forward in the Middle East peace process. What has come as a complete surprise, however, is the recent revelation that Mr Blair’s brain surgery may even

Reading Comprehension 

predate President Bush’s. For without the removal of large portions of his cerebellum, it is hard to understand how the British prime minister could have turned down Mr Bush’s no-strings offer to keep British troops out of combat in Iraq. Political commentators are thus finding it impossible to say whether it is Mr Bush or Mr Blair who has pioneered the use of executive lobotomies in the war against terrorism.

Explanation This article is a satire on the former president of the US George W Bush. Satire uses humour as a tool of healthy criticism, especially to point out flaws of the society or system at large. Don’t be bogged down by the medical jargon. Just amuse yourself and enjoy. The way the passage begins with ‘The president’s surgery has been a tremendous success’ and then ‘without the lobotomy…..it might have proved difficult to persuade the president to start wars all around the world without any good pretext’ has a touch of satire in it, as the author wants to criticize Bush’s decision to start the wars around the world, hence the tone of the passage is satirical.

PASSAGE  3  (POEM) I wandered lonely as a cloud That floats on high o’er vales and hills, When all at once I saw a crowd, A host, of golden daffodils; Beside the lake, beneath the trees, Fluttering and dancing in the breeze. Continuous as the stars that shine And twinkle on the milky way, They stretched in never-ending line Along the margin of a bay: Ten thousand saw I at a glance, Tossing their heads in sprightly dance. The waves beside them danced; but they Out-did the sparkling waves in glee: A poet could not but be gay, In such a jocund company: I gazed—and gazed—but little thought What wealth the show to me had brought: For oft, when on my couch I lie In vacant or in pensive mood, They flash upon that inward eye Which is the bliss of solitude; And then my heart with pleasure fills, And dances with the daffodils.

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Explanation This is a classic poem written by one of the greatest romantic poets William Wordsworth. The poem has a great lyrical element. It is apparent that the poet was not just elated by the sight of the daffodils, but he reached a different plane of ecstasy. The poet has used vivid imagery. Expressions like ‘sparkling wave of glee; A poet could not but be gay…in such a jocund company’ give us the impression that the tone of the passage is exalted or laudatory.

  LOGICAL MAPPING OF THE PASSAGE The author uses the reading passage as a tool to describe something, present his point of view on a particular subject, or elaborate a concept or idea. The author uses a web of words to convey his ideas and opinion. The fact is only few words and key ideas are critical to understand the passage quickly and accurately. Rest of the words which form a mass of the passage are nothing but extensions,examples,explanations and facts used by the author to elaborate the theme of passage. Some of the words may also be used to display skillful use of language (Rhetoric). Like an architect who makes a blueprint of the building, visualizing how the construction work will go in the future, an active reader makes a logical outline of ideas in his mind on the basis of how the author builds his ideas and what he wants to convey to the reader. Underlining or making a mental note of the key ideas of each paragraph as they appear in the passage helps you to understand how the theme of the passage develops. Since the passages are highly condensed, one is required to read between the lines too, to understand the important elements of the passage which are integral to answering the questions. Do not be misled by illustrations, examples or extensions given by the author but learn to seive the important details. Such focused reading also helps you to read faster as you save your time by not getting into extraneous details. It also increases the comprehension as one does not miss out on the main points.

PASSAGE  4 Read the following passage carefully and underline the key points. Identify the logical flow of the passage. Time Allowed: 8 minutes Education is a mess because politicians refuse to discipline teachers who sabotage primary education. Surveys show that government teacher absenteeism ranges from 20 per cent to 57 per cent in different states, yet they earn thrice or more than private sector teachers,

2.14 

  Verbal and Logical Reasoning

Some teachers run businesses (shops, transport services). Others skip school in the morning but give paid tuitions to richer students in the afternoon. No wonder half of all students drop out by Class 7. Barely 30-50 per cent can read the alphabet in Class1, and barely 40-50 per cent can read simply words in Class 2. Millions who complete school emerge functionally illiterate, unable to read simple paragraphs or do simple arithmetic. Yet no political party is willing to discipline teachers or demand performance. An obvious reason is the power of teacher trade union. These often launch strikes just before school exams, impelling state governments to surrender rather than jeopardize the future of students. Hence teachers get ever-higher salaries while escaping accountability for performance. Teachers’ salaries appropriate almost the whole educational budget, leaving hardly anything for other items such as teaching materials and textbooks. Between 1960 and 1980 in Uttar Pradesh, the share of non-salary pending in education fell from 12 per cent to 3 per cent in primary education, and from 28 per cent to 9 per cent in secondary education. A seasoned politician gave me a big additional reason for teacher power. You see, he said, government teachers preside over polling booths at election time. So we must cosset them, not antagonize them. Otherwise teachers will help rival parties to rig elections, and we cannot afford that at any cost. A recent book by Geeta Kingdon and Mohammed Muzammil (The Political Economy of Education in India) throws new light on teacher power in Uttar Pradesh. Teachers are politically strong because they themselves have become politicians in astonishingly large numbers. Masterji has become netaji. The Constitution provides a quota for teachers in the Upper Houses of State Legislatures. Only large states have an Upper House, but the bulk of the population is in such states. Second, while the law prohibits government servants from contesting elections, it makes an exception for teachers. Why should teachers be allowed to contest but not doctors, clerks, sanitary engineers or other officials? The only reason is teacher clout. Third, teachers are often the best educated in rural areas, and so are natural leaders. Hence they are elected in large numbers to the lower houses of state legislatures too. Since they have so much spare time—they only teach in the mornings, if at all—many do political work. Some are really politicians pretending to be teachers in order to collect a regular salary and have an institutionalized position of power Fourth, politicized teachers help provide the troops needed for rallies and elections. Teachers help organize students in secondary schools to become political campaigners. This in turn produces a peculiar breed of “student leaders” who see a future in politics but none in

education. They agitate for an automatic pass for all students, not high academic standards. Kingdon and Muzammil give some stunning figures about the teacher-politician nexus in Uttar Pradesh. In the Upper House, 8.5 per cent of seats are reserved for teachers, yet the proportion actually elected to the Upper House varies from 13 per cent to 22 per cent. Clearly, the power of teachers far exceeds their Constitutional quota. The Lower House has no teacher quota. Yet teachers accounted for 10.8 per cent of all elected MLAs in the 1993 election, and 8.7 per cent in the 1996 election, far above their 0.9 per cent share in the adult population. Their share of Cabinet posts was even higher. This share has usually been in double digits since 1985, with a peak of 16.3 per cent in 1991-92. This high share persists regardless of which party is in power—Congress, BJP, Samajwadi, BSP. Mayawati, whose party is tipped to win the next election, is herself an ex-teacher. This, then, explains why all state governments treat teachers with kid gloves, and in the bargain ignore the mess in education. One obvious way to improve education and teacher accountability is to empower panchayats and parents’ associations to discipline absentee teachers. But despite the Constitutional amendment seeking to devolve primary education to panchayats, all efforts at actual devolution have been sabotaged. The Kalyan Singh government in 1992 tried to give managers of aided private schools greater powers over teachers, but this led to a mass strike, and the government backed down. In the late 1990s the UP government tried to devolve some educational powers to panchayats, but once again teachers went on the rampage and the government caved in. This is why many state governments prefer to let panchayats hire para-teachers—local people without proper teacher qualifications. These have helped improve basic literacy at a cost one-fifth that of regular teachers. That is a short-term gain, but para-teachers cannot provide quality education. Besides, in some states para-teachers are agitating to be recognized as regular teachers. What is the way out? Kingdon and Muzammil offer no panaceas. If villagers and panchayats get sufficiently angry with the mess in education, they could create a countervailing political force. That day still seems far off.

Explanation The 1st paragraph highlights the main idea of the passage— the sorry state of education in India is primarily because of political unwillingness to reform primary education. The second and the third paragraph bring facts to support that education is in a state of complete mess like: high drop out rates of students and high absenteeism among teachers because of their personal interests. The author then discusses the real reason behind the teacher power: powerful

Reading Comprehension 

teacher unions and other political compulsions. The author presents facts from the book by Kingdon and Muzammil to support his main argument explaining the reasons behind teach power. The author presents some more facts and figures to explain the teacher-politician nexus. The last paragraph talks about one possible solution to this is to empower the local political bodies like village panchayats and parents’ associations and the challenges in implementing it.

  DIFFERENT TYPES OF RC QUESTIONS RC is a tool which is used by the examiners to test a person’s ability to understand and analyse text drawn from different areas. It also tests a person’s ability to draw inferences, and if necessary to apply the inference in a new context or framework. Reading passages do not directly test the general awareness or subject knowledge of any particular field, although a broad awareness of different areas is helpful in increasing the comfort level, and consequently the confidence level with which a person handles the passages. RC questions may test you on either what is given in the passage or what can be deduced from the passage. The idea is to get as close as possible to the mind of the author—what he wants to convey through the framework of ideas interwoven in the passage. From the examination point of view, the RC questions can be broadly subdivided into six categories. A student should try to master different RC question types to excoriate the fear of RC from his mind forever. 1. Main Idea Question 2. Explicit Detail or Direct Question 3. Inference Question 4. Logical Structure Question 5. Tone or Attitude based Question 6. Extended Application Question

Main Idea Question Main idea of a passage can be defined as the most succinct summary that encompasses the passage. These questions are very important and test one’s ability to understand the overall theme of the passage, mainly ‘what the passage is precisely about’. One needs to have a fair understanding of what the passage talks about ‘as a whole’,and not be confused by the facts, explanations and examples given by the author to support the main idea. main idea is generally indicated in the first part of the passage. Rarely, it could also come in the concluding part of the article. Sometimes, the main idea question may be based on supplying a suitable title for the passage. A suitable title is one which captures the major elements of the passage in the shortest logical manner.

  2.15

Explicit Detail or Direct Question These questions use the phrases like ‘According to the passage….’, or ‘The author/passage mentions the following except:’ These questions are easier to tackle as they test one’s ability to find specific information given in the passage. One has to locate the detail in the form of information, data or statistics as mentioned in the passage. These questions provide direct clues like line references which make them easier to crack. Sometimes, these questions can also ask the contextual meaning of an underlined or italicized word as it has been used in the passage. This type of questions may not be frequently asked in the CAT now but appear in SNAP and FMS test.

Inference Questions To infer is to draw or deduce something on the basis of what is given in or implied by the passage. These questions are favorite of the CAT. The students find these questions challenging, as answering these questions requires a careful reading of the passage, which includes the ability to read between the lines, ability to interconnect the different logical elements given in the passage. These questions typically use words like infer, imply, arrive at, deduce, surmise etc. To handle these questions one must refer back to that part of the passage from where the inference has been drawn, correlate the concepts if necessary, and narrow down the answer choices. Both the aspects are important: to read the context given in the passage, and to gradually eliminate the answer choices to arrive at the best solution. Generally, the students get stuck up between the last two options. One must settle for the answer choice which is more clearly and specific on the basis of the main idea of the passage.

Logical Structure Question These questions ask about why the author introduces a specific point, gives a particular example, or quotes somebody in the passage. Sometimes, these questions also ask about overall development of the passage about ‘WHY’ the author uses a particular example, anecdote, refutation, or counter argument to develop the passage. These questions mainly focus on ‘WHY’ of the subject matter. Therefore, it becomes important to read the mind of the author. These questions generally give you a line reference from where the example or quote has been taken. If you carefully read two to three lines above or below the line from where the text has been taken and work with the options, you can hit the bull’s eye. Remember the answer can never be within the of line reference, as the question is ‘WHY’ that particular thing has been mentioned.

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  Verbal and Logical Reasoning

Tone/Attitude Based Question These questions test your ability to find out the underlying emotion of a particular line, paragraph or passage as a whole. One has to judge the attitude of the author towards his subject. These questions are not common in the CAT and other B School entrance tests, however, a fair understanding of tone helps one to understand the passage better and faster. One must develop the ability to understand the different shades of mood displayed by the author. Vocabulary plays an important role in handling these questions as the words like eulogistic or satirical are not used commonly used in colloquial or written English. Attempt these questions only if you have a fairly clear idea of the emotional underpinning of the sentence or paragraph in question.

Extended Application Question Application based questions take the logic a step further to that involved in inference questions. They test the ability to apply what you have learnt from the passage into a

new context or framework, sometimes even unrelated to the passage. These questions are a bit challenging to the students, as they test one’s ability to think creatively and see things in new light. These questions generally look like: ‘The author would most likely/least likely agree with….’ ‘Which of the following statements if true would most strongly strengthen /weaken the argument’ ‘the writer/target audience of the passage is most likely ……’ To handle these questions one must meticulously narrow down the options keeping an eye on the main idea, scope and tone of the passage. These questions should be touched only when one has developed a clear understanding of the passage. Another format of the application question is ‘which of the following is likely to be the title of the forthcoming/next article written by the author.’ These questions can be easily cracked if you carefully read the last paragraph and find out where the author leaves the passage, what are the unexplained issues or explanations which leave room for further discussion, analysis or elucidation.

  RC EXERCISE  1 Direction for questions 1 to 3:  Read the passage below and solve the questions based on it. By many measures, the problem of poverty is no more severe anywhere else than it is in India, which still has the world’s largest number of poor people in a single country. Thirty five per cent of its billion plus population lives on less than US $ 1 per day and around 86 per cent of Indians, more than 900 million people, manage to survive on incomes of less than US $ 2 a day. Although the much-heralded economic reforms of recent years have led to impressive levels of economic prosperity and the creation of a middle class, the distribution of wealth in India continues to be highly uneven. Furthermore, despite reductions in India’s poverty level during the 1970s and 1980s, when farmers prospered, poverty reduction efforts stagnated during the 1990s, along with declines in agricultural growth, a slowing of growth in agricultural incomes and price rises of basic food staples. The causes of these setbacks, according to the World Bank, lie in the nation’s fiscal crisis, which reduced the ability of the government to underwrite technological change for agriculture and development of the non-farm economy, and in over-regulation of agriculture, forestry products, agro-industry, and the non-farm economy, which benefits neither farmers nor the poor. Others point to high rates of illiteracy, enduring social exclusion, population growth rates that exceed economic growth, and protectionist policies that inhibited foreign investment.

Poverty reduction in India will clearly remain a very long-term goal. Yet India’s poverty statistics reveal a paradox: its huge population, estimated at 1.05 billion in 2003, along with that of China, at 1.29 billion, means that when these two countries achieve reductions in poverty, which they have done since 1990, it seems that the global goal of halving poverty by 2015 from its 1990 levels, expressed in the internationally agreed and ambitious Millennium Development Goals(MDGs), may soon be reached. A rela tively modest reduction in the proportion of poor people in these countries registers as a huge reduction globally. Consequently, the scale of poverty in India (and in China) makes it possible to use the numbers simultaneously to commend as well as criticize the progress that has been made. This also means that, although poverty levels have fallen, with growing income disparities that exist, many rural Indians feel they have become worse off. In fact, India’s urban residents were twice as rich as their rural counterparts in the 1970s, but they are now eight times as rich, prompting one observer to note that poverty is now a case of relative deprivation. Additionally, pervasive as poverty is in India, it is becoming more concentrated in the country’s lagging states, its rural areas and among its disadvantaged people. As of the time of the study, more than half of India’s poor lived in four states of Bihar, Madhya Pradesh, Orissa and Uttar Pradesh, with more than two-thirds in rural areas, where the

Reading Comprehension 

poverty incidence is highest amongst agricultural workers, many of them small-scale farmers or casual labourers. People of scheduled castes and scheduled tribes, who together make up around 24 per cent of the total population of India, or 252 million people, are far more likely to be poor than those of other social groups, because low status and gender barriers still operate as social obstacles that exclude them from opportunity. Poverty is a multi-dimensional phenomenon. Income poverty is central but it is just one aspect. There are also other aspects such as powerlessness, lack of voice, vulnerability and fear (especially for women) as well as the deprivation of basic capabilities and the lack of access to education, health, natural resources, employment, land and credit, political participation, services and infrastructure. Solutions to these conditions imply a level of social restructuring that goes far beyond economic opportunities and increases in incomes. Governments and international agencies seem to agree that poverty reduction and sustainable development require a wide range of mechanisms including: sound macroeconomic policies; open trade relations; increases in human and physical capital; good governance; sound legal, incentives and regulatory frameworks; an adequately regulated and supervised financial sector; health, education and social services that reach the poor, women and girls effectively; quality infrastructure and public services to promote rural development and liveable cities; and policies to promote environmental and human sustainability. India’s progress in applying these processes to poverty problems during the last decade of the 20th century has been mixed, with sluggish rates of reduction and patchy improvements across the nation. Relieving India’s poverty requires substantial and sustained efforts in all these areas, as well as new approaches and novel techniques if gains are to be substantial and irreversible. 1. According to the passage, which of the following is not one of the reasons behind the problem of poverty in India? 1.  Technological change in the field of agriculture 2.  Fiscal crisis of the country 3.  Over-regulation of agriculture 4.  High rates of illiteracy 5.  Persisting social exclusion 2. Which of the following can best fit as a suitable title for the passage? 1.  Poverty in India: A study 2.  Poverty: A multi-dimensional phenomenon 3  Poverty: A universal phenomenon

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4.  Poverty Vs Economic growth 5.  Poverty and sustainable development 3. It can be inferred from the passage that the author would consider which of the following as the complete solution to poverty: 1. Social restructuring that goes beyond economic opportunities to the impoverished. 2. Removing status and gender barriers that still persist in the modern society. 3. Improving the quality of human and physical capital. 4. Removing the protectionist policies that inhibit foreign investment. 5. Reducing unemployment of small scale farmers and casual labours. Direction for questions 4 to 6:  Read the passage  below and solve the questions based on it. Marco Polo was the first European who travelled to China and talked to his European compatriots about the marvels of another world. Today, business relationships between Europe and China are closer than ever but the political relationship is lacking behind. India still holds a privileged relationship with the United Kingdom and maintains relations with the EU through a cooperation agreement from 1994. The European Security Strategy (ESS) sets the aim to develop “strategic partnerships” (EC 2003) both with China and India. Although the term is ambivalent, and consciously so, in general understanding it means a longterm, broad based relationship to mutual benefit. Very obviously, the EU does not have a coherent China policy (EC 2003). Such deficiency should not come as a surprise. The Common Foreign and Security Policy, aimed at coordinating the foreign policy of the EU Member States, is a work in progress. It develops in stages and in concentric circles around the European territory. However, the EU would be well advised to adopt and implement a coherent China policy for a number of reasons. Right now, the EU’s major member states compete for economic influence with China without coordinating their trade and export initiatives as part of a common bilateral framework. History has repeatedly shown that major changes in the balance of power among nations and regions have rarely occurred peacefully. The global arena has yet to adjust to the shift in balance of power away from the West to the East with the growing emergence of Asian nations, primarily of China and India. As the unique and successful example of an integrated regional community and power, the EU has much wisdom to share with other members of the global community and much to contribute in the construction of a new world order.

2.18 

  Verbal and Logical Reasoning

China’s role in international organizations is growing and can only continue to grow as the world anticipates China to replace Japan as the world’s second largest economy. In the United Nations, it holds a permanent seat in the Security Council. In the WTO, China has developed into the most prominent player next to the EU and the US. China is an active member in the Association of Southeast Asian Nations (ASEAN+3) and the Asia-Pacific Economic Cooperation (APEC). China’s currency, the Yuan, plays a growing role in both Asia’s and the global currency system. The Chinese government can influence the system significantly by controlling exchange rates and by the mere fact that it holds a significant part of the US national debt. China’s active participation is also anticipated and needed in a number of significant international treaties as the Kyoto Protocol on climate change. Given the importance of China’s potential impact in the global arena, it is in the EU’s interest to actively involve China as a responsible stakeholder. Both regionally and internationally, China has become an important partner to the European Union and others in resolving security, economic and governance crises. Ultimately, it is in the EU’s best interest as a global power to coordinate a cohesive EU-China policy in conjunction with its transatlantic policy and thereby contribute to the global balance of power. Both the EU and China have developed strategic partnerships with their common neighbour Russia. Both partnerships cover a broad array of security and economic interests. Most importantly, however, is Europe’s and China’s common interest in Russia’s oil and gas resources. Both China and the EU depend on energy imports from Russia. This dependency is projected to grow when other sources of oil and gas imports run dry and when all planned infrastructure projects with Russia are being implemented. On their summit meeting in September 2006, China and the EU signed a common declaration on energy security that mirrors the agreed principles of the G8 summit in St Petersburg. Both sides want to cooperate on new energy technologies, most notably renewable energies and CCS, as well as in the creation of common markets. Both partners also want to coordinate their actions as customers for energy imports towards third parties—again, most notably Russia. The US has recently tried to balance China’s rising influence by shifting military and technological support to India. Europe’s approach should not be to rely on a system of “balance of power” but to offer its unique experience of cooperative problem solving in common institutions to this region that is even more fragmented politically than Europe was after the Second World War. Energy cooperation could lead the way in that regard, as it did in post war Europe when the European Community for Coal and Steel (ECCS) was constructed, the first predecessor

of today’s European Union. The Northeast Asian region is beset with a growing number of challenges, including trans-national environmental issues, especially relating to air pollution, which need to be resolved by China and its neighbours. The East Asian economic alliance of ASEAN could be a crystallization point for such an effort. East Asian nations have already started to cooperate on cross border air pollution, an issue that is closely related to energy production. Those efforts are based on Europe’s agreements on trans-boundary air pollution that were negotiated under the auspices of UN-ECE in the last years of the Cold War. 4. Why does the author begin with the description of Marco Polo’s travel to China? 1. To indicate that the relation between Europe and china has its roots in history. 2. To refute the allegations of Europe’s hegemony over China. 3. To prove that china was considered one of the wonders of the ancient world. 4. To showcase the privileged relationship between India and the European Union. 5. To illustrate the favourable perception of China in the eyes of the westerners. 5. Which of the following statements is not true regarding the role played by China in international organizations? 1. China is expected to replace Japan as the 2nd largest economy of the world. 2.  It has a significant part in the US national debt. 3. China is the most prominent player of the WTO. 4. The Chinese currency plays a vital role in the global currency system. 5. Its participation is crucial in important international treaties. 6. What is the main idea of the passage? 1. China’s growing influence and stature in the global arena. 2. The European Security Strategy’s objective to develop strategic partnership with China and India. 3. China’s growing international stature and its potential impact in the global arena. 4. Europe and China’s common interest in Russian oil and gas reserves. 5. The need for energy cooperation between the European Union and China.

Reading Comprehension 

Direction for questions 7 to 10:  Read the passage  below and solve the questions based on it. Any serious educational theory must consist of two parts: a conception of the ends of life, and a science of psychological dynamics, i.e., of the laws of mental change. Two men who differ as to the ends of life cannot hope to agree about education. The educational machine, throughout Western civilization, is dominated by two ethical theories: that of Christianity, and that of nationalism. These two, when taken seriously, are incompatible, as is becoming evident in Germany. For my part, I hold that, where they differ, Christianity is preferable, but where they agree, both are mistaken. The conception which I should substitute as the purpose of education is civilization, a term which, as I mean it, has a definition which is partly individual, partly social. It consists, in the individual, of both intellectual and moral qualities: intellectually, a certain minimum of general knowledge, technical skill in one’s own profession, and a habit of forming opinions on evidence; morally, of impartiality, kindliness, and a modicum of self-control. I should add a quality which is neither moral nor intellectual, but perhaps physiological: zest and joy of life. In communities, civilization demands respect for law, justice as between man and man, purposes not involving permanent injury to any section of the human race, and intelligent adaptation of means to ends. If these are to be the purpose of education, it is a question for the science of psychology to consider what can be done towards realizing them, and, in particular, what degree of freedom is likely to prove most effective. On the question of freedom in education there are at present three main schools of thought, deriving partly from differences as to ends and partly from differences in psychological theory. There are those who say that children should be completely free, however bad they may be; there are those who say they should be completely subject to authority, however good they may be; and there are those who say they should be free, but in spite of freedom they should be always good. This last party is larger than it has any logical right to be; children, like adults, will not all be virtuous if they are all free. The belief that liberty will ensure moral perfection is a relic of Rousseauism, and would not survive a study of animals and babies. Those who hold this belief think that education should have no positive purpose, but should merely offer an environment suitable for spontaneous development. I cannot agree with this school, which seems to me too individualistic, and unduly indifferent to the importance of knowledge. We live in communities which require co-operation, and it would be utopian to expect all the necessary co-operation to result from spontaneous impulse. The existence of a large population on a limited area is only possible owing to science and technique; education must, therefore, hand on the necessary minimum of these. The educators who allow most freedom are men whose success depends upon a degree of benevolence, self-control, and trained intelligence

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which can hardly be generated where every impulse is left unchecked; their merits, therefore, are not likely to be perpetuated if their methods are undiluted. Education, viewed from a social standpoint, must be something more positive than a mere opportunity for growth. It must, of course, provide this, but it must also provide a mental and moral equipment which children cannot acquire entirely for themselves. The arguments in favour of a great degree of freedom in education are derived not from man’s natural goodness, but from the effects of authority, both on those who suffer it and on those who exercise it. Those who are subject to authority become either submissive or rebellious, and each attitude has its drawbacks. The submissive lose initiative, both in thought and action; moreover, the anger generated by the feeling of being thwarted tends to find an outlet in bullying those who are weaker. That is why tyrannical institutions are self-perpetuating: what a man has suffered from his father he inflicts upon his son, and the humiliations which he remembers having endured at his public school he passes on to ‘‘Onatives” when he becomes an empire-builder. Thus an unduly authoritative education turns the pupils into timid tyrants, incapable of either claiming or tolerating originality in word or deed. The effect upon the educators is even worse: they tend to become sadistic disciplinarians, glad to inspire terror, and content to inspire nothing else. As these men represent knowledge, the pupils acquire a horror of knowledge, which, among the English upper-class, is supposed to be part of human nature, but is really part of the well-grounded hatred of the authoritarian pedagogue. 7. Which of the following according to the author does not qualify as the purpose of education? 1.  A minimum level of general awareness. 2.  Technical proficiency of one’s occupation. 3.  Intelligent adaptation of ends to means. 4.  Lively and positive outlook of life. 5.  None of these 8. What is the meaning of the italicized word ‘utopian’ as used in the second paragraph? 1.  Ridiculous 2.  Unrealistic 3.  Banal 4.  Ignoramus 5. Impeccable 9. What is the point which the author trying to make when he says ‘the belief that liberty……not survive a study of animals and babies?’ 1. The belief that unchecked freedom will make the children virtuous is flawed.

2.20 

  Verbal and Logical Reasoning

2. Education serves no positive purpose. 3. Evolution does not support the moral perfection of animals and their young ones. 4. To support the view that children should be left completely free, however bad they may be. 5. To prove that education should be more positive than a mere opportunity for growth. 10. The author remarks ‘What a man has suffered from father he inflicts upon his son…..’ to convey the idea: 1. Humiliation suffered at school can have a lasting effect. 2. An authoritative education can turn pupils into timid tyrants. 3. Those who are thwarted lose the initiative, both of thought and action. 4. Unbridled freedom makes the educator a sadistic disciplinarian. 5. The deep rooted terror in the minds of the pupils leads to the well-grounded hatred for the authoritarian pedagogue. Direction for questions 11 to 14:  Read the passage below and solve the questions based on it. Jawaharlal Nehru’s foreign policy has been made subject to much controversy and debate, like his economic policies. However, taken in the context of India’s newly found status as a democratic republic, Nehru’s foreign affairs policies seem to be extremely apt. Socialism can be said to be one of the greatest international influences on Nehru, but Gandhi’s ideals of Satyagraha also influenced him to a great degree. But he committed himself to neither point of view in framing his foreign policy. Nehru’s foreign policies were characterized by two major ideological aspects. First, he wanted India to have an identity that would be independent of any form of overt commitment to either power bloc, the USA or the Soviet. Secondly, he had an unshaken faith in goodwill and honesty in matters of international affairs. The first policy led ultimately to the founding of the Non-Alignment Movement (NAM). His second faith was terribly shaken by the Chinese attack of 1962, openly disobeying all the clauses of the Panchsheel or five-point agreement of 1954 between New Delhi and Peking. This breach of faith was a major psychological shock for Nehru, and was partially the reason for his death. Nehru saw war and violent insurgency from very close quarters as a freedom fighter, and he believed in neither. In his foreign policies, Nehru tried to guide India in such a way, so as to steer clear from any form of violence and militarism. He rightly believed that a newly decolonized nation must invest all its economic and logistic resources towards

development and not defense and armament. Just like his economic policies, which were non-committal towards any ideological position, Nehru wanted to bring in a healthy level of pragmatism in his dealings of India’s foreign affairs as well. He understood that overt commitment to any of the two major power blocs to emerge in the aftermath of World War II, would not serve India’s path. He therefore wanted to tread a third path, which was not necessarily the middle path. It should be remembered that this dogged non-commitment of Nehru was not seen sympathetically by any of the super powers of either East or West at its initial stage. It was frequently termed as a kind of international opportunism and was accused of ‘neutralism’ —a stance reckoned to be not only dangerous but also equally immoral in the world of International politics. However, the increasing popularity of NAM among various Asian and African countries and Nehru’s growing stature as a statesman situation changed their views. India too benefited from this position, as it managed to secure rebuilding grants from member countries of either bloc. After Nehru’s successful mediation in the Korean War and the Congo problem, putting an end to a long and violent struggle, his status as a commendable and efficient statesman reached new heights. Jawaharlal Nehru’s theory of ideological non-commitment in a world that was rendered dangerous by the Cold War was appreciated by one and all. The greatest success of Jawaharlal Nehru’s non-committal international politics was the formation of the NonAlignment Movement (NAM). Nehru found allies in Tito, Nasser, Soekarno, U Nu and Nkrumah at a later stage in his formation of this new alliance. An alliance of newly independent and long colonized nations was not taken seriously in the beginning, either by the Eastern or the Western bloc. However, the importance of the alliance was soon felt, and initially led to a great degree of international pressure from both parts of the globe. However, Nehru proceeded with his mission undaunted. It was great test for his courage and it was soon found out that the NAM was not merely a passive platform of neutral and inactive nations. It had clear objectives that included the gradual decolonization of the world, and a strong statement that the member countries were not party to the ever escalating tension of the Cold War. The favoured process of decolonization as adopted by the NAM member countries was one of discussion and peaceful agreement. On many occasions, NAM met with success, often under the leadership of Nehru. Whoever supported its cause was an ally and a friend. Nehru preached a policy of issue based alliance and not one based on political and economic dogmas. He was proud of being an Asian, and wanted Asian nations to be the primary determinants of their political fate, not always guided by Western forces. Nehru’s unshaken belief in the force of international brotherhood was attested with his decision to continue with India’s Commonwealth status. He was made subject

Reading Comprehension 

to much criticism back home because of the support he extended towards the Commonwealth, particularly after the complication of the independence issue by the British government in the post World War II years, leading to the unwanted partition. However, Nehru, always the believer in peaceful alliances and solution of international affairs based on discussions, went on with his ideals. 11. According to the passage, how did Nehru display an element of pragmatism in his dealings of India’s foreign affairs? 1. By securing grants from member countries of the either bloc. 2. By his successful mediation in the Korean war and the Congo problem. 3. By adopting the policy of ‘neutralism’ during the Cold war era. 4. By forming an alliance of new independent and long colonized nations. 5. By not showing explicit commitment to either of the two power blocs post World War II. 12. Which of the following can be a suitable title for the passage? 1.  Nehru’s foreign policy a resounding success. 2. The pragmatism and idealism of Nehru’s foreign policy. 3.  Nehru: the father of Non Aligned Movement. 4.  Influence of Gandhi on Nehru’s foreign policy. 5.  India’s success as a democratic republic. 13. According to the passage what was the long term impact of Nehru’s decision to continue with India’s membership of the commonwealth? 1. It was partly responsible for the unsavory partition of India. 2. It led to the weakening of the British empire after World War II. 3. It led to the British government’s interference in India’s political affairs. 4. Nehru’s status as an efficient statesman reached new heights. 5.  All of these 14. According to the passage, why did Nehru want to keep India away from war and violence? 1. He was a pacifist and adhered to the Gandhian principles of non violence.

  2.21

2. He had an unshaken faith in the goodwill and honesty in the matters of international affairs. 3. He believed that developing should channelise all its resources towards development. 4. The breach of faith by the Chinese after the signing of the Panchsheel agreement was a major shock for Nehru. 5.  Because he adhered to the policy of ‘neutralism’. Direction for questions 15 to 19:  Read the passage below and solve the questions based on it. At the Bretton Woods Conference in July 1944, international leaders sought to insure a stable post-war international economic environment by creating a fixed exchange rate system. The United States played a leading role in the new arrangement, with the value of other currencies fixed in relation to the dollar and the value of the dollar fixed in terms of gold—$ 35 an ounce. Following the Bretton Woods agreement, the United States authorities took actions to hold down the growth of foreign central bank dollar reserves to reduce the pressure for conversion of official dollar holdings into gold. During the mid-to late-1960s, the United States experienced a period of rising inflation. Because currencies could not fluctuate to reflect the shift in relative macroeconomic conditions between the United States and other nations, the system of fixed exchange rates came under pressure. In 1973, the United States officially ended its adherence to the gold standard. Many other industrialized nations also switched from a system of fixed exchange rates to a system of floating rates. Since 1973, exchange rates for most industrialized countries have floated, or fluctuated, according to the supply of and demand for different currencies in international markets. An increase in the value of a currency is known as appreciation, and a decrease as depreciation. Some countries and some groups of countries, however, continue to use fixed exchange rates to help to achieve economic goals, such as price stability. Under a fixed exchange rate system, only a decision by a country’s government or monetary authority can alter the official value of the currency. Governments do, occasionally, take such measures, often in response to unusual market pressures. Devaluation, the deliberate downward adjustment in the official exchange rate, reduces the currency’s value; in contrast, a revaluation is an upward change in the currency’s value. For example, suppose a government has set 10 units of its currency equal to one dollar. To devalue, it might announce that from now on 20 of its currency units will be equal to one dollar. This would make its currency half as expensive to Americans, and the US dollar twice as expensive in the devaluing country. To revalue, the government might change the rate from 10 units to one dollar to five units to one dollar; this would make the currency

2.22 

  Verbal and Logical Reasoning

twice as expensive to Americans, and the dollar half as costly at home. When a government devalues its currency, it is often because the interaction of market forces and policy decisions has made the currency’s fixed exchange rate untenable. In order to sustain a fixed exchange rate, a country must have sufficient foreign exchange reserves, often dollars, and be willing to spend them, to purchase all offers of its currency at the established exchange rate. When a country is unable or unwilling to do so, then it must devalue its currency to a level that it is able and willing to support with its foreign exchange reserves. A key effect of devaluation is that it makes the domestic currency cheaper relative to other currencies. There are two implications of a devaluation. First, devaluation makes the country’s exports relatively less expensive for foreigners. Second, the devaluation makes foreign products relatively more expensive for domestic consumers, thus discouraging imports. This may help to increase the country’s exports and decrease imports, and may therefore help to reduce the current account deficit. There are other policy issues that might lead a country to change its fixed exchange rate. For example, rather than implementing unpopular fiscal spending policies, a government might try to use devaluation to boost aggregate demand in the economy in an effort to fight unemployment. Revaluation, which makes a currency more expensive, might be undertaken in an effort to reduce a current account surplus, where exports exceed imports, or to attempt to contain inflationary pressures. A significant danger is that by increasing the price of imports and stimulating greater demand for domestic products, devaluation can aggravate inflation. If this happens, the government may have to raise interest rates to control inflation, but at the cost of slower economic growth. Another risk of devaluation is psychological. To the extent that devaluation is viewed as a sign of economic weakness, the creditworthiness of the nation may be jeopardized. Thus, devaluation may dampen investor confidence in the country’s economy and hurt the country’s ability to secure foreign investment. Another possible consequence is a round of successive devaluations. For instance, trading partners may become concerned that a devaluation might negatively affect their own export industries. Neighbouring countries might devalue their own currencies to offset the effects of their trading partner’s devaluation. Such “beggar thy neighbor” policies tend to exacerbate economic difficulties by creating instability in broader financial markets. Since the 1930s, various international organizations such as the International Monetary Fund (IMF) have been established to help nations coordinate their trade and foreign exchange policies and thereby avoid successive rounds of devaluation and retaliation. The 1976 revision of Article

IV of the IMF charter encourages policymakers to avoid “manipulating exchange rates...to gain an unfair competitive advantage over other members.” With this revision, the IMF also set forth each member nation’s right to freely choose an exchange rate system. 15. Devaluation, sometimes seen as a nation’s weakness leads to: 1.  Ultimate better credit worthiness for the nation. 2.  Higher and easier foreign investment. 3.  Psychological trauma for its citizens. 4.  Lower investor confidence. 5.  Lower export potential for the country. 16. The difference between fixed and floating exchange rate fixation is 1.  Determined by USA since 1973. 2. Determined by supply and demand for a currency in the international market. 3. Determined by appreciation/depreciation in price of gold. 4.  Determined only by Governments. 5.  Used to achieve price stability in a nation. 17. The advantages/disadvantages of devaluation are 1. Makes domestic currency more expensive with respect to other countries. 2. Encourages narrowing of negative import/export current deficit. 3. A country needs more foreign exchange to sustain its currency value. 4. Encourages flow of foreign goods into the country. 5.  Unfortunately increases unemployment. 18. Revaluation is a good idea when 1.  A government wishes to fight unemployment. 2. A government wishes to improve psychological prestige of the country. 3. A government uses it as one of the tools to combat inflation. 4.  To increase current surplus of export over import. 5.  As a popular fiscal policy by a Government. 19. Under what circumstances does a nation’s exchange rate become untenable 1. When there is lack of sufficient foreign exchange reserves.

Reading Comprehension 

2. When there is shortage of gold reserves to back its own currency printing. 3. When it is willing to respond to all offers of purchase of its currency at the new rate. 4.  When exports are low and imports high. 5. When market forces and its own policies render currency value unviable. Direction for questions 20 to 24:  Read the passage below and solve the questions based on it. Cosmology in the 20th century was almost in its entirety the outgrowth of Einstein’s foundational paper in 1915 on general relativity. Two years later he presented his first model of the universe based on general relativity together with Riemann’s notion of the three-sphere. Side-by-side with the theoretical advances, observational astronomy led to great leaps in astrophysics, as the life cycles of stars were discovered and elaborated, the existence of other galaxies outside our own was confirmed, and the expansion of the universe was demonstrated to the satisfaction of nearly all. Einstein was able to use general relativity on the one hand to explain earlier observations, such as the amount of precession of the planet Mercury, and on the other hand to make new predictions for the observers to confirm or refute. The first and most widely heralded of those was the prediction of the bending of light as it passed close to a large mass such as the sun. Others, such as gravitational red-shift, gravitational lensing, and “framedragging” around a rotating body, were confirmed one by one over the course of the century. Still others, like the existence of gravity waves, remain a high priority for 21st century experimentalists. The Nobel Prize-winning work of Russell Hulse and Joseph Taylor stemmed from their discovery in 1974 of a pulsar whose “pulses” varied in a regular fashion, leading them to conclude that it had an invisible companion, the pair forming a familiar binary system each one circling the other (or actually, their common center of gravity) in an approximately elliptical orbit. In this case, the pair consisted of two bodies each as massive as the sun, but compressed into a tight ball whose diameter was the size of a small town, and each completed its orbit around the other in about eight hours. Under such extreme conditions, the relativistic effects would be considerable. One of those effects would be the production of gravity waves, and Einstein’s equations predicted that those waves would radiate energy in a way that cause the two bodies to gradually get closer, which would in turn speed up the rate that they completed each orbit by a very precise amount. After observing the variations in the pulse rate over a period of four years, Hulse and Taylor were able to show that the speedup was indeed taking place at the rate predicted, to within less than one percent deviation. That provided the first experimental evidence for the existence of gravity waves.

  2.23

That evidence, however, was indirect. In fact, the strength of the predicted waves in the case of the binary pulsars was far too weak for any hope of direct detection on earth. However, the same general principles would apply to a binary pair of black holes, and there the calculations indicated that the strength of the waves could be just within the limits of possible detectability with suitably crafted apparatus. Attempts to do so had already begun in the late 1950s with Joseph Weber. At that time, not only was the reality of gravity waves in doubt, but the existence of black holes was generally greeted with skepticism. The idea of black holes (although not the name) arose very soon after Einstein formulated general relativity. Karl Schwarzschild, despite the fact that he was in the German army stationed in Russia , and that it was in the midst of World War I, read Einstein’s paper, and almost immediately was able to solve Einstein’s equations for the case of the gravitational field surrounding a (non-rotating) spherically symmetric body. A few weeks later he was able to solve the equations and describe the space-time curvature in the interior of the body. One of the consequences of the Schwarzschild solution seemed to be that a sufficiently massive body compressed within a sufficiently small radius (where “sufficiently” was made precise by the Schwarzschild equations) would have the property that no radiation or matter could ever escape. Oddly, a very similar conclusion was reached by purely Newtonian methods in 1783 by John Michell in England , and became widely known through Laplace‘s famous 5-volume Le Système du Monde. In both cases, however, the question remained whether it was possible for a real-world physical body to exist within those parameters. The first theoretical evidence was adduced in a 1939 paper by Robert Oppenheimer and Hartland Snyder, who calculated the spacetime geometry around an imploding massive star, under certain simplifying assumptions, and concluded that the star would eventually become invisible. As for the reality of black holes, it was hard for the experts, much less the general public, to decide whether they represented science or science fiction. Many leaders in the field, from Einstein to John Wheeler had serious doubts. It was not until the advent of X-ray astronomy that the balance was tilted in favor of science. Since X-rays from outer space do not penetrate our protective atmosphere, this research developed hand-in-hand with rocket science. The big discovery was the existence of a powerful X-ray source in the constellation Cygnus, designated Cyg X-1. This discovery was made in a rocket flight in 1964. The first X-ray satellite, Uhuru , was launched in 1970, while its successor, Einstein, launched in 1978, was an X-ray telescope that was able to make X-ray images as sharp as an optical telescope. Gradually, the scientific community became

2.24 

  Verbal and Logical Reasoning

2. Through Powerful x ray telescopes mounted on space craft, which mapped CygnusX.

convinced that Cyg X-1 was indeed a real-life black hole whose physical characteristics corresponded closely to those predicted by the theory. Evidence has accumulated for other X-ray sources arising from the vicinity of black holes, as well as black holes in the center of quasars and large galaxies, such as our own.

3. Through Oppenheiners and Sneiders calculations on imploding stars. 4.  Through John Mitchells work in 1783.

20 In cosmology, what remains a high priority in the 21st century?

5. Via Mitchells work as shown in Laplaces 5 volume “Le Systems du Monde”.

1.  Gravity waves

23. How was a black hole defined?

2.  Black holes

1.  Vacuum in space.

3.  Bending of light around huge gravitational bodies

2.  Dark areas in the cosmos.

4.  Pulsars

3.  Stars which can be seen with an X ray telescope.

5.  Gravitational Red Shift

4. A huge body compressed so tightly that neither light nor matter could escape rendering it invisible.

21. What led scientists to experimentally confirm the existence of gravity waves?

5.  Areas which give off gravitational waves.

1.  Discovery of the binary nature of pulsars. 2.  Signals from black holes. 3.  Advances in equipment in astrophysics.

24. What developments led to confirmation that the universe was expanding?

4.  Einsteins relativity theory.

1.  Einsteins paper on general relativity of 1915.

5. Experimental verification of rate of increase of pulse rates emitted by binary pulsars as predicted by Einsteins calculations.

2. Discovery of the bending of light as it passed the sum. 3.  Discovery of gravitational lensing.

22. How did scientists move from conjecture to fact where black holes were concerned?

4. Observational astronomy, with developments in astrophysics.

ANSWER KEYS

1. Through Einsteinian equations solved by Schwarzchild.

5.  Reimans three sphere model of the universe.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

1

3.

1

4.

1

5.

3

6.

5

7.

3

8.

2

9.

1

10.

2

11.

5

12.

2

13.

1

14.

3

15.

4

16.

2

17.

3

18.

3

19.

5

20.

1

21.

5

22.

2

23.

4

24.

4

Reading Comprehension 

  2.25

HINTS AND EXPLANATIONS 1. It is not the tech change but the inability of the government to underwrite tech change which is the reason behind poverty, therefore option 2 is the answer. 2. Options 4 and 5 are too general, option 2 and 3 talk about only a particular aspect of the passage. The passage mainly talks about the problem of poverty in India and how to address it, hence option 1 is the answer. 3. Option 1 is the answer. The inference can be drawn from the last line of the fifth paragraph.

9. The answer has been indicated in the third sentence of the second paragraph. The second option is not the author’s point of view. The third one has not been mentioned; the last two choices are off the mark, therefore first option is the answer. 10. In the last paragraph the author talks about the chain reaction which follows as a result of subjection to authority, therefore option 2 is the answer. The first choice is not indicated in the passage. The last three are not directly related to the point made by the author.

4. Option 1 is the answer. The passage mainly talks about the need for a greater relationship between the European Union and China; the description of Marco Polo’s travel to China drives home the point that the relation between Europe and china has its roots in history.

11. The last two lines of the third paragraph indicate how Nehru did not show any overt commitment to any of the two major power blocs in the larger interest of India, therefore fifth option.

5. It has been clearly indicated in the third paragraph that China is the most prominent player next to the EU and the US, therefore option 3 is correct.

12. The passage talks about some failures of Nehru’s foreign policy like the Chinese attack on India, so the first choice is not correct. The passage talks about the practical side of the non commitment policy of Nehruvian foreign policy and also his ideological focus on goodwill and honesty in international affairs, therefore second option.

6. The last two paragraphs and more specifically the last paragraph talks about the need for energy cooperation between the EU and China. The first choice talks only about a particular aspect of the passage. The second choice is general and therefore less preferable than the last option. The fourth one is just a fact given in the passage. Therefore option 5 is the answer. 7. In the last part of the first paragraph, the author talks about intelligent adaptation of means to ends and not vice versa, so option 3 is the answer. 8. The context gives us the idea that it would be impractical to expect all necessary cooperation to result from spontaneous impulses, so unrealistic, option 2 is the answer.

13. The last paragraph clearly indicates that the Nehru’s decision to continue with India’s membership of the commonwealth was indirectly responsible for partition. The second and the third options are mentioned in the passage. The fourth choice is unrelated, so the first option is the answer. 14. The answer has been directly given in the third line of the third paragraph. The third choice is the right answer.

  RC EXERCISE  2 Direction for questions 1 to 5:  Read the passage  below and solve the questions based on it. The most curious in all respects, and for our purposes the most instructive of the ancient Pagan religious frauds, are the Sibylline Oracles, which,extensively reinforced by Jewish and Christian forgeries, were perhaps the most potent and popular “proofs” of the early Church for the divinity of Jesus Christ and the truth of the Christian religion; thus they derive special notice here. All will remember, from their school histories of ancient Rome, the well-known legend of one of the Sibyls who came to King Tarquin the Second with nine volumes of Oracles, which she offered to sell to him for a very high price; being refused, she went away and burned three of the books, and returning offered the remaining six at the same price; again the King refused to buy, and she departed, burned three more of the books,and returned with the last three for which she demanded the original price.Astonished at this conduct and greatly impressed, the King consulted his augurs and was advised to secure the remaining treasures of prophecy

before it was too late; he did so, and immediately the Seeress disappeared and was never seen again. The precious tomes were deposited with great care and jealously guarded in the Temple of Jupiter Capitolinus; a college of priests was instituted to have charge of them; and the divine Oracles were consulted with great solemnity only in times of the greatest crises of the State. The books were finally destroyed when the Capitol was burned during the wars of Sylla, but many others continued in existence. The oracles were composed in Alexandrine verse, and claimed to be the work of inspired Pagan prophetesses called Sibyls; they enjoyed the greatest vogue and were believed with the most implicit faith by Pagans and Christians alike. There were a number of these Sibyls, and the number of the volumes of oracles is differently estimated as a dozen or more; those with which we are chiefly concerned are the Roman Cumaean and Greek Erythraean Sibyls and the Oracles going under their names. The inveterate bent of the priestly mind for forgery in furtherance of its holy mission of imposture, led to the prompt adoption and corruption of these

2.26 

  Verbal and Logical Reasoning

Pagan frauds, for the propagation first of the Jewish,then of the Christian Faith. “Because of the vogue enjoyed by these heathen oracles,” says the Catholic Encyclopedia, “and because of the influence they had in, shaping the religious views of the period, the Hellenistic Jews in Alexandria, during the second century b.c, composed [i.e., forged] verses in the same form, and circulated them among the Pagans as a means of diffusing Judaistic doctrines and teaching. This custom was continued down into Christian times, and was borrowed by some Christians, so that in the second or third century, a new class of Oracles emanating from Christian sources came into being. Hence the Sibylline Oracles can be classed as Pagan, Jewish, or Christian.In many cases, however, the Christians merely revised or interpolated the Jewish documents, and thus we have two classes of Christian oracles, those adopted from Jewish sources and those entirely written by Christians. ...It seems clear, however, that the Christian Oracles and those revised from Jewish sources all emanated from the same circle and were intended to aid in the diffusion of Christianity. Most notable of these forged Christian addenda to the Pagan-Jewish forged Oracles, ‘Is found in Book VIII, a lengthy composite of Jewish and Christian fraud, consisting of some 500 hexameter verses. The first 216 verses, says the CE., “are most likely the work of a second century Jew, while the latter part (verses 217-500), beginning with an acrostic on the symbolical Christian word Ichthus is undoubtedly Christian, and dates most probably from the third century.” Ichthus is the Greek word for fish, and the fish was the fitting and universal symbol of the early Christians as typical of the “catch” of the Apostolic fishers of men. This cabalistic word Ichthus, worked into the professedly Pagan Oracle in the form of anacrostic, is composed of the initial letters of the popular name and title of the Son of the Christian God, in the Greek: “Iesous Christos Theou Uios Soter—Jesus Christ, Son of God, Saviour” This fish anagram was an ancient Pagan symbol of fecundity, of great vogue and veneration throughout Pagandom,and was adopted by Christendom for the double reason that the initials acrostically formed the name and title of its new deity, and that in the ancient science fish were supposed to be generated in the water without carnal copulation, and were thus peculiarly symbolic of the Virgin-born Christ. Says Tertullian: “We, little fishes, after the example of our Ichthus, are born in water.” 1. The Oracles: 1.  Were totally destroyed in the wars of Sylla. 2. Can be neither classified as Pagan, Christian or Jewish. 3.  Did not impress King Tarquin II. 4. Were religious fronts, which were used as proof of the truth of Christianity. 5.  Were religious frauds rejected by Christian p

2. Which religion had faith in the Oracles: 1.  Christians, Jews, and Pagans, alike. 2. Christians–indeed the Oracles were meant to disseminate Christianity. 3.  Only Jews–they used to speak Judaism. 4. Pagans–the sibyls were after all the architects of Oracles. 5.  Christians and Jews only. 3. Why was the term “Ichthus” considered appropriate for Christians: 1. The word meant fish–symbolic of Apostles being fishers of men. 2. It connected with the concept of the immaculate conception of Jesus. 3. It’s alphabets anacrostic into Jesus Christ, Son of God, 4.  All the above. 5.  None of the above. 4. Why did the Oracles become as popular as they did? 1. Because they claimed to be emanating from inspired prophetesses. 2.  Because kings like Tarquin II decreed them sacred. 3.  Because they were adopted to spread Christianity. 4. Because the clergy had a strong affinity for forgery to further their holy mission of imposture. 5. Because its contents were tailored to flatter Judaism and Christianity. 5. Which statement does not describe the Oracles? 1.  They were compiled in Alexandrian verse 2.  They were compiled in Hexameter verse. 3.  They were compiled in by Sibyls and Jews alike. 4.  They were compiled by Christians. 5. They were basically religious and were not used in matters of State Governance. Direction for questions 6 to 10:  Read the passage below and solve the questions based on it. Despite strong criticism from the opposition and even its own coalition partners, Chancellor Angela Merkel’s government agreed Wednesday to give Germany’s police forces greater powers to monitor homes, telephones and private computers, maintaining that an enhanced reach would protect citizens from terrorist attacks.

Reading Comprehension 

But opposition parties and some Social Democrats who share power with Merkel’s conservative bloc criticized the measures in the draft legislation, saying they would further erode privacy rights that they contend have already been undermined, after revelations of recent snooping operations conducted by Deutsche Telekom, one of the country’s biggest companies. Deutsche Telekom had for some time been monitoring calls of its employers, despite federal regulations on strict data protection. The proposed legislation would for the first time give federal police officers the right to take preventive measures in cases of suspected terrorism. The bill, for example, calls for video surveillance of private apartments, online computer searches and phone monitoring. But the nature of the surveillance, which would require the approval of the Bundestag, the lower house of Parliament, has worried many Germans, with some commentators recalling the Nazi past and its vast machinery of spying. They also point to the more recent role of the Stasi, the hated secret police in the once Communist-ruled East Germany, which established a pervasive system of keeping tabs on almost everyone in the country. The draft law was fashioned after months of intense debate led by Wolfgang Schäuble, the conservative interior minister, who has long wanted the security forces to be given more leeway for surveillance. Schäuble said Wednesday that, if approved, the law would strengthen the means available to the Federal Crime Office, known as the BKA, to investigate terrorism suspects and fight international crime. “The threat to our country has made it necessary to give the BKA such rights to counter threats,” Schäuble said at a news conference while presenting the so-called BKA law. “It is an important building block for Germany’s security architecture.” He also said the draft legislation was in line with the Constitution. But Sebastian Edathy, a Social Democrat and chairman of the domestic affairs committee in Parliament, told the public broadcaster ZDF that the legislation was “uncharted territory in the law.” He said sections of the legislation related to online searches should be limited to four or five years to give lawmakers a chance for evaluation. “We don’t want a spy state,” he said. “We want a state that works with tweezers instead of a sledgehammer in cases where we indeed have to protect the state’s security concerns.” The opposition Greens party said Schäuble was trying to realize his own agenda by pushing through the tougher measures.

  2.27

“All of Mr Schäuble’s security fantasies have been pushed through,” Claudia Roth, a Greens leader, said in an interview on the commercial television station N24. “We need resistance to that. I don’t want us to be a state in which everyone is suspicious.” The pro-business Free Democrats said the security forces could become a “super spying agency.” The party’s interior affairs expert, Gisela Piltz, said Schäuble’s plan would undermine a state that is based on strong constitutional rights and has transparent checks and balances. Schäuble rejected assertions of excessive state interference. “The constitutional state works,” he said. “The protection of the personal private sphere,” he said, “is no lower than in any other part of the world and it is higher than it has ever been at any other time in our history. I’m proud of that, and working for it with great determination.” But Peter Schaar, who heads the federal agency for data protection, challenged the legislation, saying he would lobby Parliament to improve the proposals so that citizens’ privacy could be protected. A poll by the independent Forsa Institute showed that 48 percent of Germans considered storage of citizens’ data by the government a necessary means to fight crime, while 46 percent said it was a disproportionate and unnecessary assault on individual freedoms. 6. Why did the German Government. give powers of spying to its security apparatus? 1.  To enhance the powers of the police. 2. To deflect criticism from its opposition and condition partners. 3.  To improve Germany’s defence preparedness. 4.  To enhance powers of the Home Ministry. 5. To protect its citizens from impending terrorist attacks. 7. What is the oppositions main concern about this legislation? 1. That it takes Germany back to the Nazi era with its vast spying network. 2. That it will become like Communist ruled East Germany where tabs were kept on every citizen. 3. That this legislation would go into uncharted territories of law. 4. That the legislation is too drastic for the problem it is supposed to solve. 5. That citizens privacy rights, already under threat will be further eroded.

2.28 

  Verbal and Logical Reasoning

8. What is the main defense of the Government. in favour of their legislation: 1. It was an important building block in Germany’s Security infrastructure. 2.  The legislation is well in line with the constitution. 3. That in spite of this legislation, citizen privacy is well protected in Germany. 4. That it gives the correct tools for its security apparatus to curb terrorism and fight international crime. 5.  That there is an imminent threat to the country. 9. Which of the following comments best conveys the theme of this passage: 1.  The German Govt. is worried about its security. 2. The German Opposition is worried that the law gives too much power to the Govt. 3. The German security apparatus welcomes this law as it gives it teeth to fight terrorism. 4. Quite a few German people are uneasy that in the name of security, their privacy is being increasingly invaded. 5. That given good checks and balances, it is necessary for the state to use all names at its disposal to protect its citizens. 10. If you were the German government, how would you justify this bill? 1. We are not really going backwards in time towards Nazism or East German Communism. 2. Extreme emerging problems like terrorism need drastic measures with checks and balances. 3. We will do our best not to interfere in citizens private lives. 4. This law will enhance Germany’s prestige in the world as a terrorism fighter. 5. We will have adequate checks and balances to prevent misuse. Direction for questions 11 to 15:  Read the passage below and solve the questions based on it. Sigmund Freud is the father of Psychoanalysis. He continued to modify his theory over a period of nearly half a century. Psychoanalysis focuses on the unconscious aspects of personality. According to Freud the human mind is like an iceberg. It is mostly hidden in the unconscious. He believed that the conscious level of the mind was similar to the tip of the iceberg which could be seen, but the unconscious was mysterious and was hidden. The

unconscious also consists of aspects of personality of which a person is unaware. The conscious on the other hand is that which is within our awareness. The preconscious consists of that which is not in immediate awareness but is easily accessible. In 1923, Freud described his constructs of the id, ego and the superego. The id is the most primitive part of our personality. It operates according to the pleasure principle and it simply seeks immediate gratification. Freud believed that every human had a life and death instinct. The life instinct is called eros while the death instinct is called thanatos. Both are integral parts of the id. And the energy for this mechanism is libido, a flowing, dynamic force. The ego is different from the id as it is extremely objective. It operates according to the “reality principle” and deals with the demands of the environment. It regulates the flow of libido and keeps the id in check, thus acting as a “control center” of the personality. It is the superego which represents the values and standards of an individual’s personality. It acts as an internal judge, it punishes the ego with feelings of guilt or it rewards, which lead to feelings of pride and heightened self esteem. The superego is a characteristic of the personality which strives for perfection. According to Freud, the disparity and development of the id, ego and the superego, determines an individuals behaviour in a given situation, which in turn results in the development of the personality. Freud placed great importance on the early years of a child as he believed that what we are as adults is determined by childhood experiences. Freud called these early years of development the psychosexual years of development. These early years proceed through a number of stages. Each child undergoes the different stages. These stages are the oral stage (first year of life), the anal stage (second year), phallic stage (third through fifth year), a period of latency (from 6 to 12), and the genital stage (after puberty). Freud believed that as every child passes through these stages there might be a likely possibility that a child may spend more time in a particular stage then they aught to. This condition can lead to a fixation or an incomplete development of the personality. A critical event during the first five years of life is the experience of Oedipus and Electra conflicts. Freud believed that both sexes encounter and must deal with these turmoils, which result from boys developing sexual attraction toward their mothers, and girls developing sexual attraction towards their fathers. A boy may have feelings of jealousy towards his father as he is an obstacle between him and his mother. And, they fear retaliation by their fathers if they are caught (fear of castration). Since the boy loves his father, these feelings are repressed and he begins to identify with the father, adopting his values. Similarly girls develop hostility towards their mothers, unconsciously blaming their mothers for not being equal with boys. They assume that something is missing and feels inadequate (penis envy).

Reading Comprehension 

Another major aspect of psychoanalysis is the development of defense mechanisms. According to the theory defense mechanisms are used by the ego to protect the person from anxiety. Repression is when information is pushed down into the unconscious. This information is either unpleasant or undesirable and may cause anxiety. Very often this information is pushed so deep down into the unconscious that is hard to retrieve. Reaction formation is when due to anxiety feelings are replaced by the extreme opposite. For instance, a person feeling hate will be replaced by love. Undoing is when the ego completely changes actions which lead to feelings of anxiety. In this mechanism the truth may be drastically distorted. Projection is when an individual tends to assign one’s own shortcomings on to someone else. Rationalization is when an irrational act is made to appear rational. Denial occurs in cases where the ego is threatened and a person refuses to acknowledge the reality or seriousness of the situation. Identification involves empathizing with the qualities or characteristics of another favorable person. Fixation and Regression are related mechanisms which occur during psychosexual development. Psychoanalysis is also a therapy. It is based on the observation that individuals are often unaware of many of the factors that determine their emotions and behaviour. Psychoanalytic treatment demonstrates how these unconscious factors affect current relationships and patterns of behaviour, traces them back to their historical origins, shows how they have changed, and helps individuals to deal better with the realities of adult life. 11. How many levels of consciousness did Freud believe existed?

1.  Two 2.  Three 3.  Four 4.  One 5.  None of the above.

12. Which of these statements do not reflect Freudian thought? 1.  Id demands short term gratification 2.  Ego caters to the demands of the environment. 3. The ratio of ID, ego and super ego determines a human’s personality. 4. The unconscious stores personality aspects and thoughts of which a person is actually aware. 5. Every child goes through psychosexual stages of development. 13. With Psychoanalysis, Freud basically 1. Explained the differences between life instinct (eros) and the death instinct (thanatos).

  2.29

2. Focussed largely on the unconscious aspects of a personality. 3. Explained why different children behaved differently. 4. Brought out anamolies in relationships between parents and children. 5.  Probed into the functioning of the human brain. 14 How does the ego protect a person from anxiety? 1.  Via Repression 2.  Via Denial 3.  Via Rationalization 4.  Via Identification 5. By using and developing defence mechanisms which utilize all the above. 15. Identify the truest statement as per the passage: 1. Psychoanalysis is the therapeutic since it assists in dealing with the realities of adult life. 2.  The id is stronger than the ego. 3. Life and death instincts define our defence mechanisms. 4.  Fixation and Regression are complexes 5. The conscious level of the mind forms at least half of a humans personality. Direction for questions 16 to 20:  Read the passage below and solve the questions based on it. The beginnings of Gnosticism have long been a matter of controversy and are still largely a subject of research. The more these origins are studied, the farther they seem to recede in the past. Whereas formerly, Gnosticism was considered mostly a corruption of Christianity, it now seems clear that the first traces of Gnostic systems can be discerned some centuries before the Christian Era. Its Eastern origin was already maintained by Gieseler and Neander; F. Ch. Bauer (1831) and Lassen (1858) sought to prove its relation to the religions of India; Lipsius (1860) pointed to Syria and Phoenicia as its home, and Hilgenfeld (1884) thought it was connected with later Mazdeism. Joel (1880), Weingarten (1881), Koffmane (1881), Anrich (1894), and Wobbermin (1896) sought to account for the rise of Gnosticism by the influence of Greek Platonic philosophy and the Greek mysteries, while Harnack described it as “acute Hellenization of Christianity”.

2.30 

  Verbal and Logical Reasoning

In more recent years (1897) Wilhelm Anz pointed out the close similarity between Babylonian astrology and the Gnostic theories of the Hebdomad and Ogdoad. Though in many instances speculations on the Babylonian Astrallehre have gone beyond all sober scholarship, yet in this particular instance the inferences made by Anz seem sound and reliable. Researches in the same direction were continued and instituted on a wider scale by W. Bousset, in 1907, and led to carefully ascertained results. In 1898, the attempt was made by M. Friedländer to trace Gnosticism in pre-Christian Judaism. His opinion that the Rabbinic term Minnim designated not Christians, as was commonly believed, but Antinomian Gnostics, has not found universal acceptance. In fact, E. Schürer brought sufficient proof to show that Minnim is the exact Armaean dialectic equivalent for ethne. Nevertheless Friedländer’s essay retains its value in tracing strong antinomian tendencies with Gnostic colouring on Jewish soil. Although the origins of Gnosticism are still largely enveloped in obscurity, so much light has been shed on the problem by the combined labours of many scholars that it is possible to give the following tentative solution: Although Gnosticism may at first sight appear a mere thoughtless syncretism of well nigh all religious systems in antiquity, it has in reality one deep root-principle, which assimilated in every soil what is needed for its life and growth; this principle is philosophical and religious pessimism. The Gnostics, it is true, borrowed their terminology almost entirely from existing religions, but they only used it to illustrate their great idea of the essential evil of this present existence and the duty to escape it by the help of magic spells and a superhuman Saviour. Whatever they borrowed, this pessimism they did not borrow—not from Greek thought, which was a joyous acknowledgment of and homage to the beautiful and noble in this world, with a studied disregard of the element of sorrow; not from Egyptian thought, which did not allow its elaborate speculations on retribution and judgment in the netherworld to cast a gloom on this present existence, but considered the universe created or evolved under the presiding wisdom of Thoth; not from Iranian thought, which held to the absolute supremacy of Ahura Mazda and only allowed Ahriman a subordinate share in the creation, or rather counter-creation, of the world; not from Indian Brahminic thought, which was Pantheism pure and simple, or God dwelling in, nay identified with, the universe, rather than the Universe existing as the contradictory of God; not, lastly, from Semitic thought, for Semitic religions were strangely reticent as to the fate of the soul after death, and saw all practical wisdom in the worship of Baal, or Marduk, or Assur, or Hadad, that they might live long on this earth. This utter pessimism, bemoaning the existence of the whole universe as a corruption and a calamity, with a

feverish craving to be freed from the body of this death and a mad hope that, if we only knew, we could by some mystic words undo the cursed spell of this existence—this is the foundation of all Gnostic thought. It has the same parent-soil as Buddhism; but Buddhism is ethical, it endeavours to obtain its end by the extinction of all desire; Gnosticism is pseudo-intellectual, and trusts exclusively to magical knowledge. Moreover, Gnosticism, placed in other historical surroundings, developed from the first on other lines than Buddhism. When Cyrus entered Babylon in 539 B.C., two great worlds of thought met, and syncretism in religion, as far as we know it, began. Iranian thought began to mix with the ancient civilization of Babylon. The idea of the great struggle between evil and good, ever continuing in this universe, is the parent idea of Mazdeism, or Iranian dualism. This, and the imagined existence of numberless intermediate spirits, angels and devas, are the conviction which overcame the contentedness of Semitism. On the other hand, the unshakable trust in astrology, the persuasion that the planetary system had a fatalistic influence on this world’s affairs, stood its ground on the soil of Chaldea. The greatness of the Seven—the Moon, Mercury, Venus, Mars, the Sun, Jupiter, and Saturn—the sacred Hebdomad, symbolized for millenniums by the staged towers of Babylonia, remained undiminished. They ceased, indeed, to be worshipped as deities, but they remained archontes and dynameis, rules and powers whose almost irresistible force was dreaded by man. Practically, they were changed from gods to devas, or evil spirits. The religions of the invaders and of the invaded effected a compromise: the astral faith of Babylon was true, but beyond the Hebodomad was the infinite light in the Ogdoad, and every human soul had to pass the adverse influence of the god or gods of the Hebdomad before it could ascend to the only good God beyond. This ascent of the soul through the planetary spheres to the heaven beyond (an idea not unknown even to ancient Babylonian speculations) began to be conceived as a struggle with adverse powers, and became the first and predominant idea in Gnosticism. The second great component of Gnostic thought is magic, properly so called, i.e., the power ex opere operato of weird names, sounds, gestures, and actions, as also the mixture of elements to produce effects totally disproportionate to the cause. These magic formulae, which caused laughter and disgust to outsiders, are not a later and accidental corruption, but an essential part of Gnosticism, for they are found in all forms of Christian Gnosticism and likewise in Mandaeism. No Gnosis was essentially complete without the knowledge of the formulae, which, once pronounced, were the undoing of the higher hostile powers. Magic is the original sin of Gnosticism, nor is it difficult to guess whence it is inherited. To a certain extent it formed part of every pagan religion, especially the ancient

Reading Comprehension 

mysteries, yet the thousands of magic tablets unearthed is Assyria and Babylonia show us where the rankest growth of magic was to be found. Moreover, the terms and names of earliest of Gnosticism bear an unmistakable similarity to Semitic sounds and words. 16. Gnostics are: 1.  Non believers in God or Supreme Being. 2.  Believers that good things will happen to us in life. 3.  Obscure and confused people. 4. Pessimistic in their religious and philosophical outlook. 5.  Connected to early Babylonians. 17. What would a Gnostic seek from life? 1.  Escape from life’s evil and misery with God’s help. 2.  Ascent to God through planets. 3.  Formulae and potions of magic. 4. Connections with all known religious, present and past. 5.  Solution to conflict between Good and Evil. 18. The Gnostic approach is. 1.  Very similar to Egyptian and Greek philosophy. 2.  Very similar to Christianity. 3.  Strongly condemnative of Buddhism. 4.  Not at all similar to the Greek outlook of life. 5.  Lost in obscurity and confusion. 19. What do Gnostics think of the planets? 1. They were evil influences who had to be struggled with before reaching God. 2. Planet worship was Babylonian nothing to do with Gnostics. 3. Planets had a Good influence on actions and helped in our passage to God. 4. Planets were the ultimate good to be propitiated and worshipped. 5.  None of the above. 20. Based on the passage, what are the two defining trends of Gnosticism? 1. Hope and the need of magic to come out of the misery of life.

  2.31

Direction for questions 21 to 25:  Read the passage below and solve the questions based on it. The union government’s present position vis-a-vis the upcoming United Nations conference on racial and related discrimination world-wide seems to be the following: discuss race please, not caste; caste is our very own and not at all as bad as you think. The gross hypocrisy of that position has been lucidly underscored by Kancha Ilaiah. Explicitly, the world community is to be cheated out of considering the matter on the technicality that caste is not, as a concept, tantamount to a racial category. Internally, however, allowing the issue to be put on agenda at the said conference would, we are patriotically admonished, damage the country’s image. Somehow, India’s virtual beliefs elbow out concrete actualities. Inverted representations, as we know, have often been deployed in human histories as balm for the forsaken—religion being the most persistent of such inversions. Yet, we would humbly submit that if globalizing our markets are thought good for the ‘national’ pocket, globalizing our social inequities might not be so bad for the mass of our people. After all, racism was as uniquely institutionalized in South Africa as caste discrimination has been within our society; why then can’t we permit the world community to express itself on the latter with a fraction of the zeal with which, through the years, we pronounced on the former? As to the technicality about whether or not caste is admissible into an agenda about race (that the conference is also about ‘related discriminations’ tends to be forgotten), a reputed sociologist has recently argued that where race is a ‘biological’ category caste is a ‘social’ one. Having earlier fiercely opposed implementation of the Mandal Commission Report, the said sociologist is at least to be complemented now for admitting, however tangentially, that caste discrimination is a reality, although, in his view, incompatible with racial discrimination. One would like quickly to offer the hypothesis that biology, in important ways that affect the lives of many millions, is in itself perhaps a social construction. But let us look at the matter in another way. If it is agreed—as per the position today at which anthropological and allied scientific determinations rest—that the entire race of homo sapiens derived from an originary black African female (called ‘Eve’) then one is hard put to understand how, on some subsequent ground, ontological distinctions are to be drawn either between races or castes. Let us also underline the distinction between the supposition that we are all God’s children and the rather more substantiated argument about our descent from ‘Eve’, lest both positions are thought to be equally diversionary. It then stands to reason that all subsequent distinctions are, in modern parlance, ‘constructed’ ones, and, like all ideological constructions, attributable to changing equations between knowledge and power among human communities through contested histories here, there, and elsewhere.

2.32 

  Verbal and Logical Reasoning

3. Occurs often as a means of keeping people oppressed.

This line of thought receives, thankfully, extremely consequential buttress from the findings of the Human Genome project. Contrary to earlier (chiefly 19th century colonial) persuasions on the subject of race, as well as, one might add, the somewhat infamous Jensen offerings in the 20th century from America, those findings deny genetic difference between ‘races’. If anything, they suggest that environmental factors impinge on gene-function, as dialectic seems to unfold between nature and culture. It would thus seem that ‘biology’ as the constitution of pigmentation enters the picture first only as a part of that dialectic. Taken together, the originary mother stipulation and the Genome findings ought indeed to furnish ground for human equality across the board, as well as yield policy initiatives towards equitable material dispensations aimed at building a global order where, in Hegel’s stirring formulation, only the rational constitutes the right. Such, sadly, is not the case as everyday fresh arbitrary grounds for discrimination are constructed in the interests of sectional dominance.

4.  Occurs often to invert the status quo. 5.  None of these 23. Based on the passage, which broad areas unambiguously fall under the purview of the UN conference being discussed? A.  Racial prejudice. B.  Racial pride. C.  Discrimination, racial or otherwise. D.  Caste-related discrimination. E.  Race-related discrimination. 1.  A, E 4.  B, C, D

2.  C, E 5.  A only

3.  A, C, E

24. According to the author, the sociologist who argued that race is a ‘biological’ category and caste is a ‘social’ one:

3. Going beyond an internal delimitation of social inequity.

1. Generally shares the same orientation as the author’s on many of the central issues discussed. 2. Tangentially admits to the existence of “Caste” as a category. 3. Admits the incompatibility between the people of different race and caste. 4. Admits indirectly that both caste-based prejudice and racial discrimination exist. 5.  None of these:

4. Achieving disadvantaged people’s empowerment, globally.

25. An important message in the passage, if one accepts a dialectic between nature and culture, is that:

21. When the author writes “globalizing our social inequities”, the reference is to: 1. Going beyond an internal deliberation on social inequity. 2. Dealing with internal poverty through the economic benefits of globalization.

5.  None of these

1. The results of the Human Genome Project reinforces racial differences.

22. According to the author, ‘inverted representations as balm for the forsaken’:

2.  Race is at least partially a social construct. 3. Discrimination is at least partially a social construct.

2. Is good for the forsaken, but not often deployed historically for the oppressed.

5.  None of these.

ANSWER KEYS

1. Is good for the forsaken and often deployed in human histories.

4.  Caste is at least partially a social construct.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

1

3.

4

4.

4

5.

5

6.

5

7.

5

8.

4

9.

4

10.

2

11.

2

12.

4

13.

2

14.

5

15.

1

16.

4

17.

1

18.

4

19.

1

20.

5

21.

1

22.

3

23.

1

24.

4

25.

2

Reading Comprehension 

  RC EXERCISE  3 Direction for questions 1 to 24:  Each of the three passages given below is followed by questions. Choose the best answer for each question.

PASSAGE  I The current debate on intellectual property rights (IPRs) raises a number of important issues concerning the strategy and policies for building a more dynamic national agricultural research system, the relative roles of public and private sectors, and the role of agribusiness multinational corporations (MNCs). This debate has been stimulated by the international agreement on Trade Related Intellectual Property Rights (TRIPs), negotiated as part of the Uruguay Round. TRIPs, for the first time, seeks to bring innovations in agricultural technology under a new worldwide IPR regime. The agribusiness MNCs (along with pharmaceutical companies) played a leading part in lobbying for such a regime during the Uruguay Round negotiations. The argument was that incentives are necessary to stimulate innovations, and that this calls for a system of patents which gives innovators the sole right to use (or sell/lease the right to use) their innovations for a specified period and protects them against unauthorized copying or use. With strong support of their national governments, they were influential in shaping the agreement on TRIPs, which eventually emerged from the Uruguay Round. The current debate on TRIPs in India—as indeed elsewhere—echoes wider concerns about ‘privatization’ of research and allowing a free field for MNCs in the sphere of biotechnology and agriculture. The agribusiness corporations, and those with unbounded faith in the power of science to overcome all likely problems, point to the vast potential that new technology holds for solving the problems of hunger, malnutrition and poverty in the world. The exploitation of this potential should be encouraged and this is best done by the private sector for which patents are essential. Some, who do not necessarily accept this optimism, argue that fears of MNC domination arc exaggerated and that farmers will accept their products only if they decisively outperform the available alternatives. Those who argue against agreeing to introduce an IPR regime in agriculture and encouraging private sector research are apprehensive that this will work to the disadvantage of farmers by making them more and more dependent on monopolistic MNCs. A different, though related apprehension is that extensive use of hybrids and genetically engineered new varieties might increase the vulnerability of agriculture to outbreaks of pests and diseases. The larger, longer-term consequences of reduced biodiversity that may follow from the use of specially bred varieties are also another cause for concern. Moreover, corporations, driven by the profit motive, will necessarily tend to underplay, if not ignore, potential adverse consequences, especially those which are unknown

  2.33

and which may manifest themselves only over a relatively long period. On the other hand, high-pressure advertising and aggressive sales campaigns by private companies can seduce farmers into accepting varieties without being aware of potential adverse effects and the possibility of disastrous consequences for their livelihood if these varieties happen to fail. There is no provision under the laws, as they now exist, for compensating users against such eventualities. Excessive preoccupation with seeds and seed material has obscured other important issues involved in reviewing the research policy. We need to remind ourselves that improved varieties by themselves are not sufficient for sustained growth of yields. In our own experience, some of the early high yielding varieties (HYVs) of rice and wheat were found susceptible to widespread pest attacks; and some had problems of grain quality. Further research was necessary to solve these problems. This largely successful research was almost entirely done in public research institutions. Of course, it could in principle have been done by private companies, but whether they choose to do so depends crucially on the extent of the loss in market for their original introductions on account of the above factors and whether the companies are financially strong enough to absorb the ‘losses’, invest in research to correct the deficiencies and recover the lost market. Public research, which is not driven by profit, is better placed to take corrective action. Research for improving common pool resource management, maintaining ecological health and ensuring sustainability is both critical and also demanding in terms of technological challenge and resource requirements. As such research is crucial to the impact of new varieties, chemicals and equipment in the farmer’s field, private companies should be interested in such research. But their primary interest is in the sale of seed material, chemicals, equipment and other inputs produced by them. Knowledge and techniques for resource management are not ‘marketable’ in the same way as those inputs. Their application to land, water and forests has a long gestation and their efficacy depends on resolving difficult problems-such as designing institutions for proper and equitable management of common pool resources. Public or quasi-public research institutions informed by broader, long-term concerns can only do such work. The public sector must therefore continue to play a major role in the national research system. It is both wrong and misleading to pose the problem in terms of public sector versus private sector or of privatization of research. We need to address problems likely to arise on account of the public-private sector complementarity, and ensure that the public research system performs efficiently. Complementarity between various elements of research raises several issues in implementing an IPR regime. Private companies do not produce new varieties and inputs entirely as a result of their own research. Almost all technological improvement is based on knowledge and experience accumulated from the past, and the results of basic and

2.34 

  Verbal and Logical Reasoning

applied research in public and quasi-public institutions (universities, research organizations). Moreover, as is increasingly recognized, accumulated stock of knowledge does not reside only in the scientific community and its academic publications, but is also widely diffused in traditions and folk knowledge of local communities all over. The deciphering of the structure and functioning of DNA forms the basis of much of modern biotechnology. But this fundamental breakthrough is a ‘public good’ freely accessible in the public domain and usable free of any charge. Varieties/techniques developed using that knowledge can however be, and are, patented for private profit. Similarly, private corporations draw extensively, and without any charge, on germ plasm available in varieties of plants species (neem and turmeric are by now famous examples). Publicly funded gene banks as well as new varieties bred by public sector research stations can also be used freely by private enterprises for developing their own varieties and seek patent protection for them. Should private breeders be allowed free use of basic scientific discoveries’! Should the repositories of traditional knowledge and germ plasm be collected which arc maintained and improved by publicly funded institutions? Or should users be made to pay for such use? If they are to pay, what should be the basis of compensation? Should the compensation be for individuals or for communities/institutions to which they belong? Should individuals/institutions be given the right of patenting their innovations? These are some of the important issues that deserve more attention than they now get and need serious detailed study to evolve reasonably satisfactory, fair and workable solutions. Finally, the tendency to equate the public sector with the government is wrong. The public space is much wider than government departments and includes co-operatives, universities, public trusts and a variety of non-governmental organizations (NGOs). Giving greater autonomy to research organizations from government control and giving non-government public institutions the space and resources to play a larger, more effective role in research, is therefore an issue of direct relevance in restructuring the public research system. 1. Which of the following statements describes an important issue, or important issues, not being raised in the context of the current debate on IPRs? 1. The role of MNCs in the sphere of biotechnology and agriculture. 2. The strategy and policies for establishing an IPR regime for Indian agriculture. 3.  The relative roles of public and private sectors.

1. Breakthroughs in fundamental research on DNA are accessible by all without any monetary considerations. 2. The fundamental research on DNA has the characteristic of having beneficial effects for the public at large. 3. Due to the large scale of fundamental research on DNA, it falls in the domain of public sector research institutions. 4. The public and other companies must have free access to such fundamental breakthroughs in research. 3. In debating the respective roles of the public and private sectors in the national research system, it is important to recognize: 1. that private companies do not produce new varieties and inputs entirely on their own research. 2. that almost all technological improvements are based on knowledge and experience accumulated from the past. 3. the complementary role of public and private sector research. 4. that knowledge repositories are primarily the scientific community and its academic publications. 4. Which one of the following may provide incentives to address the problem of potential adverse consequences of biotechnology? 1.  Include IPR issues in the TRIPs agreement. 2. Nationalize MNCs engaged in private research in biotechnology. 3. Encourage domestic firms to patent their innovations. 4. Make provisions in the law for user compensation against failure of newly developed varieties. 5. Which of the following statements is not a likely consequence of emerging technologies in agriculture? 1. Development of newer and newer varieties will lead to increase in biodiversity. 2. MNCs may underplay the negative consequences of the power technology on environment.

4.  Wider concerns about ‘privatization’ of research.

3. Newer varieties of seeds may increase vulnerability of crops to pests and diseases.

2. The fundamental breakthrough in deciphering the structure and functioning of DNA has become a public good. This means that:

4. Reforms in patent laws and user compensation against crop failures would be needed to address new technology problems.

Reading Comprehension 

6. The TRIPs agreement emerged from the Uruguay Round to: 1. address the problem of adverse consequences of genetically engineered new varieties of grain. 2. fulfill the WTO requirement to have an agreement on trade related property rights. 3. provide incentives to innovators by way of protecting their intellectual property. 4. give credibility to the innovations made by MNCs in the field of pharmaceuticals and agriculture. 7. Public or quasi-public research institutions are more likely than private companies to address the negative consequences of new technologies, because of which of the following reasons? 1.  Public research is not driven by profit motive. 2. Private companies may not be able to absorb losses arising out of the negative effects of the new technologies. 3. Unlike new technology products, knowledge and techniques for resource management are not amenable to simple market transactions. 4.  All of the above. 8. While developing a strategy and policies for building a more dynamic national agricultural research system, which one of the following statements needs to be considered? 1. Public and quasi-public institutions are not interested in making profits. 2. Public and quasi-public institutions have a broader and long-term outlook than private companies. 3. Private companies are incapable of building products based on traditional and folk knowledge. 4. Traditional and folk knowledge cannot be protected by patents.

PASSAGE  II One of the criteria by which we judge the vitality of a style of painting is its ability to renew itself—its responsiveness to the changing nature and quality of experience, the degree of conceptual and formal innovation that it exhibits. By this criterion, it would appear that the practice of abstractionism has failed to engage creatively with the radical change in human experience in recent decades. It has, seemingly, been unwilling to re-invent itself in relation to the systems of artistic expression and viewers’ expectations that have developed under the impact of the mass media. The judgement that abstractionizm has slipped into ‘inertia gear’ is gaining endorsement, not only among discerning viewers and practitioners of other art forms, but also

  2.35

among abstract painters themselves. Like their companions elsewhere in the world, abstractionists in India are asking themselves an overwhelming question today: Does abstractionizm have a future? The major crisis that abstractionists face is that of revitalizing their picture surface; few have improvised any solutions beyond the ones that were exhausted by the 1970s. Like all revolutions, whether in politics or in art, abstractionism must now confront its moment of truth: having begun life as a new and radical pictorial approach to experience, it has become an entrenched orthodoxy itself. Indeed, when viewed against a historical situation in which a variety of subversive, interactive and richly hybrid forms are available to the art practitioner, abstractionism assumes the remote and defiant air of an aristocracy that has outlived its age; trammelled by formulaic conventions yet buttressed by a rhetoric of sacred mystery, it seems condemned to being the last citadel of the self-regarding ‘fine art’ tradition, the last hurrah of painting for painting’s sake. The situation is further complicated in India by the circumstances in which an indigenous abstractionizm came into prominence here during the 1960s. From the beginning it was propelled by the dialectic between two motives, one revolutionary and the other conservative—it was inaugurated as an act of emancipation from the dogmas or the nascent Indian nation state, when art was officially viewed as an indulgence at worst, and at best, as an instrument for the celebration of the republic’s hopes and aspirations. Having rejected these dogmas, the pioneering abstractionists also went on to reject the various figurative styles associated with the Santiniketan circle and others. In such a situation, abstractionism was a revolutionary move. It led art towards the exploration of the subconscious mind, the spiritual quest and the possible expansion of consciousness. Indian painting entered into a phase of self-inquiry, a meditative inner space where cosmic symbols and non-representational images ruled. Often, the transition from figurative idioms to abstractionist ones took place within the same artist. At the same time, Indian abstractionists have rarely committed themselves wholeheartedly to a non-representational idiom. They have been preoccupied with the fundamentally metaphysical project of aspiring to the mystical-holy without altogether renouncing the symbolic. This has been sustained by a hereditary reluctance to give up the murti, the inviolable iconic form, which explains why abstractionizm is marked by the conservative tendency to operate with images from the sacred repertoire of the past. Abstractionizm thus entered India as a double-edged device in a complex cultural transaction. Ideologically, it served as an internationalist legitimization of the emerging revolutionary local trends. However, on entry, it was’ conscripted to serve local artistic preoccupations—a survey of indigenous abstractionism will show that its most obvious points of affinity with European and American abstract art were with the more mystically oriented of the

2.36 

  Verbal and Logical Reasoning

major sources of abstractionist philosophy and practice, for instance the Kandinsky-Klee school. There have been no takers for Malevich’s Suprematism, which militantly rejected both the artistic forms of the past and the world of appearances, privileging the new-minted geometric symbol as an autonomous sign of the desire for infinity. Against this backdrop, we can identify three major abstractionist idioms in Indian art. The first develops from a love of the earth, and assumes the form of a celebration of the self’s dissolution in the cosmic panorama; the landscape is no longer a realistic transcription of the scene, but is transformed into a visionary occasion for contemplating the cycles of decay and regeneration. The second idiom phrases its departures from symbolic and archetypal devices as invitations to heightened planes of awareness. Abstractionism begins with the establishment or dissolution of the motif, which can be drawn from diverse sources, including the hieroglyphic tablet, the Sufi meditation dance or the Tantric diagram. The third idiom is based on the lyric play of forms guided by gesture or allied with formal improvisations like the assemblage. Here, sometimes, the line dividing abstract image from patterned design or quasi-random expressive marking may blur. The flux of forms can also be regimented through the poetics of pure colour arrangements, vectordiagrammatic spaces and gestural design. In this genealogy, some pure lines of descent follow their logic to the inevitable point of extinction, others engage in cross-fertilization, and yet others undergo mutation to maintain their energy. However, this genealogical survey demonstrates the wave at its crest.” those points where the metaphysical and the painterly have been fused in images of abiding potency, ideas sensuously ordained rather than fabricated programmatically to a concept. It is equally possible to enumerate the troughs where the two principles do not come together, thus arriving at a very different account. Uncharitable as it may sound, the history of Indian abstractionism records a series of attempts to avoid the risks of abstraction by resorting to an overt and near-generic symbolism, which many Indian abstractionists embrace when they find themselves bereft of the imaginative energy to negotiate the union of metaphysics and painterliness. Such symbolism falls into a dual trap: it succumbs to the pompous vacuity of pure metaphysics when the burden of intention is passed off as justification; or then it is desiccated by the arid formalizm of pure painterliness, with delight in the measure of chance or pattern guiding the execution of a painting. The ensuing connict of purpose stalls the progress of abstractionizm in an impasse. The remarkable Indian abstractionists are precisely those who have overcome this and addressed themselves to the basic elements of their art with a decisive sense of independence from prior models. In their recent work, we see the logic of Indian abstractionizm pushed almost to the furthest it can be taken. Beyond such artists stands a lost generation of

abstractionists whose work invokes a wistful, delicate beauty but stops there. Abstractionizm is not a universal language; it is an art that points up the loss of a shared language of signs in society. And yet, it affirms the possibility of its recovery through the effort of awareness. While its rhetoric has always emphasised a call for new forms of attention, abstractionist practice has tended to fall into a complacent pride in its own incomprehensibility; a complacency fatal in an ethos where vibrant new idioms compete for the viewers’ attention. Indian abstractionists ought to really return to basics, to reformulate and replenish their understanding of the nature of the relationship between the painted image and the world around it. But will they abandon their favourite conceptual habits and formal conventions, if this becomes necessary? 9. Which of the following is not stated by the author as a reason for abstractionism losing its vitality? 1. Abstractionism has failed to reorient itself in the context of changing human experience. 2. Abstractionism has not considered the developments in artistic expression that have taken place in recent times. 3. Abstractionism has not followed the path taken by all revolutions, whether in politics or art. 4. The impact of mass media on viewers’ expectations has not been assessed, and responded to, by abstractionizm. 10. Which of the folllowing, according to the author, is the role that abstractionism plays in a society? 1. It provides an idiom that can be understood by most members in a society. 2. It highlights the absence of a shared language of meaningful symbols which can be recreated through greater awareness. 3. It highlights the contradictory artistic trends of revolution and conservatism that any society needs to move forward. 4. It helps abstractionists invoke the wistful, delicate beauty that may exist in society. 11. According to the author, which one of the following characterizes the crisis faced by abstractionism? 1. Abstractionists appear to be unable to transcend the solutions tried out earlier. 2. Abstractionism has allowed itself to be confined by set forms and practices. 3. Abstractionists have been unable to use the multiplicity of forms now becoming available to an artist. 4.  All of the above.

Reading Comprehension 

  2.37

12. According to the author, the introduction of abstractionism was revolutionary because it:

3. Many artists have avoided the trap of a near-generic and an open symbolism.

1. celebrated the hopes and aspirations of a newly independent nation.

4. Many artists have found it difficult to fuse the twin principles of the metaphysical and the painterly.

2. provided a new direction to Indian art, towards selfinquiry and non-representational images.

PASSAGE  III

3. managed to obtain internationalist support for the abstractionist agenda. 4. was an emancipation from the dogmas of the nascent nation state. 13. Which one of the following is not part of the author’s characterization of the conservative trend in India abstractionism? 1.  An exploration of the subconscious mind. 2. A lack of full commitment to non-representational symbols. 3. An adherence to the symbolic while aspiring to the mystical. 4.  Usage of the images of gods or similar symbols. 14. Given the author’s delineation of the three abstractionist idioms in Indian art, the third idioms can be best distinguished from the other two idioms through its: 1.  depiction of nature’s cyclical renewal. 2.  use of non-representational images. 3.  emphasis on arrangement of forms. 4.  limited reliance on original models. 15. According to the author, the attraction of the Kandinsky-Klee school for Indian abstractionists can be explained by which one of the following? 1. The conservative tendency to aspire to the mystical without a complete renunciation of the symbolic. 2. The discomfort of Indian abstractionists with Malevich’s Suprematism. 3. The easy identification of obvious points of affinity with European and American abstract art, of which the Kandinsky-Klee school is an example. 4. The double-edged nature of abstractionism which enabled identification with mystically-oriented schools. 16. Which one of the following, according to the author, is the most important reason for the stalling of abstractionizms progress in an impasse? 1. Some artists have followed their abstractionist logic to the point of extinction. 2.  Some artists have allowed chance or pattern to dominate the execution of their paintings.

In a modern computer, electronic and magnetic storage technologies play complementary roles. Electronic memory chips are fast but volatile (their contents are lost when the computer is unplugged). Magnetic tapes and hard disks are slower, hut have the advantage that they are non-volatile, so that they can be used to store software and documents even when the power is off. In laboratories around the world, however, researchers are hoping to achieve the best of both worlds. They are trying to build magnetic memory chips that could be used in place of today’s electronic ones. These magnetic memories would be non-volatile; but they would also be faster, would consume less power, and would be able to stand up to hazardous environments more easily. Such chips would have obvious applications in storage cards for digital cameras and music- players; they would enable handheld and laptop computers to boot up more quickly and to operate for longer; they would allow desktop computers to run faster; they would doubtless have military and space-faring advantages too. But although the theory behind them looks solid, there are tricky practical problems and need to be overcome. Two different approaches, based on different magnetic phenomena, are being pursued. The first, being investigated by Gary Prinz and his colleagues at the Naval Research Laboratory (NRL) in Washington, D.C., exploits the fact that the electrical resistance of some materials changes in the presence of a magnetic field-a phenomenon known as magneto-resistance. For some multi-layered materials this effect is particularly powerful and is, accordingly, called “giant” magneto-resistance (GMR). Since 1997, the exploitation of GMR has made cheap multi-gigabyte hard disks commonplace. The magnetic orientations of the magnetized spots on the surface of a spinning disk are detected by measuring the changes they induce in the resistance of a tiny sensor. This technique is so sensitive that it means the spot..” can be made smaller and packed closer together than was previously possible, thus increasing the capacity and reducing the size and cost of a disk drive. Dr Prinz and his colleagues are now exploiting the same phenomenon on the surface of memory chips, rather than spinning disks. In a conventional memory chip, each binary digit (bit) of data is represented using a capacitor-reservoir of electrical charge that is either empty or full-to represent a zero or a one. In the NRL’s magnetic design, by contrast, each bit is stored in a magnetic element in the form of a vertical pillar of magnetisable material. A matrix of wires passing above and below the elements allows each to be magnetised,

2.38 

  Verbal and Logical Reasoning

either clockwise or anticlockwise, to represent zero or one. Another set of wires allows current to pass through any particular element. By measuring an element’s resistance you can determine its magnetic orientation, and hence whether it is storing a zero or a one. Since the elements retain their magnetic’ orientation even when the power is off, the result is nonvolatile memory. Unlike the elements of an electronic memory, a magnetic memory’s elements are not easily disrupted by radiation. And compared with electronic memories, whose capacitors need constant topping up, magnetic memories are simpler and consume less power. The NRL researchers plan to commercialize their device through a company called Non-Volatile Electronics, which recently began work on the necessary processing and fabrication techniques. But it will be some years before the first chips roll off the production line. Most attention in the field is focused on an alternative approach based on magnetic tunnel-junctions (MTJs), which are being investigated by researchers at chip makers such as IBM, Motorola, Siemens and Hewlett-Packard. IBM’s research team, led by Stuart Parkin, has already created a SOD-element working prototype that operates at 20 times the speed of conventional memory chips and consumes 1 per cent of the power. Each element consists of a sandwhich of two layers of magnetisable material separated by a barrier of aluminium oxide just four or five atoms thick. The polarization of lower magnetisable layer is fixed in one direction, but that of the upper layer can be set (again, by passing a current through a matrix of control wires) either to the left or to the right, to store a zero or a one. The polarizations of the two layers are then in either the same or opposite directions. Although the aluminium-oxide barrier is an electrical insulator, it is so thin that electrons are able to jump across it via a quantum-mechanical effect called tunnelling. It turns out that such tunnelling is easier when the two magnetic layers are polarized in the same direction than when they are polarized in opposite directions. So, by measuring the current that flows through the sandwich, it is possible to determine the alignment of the topmost layer, and hence whether it is storing a zero or a one. To build a full-scale memory chip based on MTJs is. however, no easy matter. According to Paulo Freitas, an expert on chip manufacturing at the Technical University of Lisbon. magnetic memory elements will have to become far smaller and more reliable than current prototypes if they are to compete with electronic memory. At the same time, they will have to be sensitive enough to respond when the appropriate wires in the control matrix are switched on, but not so sensitive that they respond when a neighbouring element is changed. Despite these difficulties, the general consensus is that MTJs are the more promising ideas. Dr Parkin says his group evaluated the GMR approach and decided not to pursue it. despite the fact that IBM pioneered

GMR in hard disks. Dr Prinz, however, contends that his plan will eventually offer higher storage densities and lower production costs. Not content with shaking up the multi-billion-dollar market for computer memory, some researchers have even more ambitious plans for magnetic computing. In a paper published last month in Science, Russell Cowburn and Mark Weiland of Cambridge University outlined research that could form the basis of a magnetic microprocessor-a chip capable of manipulating (rather than merely storing) information magnetically. In place of conducting wires. a magnetic processor would have rows of magnetic dots, each of which could be polarized in one of two directions. Individual bits of information would travel down the rows as magnetic pulses, changing the orientation of the dots as they went. Dr Cowburn and Dr Welland have demonstrated how a logic gate (the basic element of a microprocessor) could work in such a scheme. In their experiment. they fed a signal in at one end of the chain of dots and used a second signal to control whether it propagated along the chain. It is, admittedly, a long way from a single logic gate to a full microprocessor. but this was true also when the transistor was first invented. Dr Cowburn, who is now searching for backers to help commercialise the technology, says he believes it will be at least ten years before the first magnetic microprocessor is constructed. But other researchers in the field agree that such a chip is the next logical step. Dr Prinz says that once magnetic memory is sorted out “the target is to go after the logic circuits.” Whether all-magnetic computers will ever be able to compete with other contenders that are jostling to knock electronics off its perchsuch as optical, biological and quantum computing-remains to be seen. Dr Cowburn suggests that the future lies with hybrid machines that use different technologies. But computing with magnetism evidently has an attraction all its own. 17. In developing magnetic memory chips to replace the electronic ones, two alternative research paths are being pursued. These are approaches based on 1.  volatile and non-volatile memories. 2.  magneto-resistance and magnetic tunnel-junctions 3.  radiation-disruption and radiation-neutral effects. 4. orientation of magnetized spots on the surface of a spinning disk and alignment of magnetic dots on the surface of a conventional memory chip. 18. A binary digit or bit is represented in the magnetoresistance based magnetic chip using 1.  a layer of aluminum oxide. 2.  a capacitor. 3.  a vertical pillar of magnetized material. 4.  a matrix of wires.

Reading Comprehension 

19. In the magnetic tunnel-junctions (MTJs) tunnelling is easier when 1. two magnetic layers are polarized in the same direction. 2. two magnetic layers are polarized in the opposite directions. 3. two aluminium-oxide barriers are polarized in the same direction. 4. two aluminium-oxide barriers are polarized in opposite directions.

22. A line of research which is trying to build magnetic chip that can both store and manipulate information, is being pursued by 1.  Paul Freitas 2.  Stuart Parkin 3.  Gary Prinz 4.  None of the above 23. Experimental research currently underway, using rows of magnetic dots, each of which could be polarized in one of the two directions, has led to the demonstration of:

20. A major barrier on the way to build a full-scale memory chip based on MTJs is 1. the low sensitivity of the magnetic memory elements. 2.  the thickness of aluminium oxide barriers. 3. the need to develop more reliable and far smaller magnetic memory chips. 4.  all of the above.

1.  working of a microprocessor. 2.  working of a logic gate. 3.  working of a magneto-resistance based chip. 4. working of a magneto tunnelling-junction (MTJ) based chip. 24. From the passage, which of the following cannot be inferred?

ANSWER KEYS

21. In the MTJs approach, it is possible to identify whether the topmost layer of the magnetised memory element is storing a zero or one by 1. measuring an element’s resistance and thus determining its magnetic orientation. 2. measuring the degree of disruption caused by radiation in the elements of the magnetic memory. 3. magnetising the elements either clockwise or anticlockwise. 4. measuring the current that flows through the sandwich.

1. Electronic memory chips are faster and non-volatile. 2. Electronic and magnetic storage technologies play a complementary role. 3. MTJs are the more promising idea, compared to the magneto-resistance approach. 4. Non-volatile Electronics is the company set up to commercialize the GMR chips.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

1

3.

3

4.

4

5.

1

6.

3

7.

4

8.

2

9.

3

10.

2

11.

4

12.

2

13.

1

14.

3

15.

1

16.

4

17.

2

18.

3

19.

1

20.

3

21.

4

22.

4

23.

2

24.

1

  RC EXERCISE  4 Direction for questions 1 to 21:  Each of the four  passages given below is followed by questions. Choose the best answer for each question.

  2.39

PASSAGE  I The story begins as the European pioneers crossed the Alleghenies and started to settle in the Midwest. The land they found was covered with forests. With incredible effort they felled the trees, pulled the stumps and planted their

2.40 

  Verbal and Logical Reasoning

crops in the rich, loamy soil. When they finally reached the western edge of the place we now call Indiana, the forest stopped and ahead lay a thousand miles of the great grass prairie. The Europeans were puzzled by this new environment. Some even called it the “Great Desert”. It seemed untillable. The earth was often very wet and it was covered with centuries of tangled and matted grasses. With their cast iron plows, the settlers found that the prairie sod could not be cut and the wet earth stuck to their plowshares. Even a team of the best oxen bogged down after a few years of tugging. The iron plow was a useless tool to farm the prairie soil. The pioneers were stymied for nearly two decades. Their western march was halted and they tilled in the eastern regions of the Midwest. In 1837, a blacksmith in the town, of Grand Detour, Illinois, invented a new tool. His name was John Deere and the tool was a plow made of steel. It was sharp enough to cut through matted grasses and smooth enough to cast off the mud. It was a simple tool, the “sod buster” that opened the great prairies to agricultural development. Sauk County, Wisconsin is the part of that prairie where I have a home. It is named after the Sauk Indians. In 1673, Father Marquette was the first European to lay his eyes upon their land. He found a village laid out in regular patterns on a plain beside the Wisconsin River. He called the place Prairie du Sac. The village was surrounded by fields that had provided maize, beans and squash for the Sauk people for generations reaching back into the unrecorded time. When the European settlers arrived at the Sauk prairie in 1837, the government forced the native Sauk people west of the Mississippi River. The settlers came with John Deere’s new invention and used the tool to open the area to a new kind of agriculture. They ignored the traditional ways of the Sauk Indians and used their sod-busting tool for planting wheat. Initially, the soil was generous and the farmers thrived. However, each year the soil lost more of its nurturing power. It was only thirty years after the Europeans arrived with their new technology that the land was depleted. Wheat farming became uneconomic and tens of thousands of farmers left Wisconsin seeking new land with sod to bust. It took the Europeans and their new technology just one generation to make their homeland into a desert. The Sauk Indians who knew how to sustain themselves on the Sauk prairie land were banished to another kind of desert called a reservation. And they even forgot about the techniques and tools that had sustained them on the prairie for generations unrecorded. And that is how it was that three deserts were created-Wisconsin, the reservation and the memories of a people. A century later, the land of the Sauks is now populated by the children of a second wave of European farmers who learned to replenish the soil through the regenerative powers of dairying, ground cover crops and

animal manures. These third and fourth generation farmers and townspeople do not realise, however, that a new settler is coming soon with an invention as powerful as John Deere’s plow. The new technology is called ‘bereavement counselling’. It is a tool forged at the great state university, an innovative technique to meet the needs of those experiencing the death of a loved one, a tool that can “process” the grief of the people who now live on the Prairie of the Sauk. As one can imagine the final days of the village of the Sauk Indians before the arrival of the settlers with John Deere’s plow, one can also imagine these final days before the arrival of the first bereavement counsellor at Prairie du Sac. In these final days, the farmers and the town speople mourn at the death of a mother, brother, son or friend. The bereaved is joined by neighbours and kin. They meet grief together in lamentation, prayer and song. They call upon the words of the clergy and surround themselves in community. It is in these ways that they grieve and then go on with life. Through their mourning they are assured of the bonds between them and renewed in the knowledge that this death is a part of the Prairie of the Sauk. Their grief is common property, an anguish from which the community draws strength and gives the bereaved the courage to move ahead. It is into this prairie community that the bereavement counsellor arrives with the new grief technology. The counsellor calls the invention a service and assures the prairie folk of its effectiveness and superiority by invoking the name of the great university while displaying a diploma and certificate. At first, we can imagine that the local people will be puzzled by the bereavement counsellor’s claim. However, the counsellor will tell a few of them that the new technique is merely to assist the bereaved’s community at the time of death. To some other prairie flock who are isolated or forgotten, the counsellor will approach the County Board and advocate the right to treatment for these unfortunate souls. This right will be guaranteed by the Board’s decision to reimburse those too poor to pay for counselling services. There will be others, schooled to believe in the innovative new tools certified by universities and medical centres, who will seek out the bereavement counsellor by force of habit. And one of these people will tell a bereaved neighbour who is unschooled that unless his grief is processed by a counsellor, he will probably have major psychological problems in later life. Several people will begin to use the bereavement counsellor because, since tile County Board now taxes them to insure access to the technology, they will feel that to fail to be counselled is to waste their money, and to be denied a benefit, or even a right. Finally, one day, the aged father of a Sauk woman will die. And the next door neighbour will not drop by because he doesn’t want to interrupt the bereavement counsellor. The woman’s kin will stay home because they will have learned that only the bereavement counsellor knows how

Reading Comprehension 

to process grief the proper way. The local clergy will seek technical assistance from the bereavement counsellor to learn the correct form of service to deal with guilt and grief. And the grieving daughter will know that it is the bereavement counsellor who really cares for her because only the bereavement counsellor comes when death visets this family on the Prairie of the Sauk. It will be only one generation between the bereavement counsellor arrives and the community of mourners disappears. The counsellor’s new tool will cut through the social fabric, throwing aside kinship, care, neighbourly obligations and community ways of coming together and going on. Like John Deere’s plow, the tools of bereavement counselling will create a desert where a community once flourished. And finally, even the bereavement counsellor will see the impossibility of restoring hope in clients once they are genuinely alone with nothing but a service for consolation. In the inevitable failure of the service, the bereavement counsellor will find the deserts even in herself. 1. Which of the following best describes the approach of the author?

  2.41

2. She is working in an environment where the disappearance of community mourners makes her work place a social desert. 3. Her efforts at grief processing with the bereaved will fail as no amount of professional service can make up for the loss due to the disappearance of community mourners. 4. She has been working with people who have settled for a long time in the Great Desert. 4. According to the author, the bereavement counsellor is 1. a friend of the bereaved helping him or her handle grief. 2. an advocate of the right to treatment for the community. 3. a kin of the bereaved helping him/her handle grief. 4. a formally trained person helping the bereaved handle grief.

1. Comparing experiences with two innovations tried, in order to illustrate the failure of both.

5. The Prairie was a great puzzlement for the European pioneers because

2. Presenting community perspectives on two technologies which have had negative effects on people.

1. it was covered with thick, untillable layers of grass over a vast stretch.

3. Using the negative outcomes of one innovation to illustrate the likely outcomes of another innovation. 4. Contrasting two contexts separated in time, to illustrate how ‘deserts’ have arisen.

2. According to the passage, bereavement handling traditionally involves

2. it was a large desert immediately next to lush forests. 3.  it was rich cultivable land left fallow for centuries. 4.  it could be easily tilled with iron plows. 6. Which of the following does the ‘desert’ in the passage refer to? 1.  Prairie soil depleted by cultivation of wheat.

1. the community bereavement counsellors working with the bereaved to help him/her overcome grief.

2. Reservations in which native Indians were resettled.

2. the neighbours and kin joining the bereaved and meeting grief together in mourning and prayer.

3. Absence of, and emptiness in, community kinship and relationships.

3. using techniques developed systematically in formal institutions of learning, a trained counsellor helping the bereaved cope with grief.

4.  All of the above.

4. the Sauk Indian Chief leading the community with rituals and rites to help lessen the grief of the bereaved. 3. Due to which of the following reasons, according to the author, will the bereavement counsellor find the deserts even in herself ? 1. Over a period of time, working with Sauk Indians who have lost their kinship and relationships, she becomes one of them.

7. According to the author, people will begin to utilize the service of the bereavement counsellor because 1. new County regulations will make them feel it is a right, and if they don’t use it, it would be a loss. 2. the bereaved in the community would find her a helpful friend. 3. she will fight for subsistence allowance from the County Board for the poor among the bereaved. 4. grief processing needs tools certified by universities and medical centres.

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  Verbal and Logical Reasoning

8. Which one of the following parallels between the plow and bereavement counselling is not claimed by the author? 1.  Both are innovative technologies. 2. Both result in migration of the communities into which the innovations are introduced. 3. Both lead to ‘deserts’ in the space of only one generation. 4. Both are tools introduced by outsiders entering existing communities.

PASSAGE  II The teaching and transmission of North Indian classical music is, and long has been, achieved by largely oral means. The raga and its structure, the often breathtaking intricacies of tala or rhythm, and the incarnation of raga and tala as bandish or composition, are passed thus, between guru and shishya by word of mouth and direct demonstration, with no printed sheet of notated music, as it were, acting as a go-between. Saussure’s conception of language as a communication between addresser and addressee is given, in this model, a further instance, and a new, exotic complexity and glamour. These days, especially with the middle class having entered the domain of classical music and playing not a small part in ensuring the continuation of this ancient tradition, the tape recorder serves as a handy technological slave and prserves, from oblivion, the vanishing, elusive moment of oral transmission. Hoary gurus, too, have seen the advantage of this device, and increasingly use it as an aid to instructing their pupils; in place of the shawls and other traditional objects that used to pass from shishya to guru in the past, as a token of the regard of the former for the latter, it is not unusual, today, to see cassettes changing hands. Part of my education in North Indian classical music was conducted via this rather ugly but beneficial rectangle of plastic, which I carried with me to England when I was an undergraduate. One cassette had stored in it various talas played upon the tabla, at various tempos, by my music teacher’s brother-in-law, Hazarilalji, who was a teacher of Kathak dance, as well as a singer and a tabla player. This was a work of great patience and prescience, a one-and-ahalf hour performance without any immediate point or purpose, but intended for some delayed future moment when I’d practise the talas solitarily. This repeated playing out of the rhythmic cycles on the tabla was inflected by the noises-an irate auto driver blowing a horn; the sound of overbearing pigeons that were such a nuisance on the banister; even the cry of a kulfi seller in summer—entering from the balcony of the third floor flat we occupied in those days, in a lane in a Bombay suburb, before we left the city for good. These sounds, in turn,

would invade, hesitantly, the ebb and flow of silence inside the artificially heated room, in a borough of West London, in which I used to live as an undergraduate. There, in the trapped dust, silence and heat, the theka of the tabla, qualified by the imminent but intermittent presence of the Bombay suburb, would come to life again. A few years later, the tabla and, in the background, the pigeons and the itinerant kulfi seller, would inhabit a small graduate room in Oxford. The tape recorder, though, remains an extension of the oral transmission of music, rather than a replacement of it. And the oral transmission of North Indian classical music remains, almost uniquely, a testament to the fact that the human brain can absorb, remember and reproduce structures of great complexity and sophistication without the help of the hieroglyph or Written mark or a system of notation. I remember my surprise on discovering that Hazarilalji-who had mastered Kathak dance, tala and North Indian classical music, and who used to narrate to me, occasionally, compositions meant for dance that were grand and intricate in their verbal prosody, architecture and rhythmic complexitywas near illiterate and had barely learnt to write his name in large and clumsy letters. Of course, attempts have been made, throughout the 20th century, to formally codify and even notate this music, and institutions set up and degrees created, specifically to educate students in this “scientific” and codified manner. Paradoxically, however, this style of teaching has produced no noteworthy student or performer; the most creative musicians still emerge from the guru-shishya relationship, their understanding of music developed by oral communication. The fact that North Indian classical music emanates from, and has evolved through, oral culture, means that this music has a significantly different aesthetic, and that this aesthetic has a different politics, from that of Western classical music. A piece of music in the Western tradition, at least in its most characteristic and popular conception, originates in its composer, and the connection between the two, between composer and the piece of music, is relatively unambiguous precisely because the composer writes down, in notation, his composition, as a poet might write down and publish his poem. However far the printed sheet of notated music might travel thus from the composer, it still remains his property; and the notion of property remains at the heart of the Western conception of “genius”, which derives from the Latin gignere or ‘to beget’. The genius in Western classical music is, then, the originator, begetter and owner of his work-the printed, notated sheet testifying to his authority over his product and his power, not only of expression or imagination, but of origination. The conductor is a custodian and guardian of this property. Is it an accident that Mandelstam, in his notebooks, compares—celebratorily—the conductor’s baton to a policeman’s, saying all the music of the orchestra lies mute

Reading Comprehension 

within it, waiting for its first movement to release it into the auditorium? The raga transmitted through oral means is, in a sense, no one’s property; it is not easy to pin down its source, or to know exactly where its provenance or origin lies. Unlike the Western classical tradition, where the composer begets his piece, notates it and stamps it with his ownership and remains, in effect, larger than, or the father of, his work, in the North Indian classical tradition, the raga unconfined to a single incarnation, composer or performer remains necessarily greater than the artiste who invokes it. This leads to a very different politics of interpretation and valuation, to an aesthetic that privileges the evanescent moment of performance and invocation over the controlling authority of genius and the permanent record. It is a tradition, thus, that would appear to value the performer, as medium, more highly than the composer who presumes to originate what, effectively, cannot be originated in a single person because the raga is the inheritance of a culture. 9. The author’s contention that the notion of property lies at the heart of the Western conception of genius is best indicated by which one of the following? 1. The creative output of a genius is invariably written down and recorded. 2. The link between the creator and his output is unambiguous. 3. The word “genius” is derived from a Latin word which means “to beget.” 4. The music composer notates his music and thus becomes the “father” of a particular piece of music. 10. Saussure’s conception of language as a communication between addresser and addressee, according to the author, is exemplified by the 1. teaching of North Indian classical music by word of mouth and direct demonstration. 2. use of the recorded cassette as a transmission medium between the music teacher and the trainee. 3. written down notation sheets of musical compositions. 4.  conductor’s baton and the orchestra. 11. The author holds that the “rather ugly but beneficial rectangle of plastic” has proved to be a “handy technological slave” in 1. storing the talas played upon the tabla, at various tempos. 2.  ensuring the continuance of an ancient tradition.

  2.43

3. transporting North Indian classical music across geographical borders. 4.  capturing the transient moment of oral transmission. 12. The oral transmission of North Indian classical music is an almost unique testament of the 1.  efficacy of the guru-shishya tradition. 2.  learning impact of direct demonstration. 3. brain’s ability to reproduce complex structures without the help of written marks. 4. the ability of an illiterate person to narrate grand and intricate musical compositions. 13. According to the passage, in the North Indian classical tradition, the raga remains greater than the artiste who invokes it. This implies an aesthetic which 1. emphasises performance and invocation over the authority of genius and permanent record. 2.  makes the music no one’s property. 3. values the composer more highly than the performer. 4.  supports oral transmission of traditional music. 14. From the author’s explanation of the notion that in the Western tradition, music originates in its composer, which one of the following cannot be inferred? 1. It is easy to transfer a piece of Western classical music to a distant place. 2. The conductor in the Western tradition, as a custodian, can modify the music, since it ‘lies mute’ in his baton. 3. The authority of the Western classical music composer over his music product is unambiguous. 4. The power of the Western classical music composer extends to the expression of his music. 15. According to the author, the inadequacy of teaching North Indian classical music through a codified, notation based system is best illustrated by 1.  a loss of the structural beauty of the ragas. 2. a fusion of two opposing approaches creating mundane music. 3. the conversion of free-flowing ragas into stilted set pieces. 4. its failure to produce any noteworthy student or performer.

2.44 

  Verbal and Logical Reasoning

16. Which of the following statements best conveys the overall idea of the passage? 1. North Indian and Western classical music are structurally different. 2. Western music is the intellectual property of the genius while the North Indian raga is the inheritance of a culture. 3. Creation as well as performance are important in the North Indian classical tradition. 4. North Indian classical music is orally transmitted while Western classical music depends on written down notations.

PASSAGE  III Since the time of the ancient Greeks, sound had been an object of observation and speculation, and at least since early modernity sound has been explored experimentally: acoustical research investigated the motions of vibrating bodies and the supporting medium of sound. But neither acoustical nor music theory prior to the nineteenth-century conceived of sound as material. Instead music was thought to consist of “tonally moving forms” (Hanslick 1854) and the field of physical acoustics sought a formal description of sound waves. The theories of sound and music did not address what the ear discriminates as a matter of course: a note of the same pitch and volume played on a flute does not sound like that of an oboe. Developments in nineteenthcentury physiology contributed to an increasingly material conception of sound. With this an interdisciplinary form of research came into being that involved physics and instrument making, musicology, phonetics or ethnology. The functioning of the ear was recreated in laboratories: sounds were synthesized and new sound sources invented; music and its instruments were investigated to lay bare the implicit knowledge that was assumed to be hidden in compositions, theories of harmony or in musical instruments. This research was accompanied by a constant adjustment of a material culture of experiment to what could be heard as the materiality of sound. This includes the experiments and the standardization of instruments and measuring devices; it concerns the exchange between scientists and musicians, laboratories and workshops for musical and scientific instruments; it also comprises the invention of new sounds in music and the advent of electricity in the lab. All of this caused sound to be heard in new ways. The first part of the workshop will discuss how sound that was heard became a new scientific object. How did sound become material? What was the role of physiological experiments in this development? How do new sound objects emerge and how do sound objects take part in the emergence of new concepts in experimental research? What paths did this materiality of sound take through the various disciplines and research domains? And what transformations

occurred in the knowledge of sound? How do the histories of phonetics and musical instruments contribute to a history of sound? Concepts of sound, as they were understood in older music theory of acoustics, were independent of time. Time remained in a way external: Fourier-Analysis presupposes infinite waves, and the theories of harmony erected timeless architectures of sound relationships. In the 19th century, however, physiology and psychology shifted focus to the temporal nature of sound. Hearing was resolved into a series of processes of registration, transmission and transformation, which were then emulated and reenacted experimentally. Technical devices that could perform these functions served as a model in these processes, and at the same time new technologies of recording, broadcasting and reproduction of sound found their model in the ear. In the experiments, these technical devices filled the functions of hearing, while the physiology of the senses guided the construction of speaking machines and sound recording apparatus. The ephemeral sound was molded into a scientific object by the interplay of experimental science and media technologies. The “méthode graphique” or the “phonautograph” allowed repeated access to their recordings of fleeting sound events. Ensembles of sirens, resonators, the harmonium and tuning forks enabled the arbitrary production of well-defined sound. With the use of the phonograph and gramophone, sound became independent of its original context. The media technologies of recording transmission and transformation made a new phenomenality of sound audible. In sound there were tones and clangs, signals and noise, information and distortion, and the vibration of a sounding body was only one form of energy among others. The second part of the workshop will ask how the technologies and procedures of recording, transmission, and transformation of sound are brought into action in the laboratory. What is the role of symbolic code of music in this? And how did the new devices of sound registration and recording change the role of the symbolic code in music? To what extent did telecommunications engineering take the knowledge of hearing into account, for example, in the construction of hearing aids or loudspeakers? In what way do concepts of hearing take part in the development of new media technologies? How did laboratory experiments advance the emergence of techniques for the registration, transmission and reproduction of sound? And just how far does the mutual metaphorization of sense perception and media technology extend? Nineteenth-century physiology appropriated the history of music as a kind of prehistory of the physiological theory of hearing. Experimenters believed that the Western tonal system reflected the ear’s ability to analyze sound, that music theory and composition were both grounded in calculable processes of hearing, and that the history of music mirrored the physical laws of hearing. Some

Reading Comprehension 

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18. What was lacking in ancient studies of sound?

fundamental notions of musical aesthetics—consonance and dissonance, scales, triads and modes—apparently could be confirmed experimentally, and yet the postulated systematic connection between physiology and musical aesthetics did not hold. The experiments did not reveal a natural order in the system of music, but instead deciphered an arbitrary ordering in it. Nineteenth-century research on hearing could not provide a physiological foundation for musical aesthetics. Musical aesthetics did, however, heavily inform research on hearing. This can be seen in the choice of sound sources which were brought into action in the laboratory, it can be followed in the experimental set-ups that produced beats and combination tones, and finally in the wordings and choices of hypotheses that were tested experimentally. The third part of the workshop will investigate exchanges between music and the laboratory. How did experiments on hearing affect the teaching of music? In what sense did orchestral music experiment with sounds? What is the connection between the debate on tuning systems and temperaments and the beginnings of so called “authentic” performance? In this context, the importance of 19th-century experimental culture for a modern aesthetics of music will be considered: How did a new ideal of tone emerge from the attempt to produce a sound which does not belong to any aesthetic order, out of presumably ‘pure’ sinusoidal waves? Or, how could a single instrument, the siren, whose infinitely variable tone was supposed to demonstrate the validity of the tonal system, eventually abolish this very system?

1. They refused to believe sound was a material phenomenon. 2. They could not distinguish between volume and pitch. 3. They didn’t have electricity hence couldn’t video sound. 4. They couldn’t reproduce random sound events for study. 19. What caused sound to be “heard in new ways” after the 19th, century? 1. Sound was no longer considered ephemeral but temporal. 2. Sound was not merely confined to music. 3. Sound research became interdisciplinary. 4. Standardisation of instruments and measuring devices. 20. As per nineteenth century wisdom, which of the fol-

lowing best describes the relationship between sound and music.

1. There was no real connection between sound and music. 2.  Sound is random—music is structured. 3.  Music is aesthetic unlike new sound. 4. The history of music was a prelude to the physiology of hearing and sound.

17. What was the basic principle guiding the technologies and devices dealing with the propagation, registration and transmission of sound?

21. What finally triggered scientists to conclude that sound was a scientific and not an ephemeral phenomenon?

1. New concepts which postulated that sound was time dependent.

1. An interplay of experimental science and media technology development.

2. Principles of working of the human ear and the senses.

2. The fact that sound was connected to physiology of the ear.

3.  Sound was studied as part of music.

3.  Development of electricity. 4. Realization that music was not tonally moving forms.

ANSWER KEYS

4.  Experiments using devices that duplicated nature.

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1.

3

2.

2

3.

3

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4

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1

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4

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9.

3

10.

1

11.

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1

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1

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  Verbal and Logical Reasoning

  RC EXERCISE  5 Direction for questions 1 to 6:  Read the passage below and solve the questions based on it. There is absolutely no point in complaining that over the years, there has been pressure for increased productivity and higher earnings for workers in industry. There are several ways for increasing employees’ earnings. Employee earnings can be increased by raising the selling price of the firm’s products and services, reducing profits or costs of raw materials, or augmenting labour productivity. However, increasing employee earning by means other than increased labour productivity jeopardises the firm’s competitive strength in the market. Higher prices usually means fewer customers, reduced profit means less capital investment, and low-cost materials mean poor product quality. But increasing labour productivity by enhancing skills and motivation creates an almost unlimited resource. The development of economic reassures, human as well as nonhuman, is the product of human effort, and the quality of human effort in large part depends on human motivation. Enthusing employees with workaholic spirit through traditional authority and financial incentives has become increasingly difficult as employees become economically secure and their dependency on any one particular organization decreases. According to expectancy theorists, the motivation to work increases when an employee feels his performance is an instrument for obtaining desired rewards; Nevertheless, in many organisations today employees are entitled to organizational rewards just by being employed. Unions, governmental regulations, and the nature of the job itself in some cases prevent management from relating financial rewards to performance. People may be attracted to join and remain in organizations to receive organizational rewards, but being motivated to join an organization is not the same as being motivated to exert effort in an organization. The challenge to management is to find and administer alternative form of incentives which will induce employees to improve work performance. Such alternative forms of reinforcement will require increased understanding of motivational theories and programmes. 1. Which of the following statements is true in the context of the passage? 1. Development of economic resources is primarily the product of market conditions. 2. Earnings can be increased by lowering the selling price of products. 3. Employees can be best motivated by providing financial incentives. 4. All employees should be entitled to organizational rewards just by being employed. 5.  None of these

2. Organizations can derive maximum advantages by 1. providing financial incentives to employees regardless of performance. 2. enhancing labour productivity by increasing skills and motivation. 3. encourage employees to expend greater physical energy. 4. inducing employees to improve work performance and control their demands. 5.  strictly adhering to governmental regulations. 3. According to the passage, all of the following contribute to and increase in employee earnings except 1. increasing the selling price of the company’s products. 2.  reducing profits in favour of employees. 3.  providing incentives and fringe benefits to employees. 4.  enhancing labour productivity. 5.  increasing capital investment. 4. Choose the word which is most similar in meaning to the word ‘Induce’ as used in the passage. 1.  appreciate 2.  stimulate 3.  exhibit 4.  inflate 5. threaten 5. In the context of the passage, a company’s competitive strength in the market is affected mainly because of A.  a slump in the international market. B.  poor inter-departmental coordination. C.  decreased labour productivity. 1.  Only (A) 2.  Only (B) 4.  Both (B) and (C) 5.  None of these

3.  Only (C)

6. Which of the following words is most opposite in meaning to the word ‘jeopardizes’ as used in the passage? 1.  safeguards 4.  devalues

2.  endangers 5.  decrease

3.  projects

Direction for questions 7 to 12:  Read the passage  below and solve the questions based on it. Hiero, King of Syracus, had commissioned from a goldsmith of the town a crown of pure gold, but having taken delivery of the finished article, he was suspicious. There

Reading Comprehension 

was reason to believe that the craftsman had mixed with the gold a certain amount of other metal of inferior value. But how to find out? There was no direct evidence, and it was therefore obviously a case for the learned men of the city. And who more learned than Archimedes? The mathematician was therefore charged with the task which would now a day be considered a simple one, but was then a matter for serious thought. Nothing known to science could be brought forward to prove fraud or otherwise on the part of the goldsmith. It is more than probable that the human side of the problem interested Archimedes not at all, but the scientific puzzle worried him intensely. This worry pursued him everywhere he went for days, and persisted through the routine acts of his daily round. In the normal course of that routine, he went to the public baths. We can imagine him standing at the edge of bath tub as he prepares to enter, it, absently allowing the water to flow until he cannot help noticing it. Suddenly, he splashed out of his tub, shouting at the top of his voice: “Eureka! Eureka! (I have found it! I have found it!) Without waiting, or even thinking of such a detail as clothes, he tore out of the building and rushed through the streets of Syracuse, still shouting: “Eureka! Eureka!” Arrived at his house, the mathematician put his newly found discovery to a practical test, and found indeed that a body plunged in a fluid loses an amount of its weight which is equal to the weight of the fluid displaced by it. With this as a starting point—as it was to prove the starting point of many subsequent discoveries of importance—Archimedes was able to tell his king how much pure gold was in his crown. Thus was the first fundamental law in hydrostatics enunciated. 7. Why could the king not punish the fraudulent goldsmith? 1. By the time Archimedes had not discovered the law of hydrostatics. 2. The king did not have concrete evidence to prove the fraud. 3.  The finishing of the crown perfect but deceptive. 4.  The king had lot of faith in the goldsmith.

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4.  The finishing of the crown was not upto the mark 5.  None of these 9. Which of the following statements is definitely true in the context of the passage? 1. Archimedes’ action of running nude through public places was not taken lightly by the onlookers. 2. Archimedes’ eccentric actions used to create anguish among the public. 3. The goldsmith has mixed inferior quality metal in the crown. 4. Archimedes could prove that there was no impurity in the gold used by the goldsmith in the crown. 5. Archimedes was not a mathematician. 10. “Eureka! Eureka!” as spelt out by Archimedes was 1. an outburst of unreasonable pride of inventing a novel principle. 2. a spontaneous reaction of excitement due to a discovery. 3.  an immature expression of a half-baked idea. 4. an exhibition of encouragement for a useful discovery. 5.  None of these 11. What was the impact of Archimedes’ tremendous mental involvement in solving the king’s riddle? 1. He was worried but able to take care of his daily routine. 2. The involvement ultimately led to a failure in completing the assignment. 3. He was not able to think of the details of the problem entrusted to him. 4. Because of his involvement he forgot to put the discovery to a practical test. 5.  None of these

5.  None of these

12. Which of the following is false in the context of the passage?

8. What was the king’s suspicion?

A.  Archimedes’ father was not an astronomer.

1. The goldsmith had made a crown with some inferior metal instead of gold.

B. Before Archimedes’ discovery, science and limitation to detect the goldsmith’s fraud.

2. The craftsman had replaced god with a cheaper metal.

C. Archimedes discovered his principle while he was in the tub for bath.

3. The goldsmith had mixed a cheaper metal with gold in the crown.

1.  A and B 4.  A only

2.  B and C 5.  B only

3.  A and C

2.48 

  Verbal and Logical Reasoning

Direction for questions 13 to 18:  Read the passage below and solve the questions based on it. It is said that there is a dismal fall of standards everywhere. The leaders who are not equal to the task misguide their followers. The remedy of the malady that affects our political economic and social practices lies in the human individual. What is needed is a change in his nature. For that we should read great classics. Literature brings that change for the better. It improves the quality of human beings. Great books give great thoughts, broaden our outlook and awaken our souls. They also provide a moral base as the lack of discipline and Ideals in inimical to civilized value. There are various kinds of books. Some arouse or instruct while others elevate our nature. The first kind of books destroys our ego and gives us joy. Now joy is different from pleasure. The books which give joy contain emotions and thoughts recollected in tranquility. Only a seer can produce such books. They deserve not only to read but also to be digested. Through them we establish contract with the mastermind of the past. They had on to us our tradition. But maintaining a tradition does not mean peaking or doing as our forefathers did following a tradition blindly will render it dead and useless. We must make adaptations and bring modifications. However, the individual contribution is largely determined by the pressure brought to bear up on him by the new problems of the new age. There are three clearly marked features of the age in which we live. They are the scientific and technological revolution, the liberation of dependent countries in Asia and Africa and the growing unity of the world. We should read books which trace the history of the above mentioned three moments. The intellectual wealth of all mankind is at our disposal, we should break the barriers or language. Books build bridge between cultures, that is, they bring them together. They promote understanding and love and remove suspicion, fear and hatred. Great books to our help when our values are at the discount, many of us are mere shadows of human beings. We are the victims of contradictory impulses; we are a bundle of fear, suspicion, greed, jealousy as well as kindliness and goodwill. For creating a normal harmonious human society the former instincts should be curbed and the latter kindled, we must guard against corrupting the minds of our people with trivialities. A general spiritual awakening is essential. 13. What are three chief features of our age according to the passage? 1.  It is age of scientific and technological revolution. 2. Many countries in Asia and Africa have not freedom from dependence. 3. A sense of unity is growing among the different countries of the world.

14. What is the main argument of the passage? 1. We should think in terms of the welfare of humanity as a whole. 2. One should read good books and do the works relevant to one’s own welfare. 3. We should use scientific and technological know how in terms of our welfare. 4.  All of these 5. None of these 15. What distinction does the author make between joy and pleasure? 1. Pleasure is a spiritual state whereas joy is physical and intellectual. 2. Joy is a spiritual state whereas pleasure is physical and intellectual. 3. Pleasure is a sign of maturity and lasts longer than joy. 4. Pleasure sustains even in pain, but joy is thing only felt in pleasant situation. 5.  None of these 16. How can the nature of the individual be changed according to the passage? 1. If he reads great books, his outlook will be broad, his psychological health will improve and he will have moral contentment and spiritual Joy. 2. If he reads great books only his psychological health will improve. 3. If he reads great books, he will have only moral contentment and spiritual joy. 4.  Not given in the passage. 5.  None of these 17. What are the qualities of great classics, according to the passage? A.  They are impersonal and a source of joy. B. They contain emotions and thoughts recollected in tranquility. C. They are written by prophets and are best interpreters of our past. 1.  Only (A) and (B) 2.  Only (B) and (C) 3.  Only (A) and (C)

4.  All of these

4.  Only (A)

5.  None of these

5.  All (A), (B) and (C)

Reading Comprehension 

18. What does the author consider essential for creating a normal harmonious human society? A. We should control our emotions of fear, greed, suspicion and jealousy. B.  We should encourage kindliness. C. We should not engage our mind in petty and mean things. D. There should be a general spiritual awakening among us. 1.  Only (A) and (B) 2.  Only (A), (B) and (C) 3.  Only (B) and (D) 4.  Only (B), (C) and (D) 5.  All (A), (B), (C) and (D) Direction for questions 19 to 23:  Read the passage below and solve the questions based on it. We are well into the 21st century yet half the world’s population live in squatter settlement and work in shadow economies, which generate more than one-third of the developing world’ GDP. Slums are not caused by the poor but by government denying people the right to own and exchange property. When people own their own property they have incentives to invest time, money and energy to improve it because they know that they will be able to benefit from any such improvements, i.e., the ability to obtain mortgage etc. In short, property rights begets capital, which begets innovation, which begets wealth, Sadly, the poor typically don’t have secure title to their land as there are bureaucratic restrictions on transferring title or there is not clear system for titling. Without legal deeds they live in constant fear of being evicted by landlords or municipal officials. Illiteracy is a major reason poor people often choose not to seek the protection of local courts since in so many countries laws established under colonial rule have never been translated into local languages. When entrepreneurs to do set out to legally register business they are discouraged by red tape and costly fees. In Egypt, starting a bakery takes 500 days, compliance with 315 laws and 27 times the monthly minimum wage. The proprietors of such business cannot get loans, enforce contracts of expand a personal network of familiar customers and partners. As a result the poor have no choice but to accept insecurity and instability as a way of life. In India, there are severe restrictions on free transfer of property. In most rural areas inhibit investment and encourage urban flight. Planning policies however discourage building homes for these migrants as numerous homes are destroyed if they do not comply with planning rules, essentially forcing people to live in slums and perversely blaming it on population growth. UN Habitat, the UN agency for housing the poor,

  2.49

has implemented more plans to stabilize the unplanned aspects of urban growth but grandiose plans like UN Schemes and government housing projects simply ignore or worsen the underlying problems. It is when governments grant people legal means to control their assets that they empower them to invest and plan ahead. In Buenos Aires, economists studied the experience of two Argentine communities. One had received legal title to its land in the 1980s and surpassed i.e., other group which had not, in a range of social indicators including quality of house construction and education levels. The Commission on Legal Empowerment of the Poor—a UN affiliated initiative made up two dozen leaders—is exploring leas to extend enforceable legal rights to impoverished members of society and is seeking to bring about a consensus on incentives for national and local leaders. As the growth of illegal settlement amply demonstrates, the poor are not helpless; all they need is government to grant them fundamental human rights of freedom and responsibility. 19. What did the Argentina study indicate? A. Argentina’s economy is booming and the percentage of poor has fallen. B. When the government gives people the legal means to control their assets they plan for the future. C. Government succeeded in widening the gap between the rich and the poor. 1.  Only A 2.  Both A and B 3.  Only B 4.  A, B and C 5.  None of these 20. According to the author, which of the following factors is responsible for the creation of a slum? 1.  Migration of landless labourers to cities 2. Municipal authorities building low-housing for the poor 3.  Unchecked population growth 4. Government failure to secure property rights for citizens 5.  Exorbitant cost of living in cities 21. The author’s main objectives in writing passage is to 1. exhort the UN to play a greater role in rehabilitating slum-dwellers. 2. praise government initiatives for migrant slumdwellers. 3.  convince governments to empower the poor.

2.50 

  Verbal and Logical Reasoning

4. enlist the aid of developed countries to tackle the is sue of slums. 5. chastise slum-dwellers for illegal activities that they engage in.

23. Which of the following is TRUE in the context of the passage?

22. What benefit does the author see in providing land ownership rights to the poor?

2. Although the government allocates land for them the poor choose not to invest in building houses.

1.  Steady increase in GDP 2.  Gaining independence from colonial rulers

3. With the spread of slums populations are drifting back to rural area.

3. Municipal services afforded to the poor will improve.

4. In order to accumulate profit slum-dwellers avoid legally registering their business.

4.  It will be an inheritance for future generations.

5. UN has declared the right to housing as a fundamental right.

1. Additional UN projects will exacerbate the plight of slum-dwellers.

ANSWER KEYS

5.  None of these

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Ans.

Q.

Ans.

1.

5

2.

2

3.

5

4.

2

5.

3

6.

1

7.

2

8.

3

9.

4

10.

2

11.

5

12.

4

13.

4

14.

1

15.

2

16.

1

17.

5

18.

5

19.

3

20.

4

21.

3

22.

5

23.

2

HINTS AND EXPLANATIONS 4. The meaning of the word Induce (Verb) as used in the passage is : to persuade or influence somebody to do something. 6. The meaning of the word Jeopardise (Verb) as used in the passage is: to risk harming or destroying something/somebody; endanger

Look at the sentences: The new card will safeguard the company against fraud. The leaflet explains how to safeguard against dangers in the home. Hence, the words jeopardises and safeguards are antonymous.

c h a p t e r

 2

English Usage

1. English grammar 2. Vocabulary

•  Antonyms



•  Synonyms



•  Fill in the blanks—Single and multiple



•  Analogies

3. Modifiers 4. Sentence Arrangement 5. Critical Reasoning 6. Fact—Inference—Judgement 7. Best Summary 8. Paragraph Completion

2.52 

  Verbal and Logical Reasoning

ENGLISH GRAMMAR English grammar can be divided into 2 broad categories:

GRAMMAR Theoretical

Applied

When we talk of the CAT, it is the application of the grammar that is of relevance. The kind of questions that are asked are tricky so one needs to be clear with the fundamentals. In this chapter, we shall discuss the latest rules of British grammar in as much detail as relevant to the CAT. The examples given will make the application clear. For the last couple of years, in the CAT, the English Usage chapter (composition as given in this book) comprise almost half of the English section. Therefore, the time given to the preparation of EU portion should be in proportion. In this chapter, we are going to discuss: 1. Parts of speech 2. Tenses

5. Plural Noun forms

1.  Parts of speech

Verb

action or state

Noun

thing or person

Adjective

describes a noun

Adverb

describes a verb, adjective or adverb

Preposi- links a noun to another tion word joins clauses Conjunction or sentences or words Interjec- short exclamation, tion sometimes inserted into a sentence

to, at, after, on, but and, but, when oh!, ouch!, hi!, well

Mr D Singh is our director. He is clever. He went to movie on Monday. I like dogs and I like cats. Hi! How are you?

Let us see some of these one by one

Noun A noun is a word used to name a person, animal, place, thing, and abstract idea. A noun can function in a sentence as a subject, a direct object, an indirect object, a subject complement, an object complement, an adjective or an adverb.

Many common nouns, like “engineer” or “teacher,” can refer to men or women. Once, many English nouns would change form depending on their gender. For example, a man was called an “author” while a woman was called an “authoress”—but this use of gender-specific nouns is very rare today. Those that are still used occasionally tend to refer to occupational categories.

4. Articles

Function

I, you, he, she, some

Noun Gender

3. Subject Verb agreement

Parts of speech

Pronoun replaces a noun

Examples

Usage

(to) be, have, do, I like pizzas. like, work, sing, can, must pen, dog, work, Rohan lives music, town, in my house. London, teacher, John a/an, the, some, My cat is big. good, big, red, well, interesting quickly, silently, He eats well, badly, very, quickly. really

Noun Plurals Most nouns change their form to indicate number by adding “-s” or “-es in good number of cases. Other nouns form the plural irregularly. For example, plural of ox is oxen. We’ll discuss more about plurals in the next pages of this chapter.

Possessive Nouns In the possessive case, a noun or pronoun changes its form to show that it owns or is closely related to something else. Usually, nouns become possessive by adding a combination of an apostrophe and the letter “s”. Possessive case of a singular noun that does not end in “s” can be made by adding an apostrophe and “s”. Possessive case of a singular noun that ends in “s” can be made by adding an apostrophe alone.

English Usage  Possessive case of a plural noun that does not end in “s” can be made by adding an apostrophe and a “s”. Possessive case of a plural noun that does end in “s” can be made by adding an apostrophe.

Types of Nouns Proper Nouns

Proper noun represents the name of a specific person, place, or thing. The names of days of the week, months, historical documents, institutions, organizations, religions, their holy texts and their adherents are proper nouns. A proper noun can be seen as the opposite of a common noun. A proper noun is written with a capital letter. Example, Saturday, May, Oxford University, Islam etc.,

Common Nouns A common noun is a noun referring to a person, place, or thing in a general sense. A common noun can be seen as the opposite of a proper noun. Example, Man, hotel, chair etc.,

members of the group, but usually group is seen as a whole and generally as one unit. It is important to be able to recognize collective nouns in order to maintain subject-verb agreement. A collective noun is similar to a non-countable noun, and is roughly the opposite of a countable noun. Example, army, class, crew, jury, family etc.

Pronoun Pronouns are words used in place of noun or other pronoun. Pronouns like “he,” “which,” “none,” and “you” are used to make sentences less cumbersome and less repetitive. Grammarians classify pronouns into several types, including the personal pronoun, the demonstrative pronoun, the interrogative pronoun, the indefinite pronoun, the relative pronoun, the reflexive pronoun, and the intensive pronoun.

Personal Pronouns A personal pronoun refers to a specific person or thing and changes its form to indicate person, number, gender. Various ways in which they are used are illustrated below.

Concrete Nouns A concrete noun refers to objects and substances, including people and animals, physical items that we can perceive through our senses, that mean concrete nouns can be touched, felt, held, something visible, smelt, taste, or be heard. A concrete noun is the opposite of abstract noun. Example, desk, cake, water etc.

  2.53

 

 

1st person

Singular I teach Divya

Divya teaches me

Plural

Divya teaches us

2nd person

Singular You teach Divya

Divya teaches you

Plural

You teach Divya

Divya teaches you

An abstract noun is a noun which names anything which can not perceive through five physical senses. It is opposite of a concrete noun. Example, happiness, knowledge, kindness etc.

3rd person

Singular

He/She/It teaches Divya teaches Divya him/her/it

Plural

They teach Divya Divya teaches them

Countable Nouns

It is to be noted that ‘IT’ is an impersonal pronoun and is used for the following:

Abstract Nouns

A countable noun is a noun with both a singular and a plural form, and it names anything (or anyone) that can be counted. A countable noun can be made plural. Countable nouns are the opposite of non-countable nouns and collective nouns. Example, pens, bottles, trees, men etc.

Non-Countable Nouns A non-countable noun (or mass noun) is a noun which does not have a plural form, and which refers to something that could (or would) not be usually counted. A noncountable noun always takes a singular verb in a sentence. Non-countable nouns are similar to collective nouns, and are the opposite of countable nouns. Example, furniture hair, coffee, ink etc.

Collective Nouns A collective noun is a noun naming a group of things, animals, or persons. One can count the individual

Subjective We teach Divya

Objective

a. Inanimate objects b. Animals without name c. Babies without name d. Human beings (when the gender is not clear). Subjective Personal Pronouns

Objective Personal Pronouns

Possessive

Indicates that the pronoun is acting as the subject of the sentence.

Indicates that the pronoun is acting as an object of a verb, or preposition.

Indicates that the pronoun is acting as who owns a particular object or person.

“I,” “you,” “she,” “he,” “it,” “we,” “you,” “they.”

“Me,” “you,” “her,” “him,” “it,” “us,” “you,” and “them.”

“Mine,” “yours,” “hers,” “his,” “its,” “ours,” and “theirs.”

Personal Pronouns

2.54 

  Verbal and Logical Reasoning

Demonstrative Pronouns

Errors in Pronouns

A demonstrative pronoun points to and identifies a noun or a pronoun. “This” and “these” refer to things that are nearby either in space or in time, while “that” and “those” refer to things that are farther away in space or time.

1. Aditi bought an eclair and a pastry and she ate it quickly. [What does this ‘it’ refer to]. This is pronoun-antecedent (the noun for which we use pronoun) ambiguity. 2. As people age, the concern a person has change as well. This is pronoun-antecedent inconsistency. 3. Nitika was surprised that despite working hard he did not get a promotion. Pronoun must agree with its antecedent in number and gender.

The demonstrative pronouns are “this,” “that,” “these,” and “those.” “This” and “that” are used to refer to singular nouns and “these” and “those” are used to refer to plural nouns. It is also important to note that “that” can also be used as a relative pronoun.

Interrogative Pronouns An interrogative pronoun is used to ask questions. The interrogative pronouns are “who,” “whom,” “which,” “what” and the compounds formed with the suffix “ever” (“whoever,” “whomever,” “whichever,” and “whatever”). Note that “who,” “whom,” or “which” can also be used as a relative pronoun. “Who,” “whom,” and occasionally “which” are used to refer to people, and “which” and “what” are used to refer to things and to animals. “Who” acts as the subject of a verb, while “whom” acts as the object of a verb,

Relative Pronouns A relative pronoun is used to link one phrase or clause to another phrase or clause. The relative pronouns are “who,” “whom,” “that,” and “which”. Compounds formed with the suffix “ever” (“whoever,” “whomever,” “whichever,” are also relative pronouns.

Indefinite Pronouns An indefinite pronoun is a pronoun referring to an identifiable but not specified person or thing. An indefinite pronoun conveys the idea of all, any, none, or some. Commonly used indefinite pronouns are “all,” “another,” “any,” “anybody,” “anyone,” “anything,” “each,” “everybody,” “everyone,” “everything,” “few,” “many,” “nobody,” “none,” “one,” “several,” “some,” “somebody,” and “someone.”

Reflexive Pronouns A reflexive pronoun refers back to the subject of the clause or sentence. Reflexive pronouns are “myself,” “yourself,” “herself,” “himself,” “itself,” “ourselves,” “yourselves,” and “themselves.”

Verb A verb or compound verb express actions, events, or states of being. The verb or compound verb is the critical element of the predicate of a sentence.

Example Monster bites his victims on the neck. The verb “bites” describes the action monster takes. I will marry in 2010. Here the compound verb “will marry” describes an action that will take place in the future. Kapil Dev played in 3 world cups, but his diaries were destroyed. In this sentence, the compound verb “were destroyed” describes an action which took place in the past.

Adverb An adverb can modify a verb, an adjective. An adverb indicates manner, time, place, cause, or degree and tries to answer questions such as “how,” “when,” “where,” “how much”. Some adverbs are easily identifiable by their characteristic “ly” suffix; others are required to be identified by untangling the grammatical relationships within the sentence as a whole. Example, (1) Dennis is thinking quietly. (2) The ball is rolling slowly. In the above examples, ‘quietly’ and ‘slowly’ are the adverbs qualifying the verbs ‘thinking’ and ‘rolling’ respectively. (3) Nayani is wearing a bright red shirt. Here ‘bright’ is an adverb qualifying the adjective ‘red’.

Conjunctive Adverbs A conjunctive adverb joins two clauses together. Some of the most commonly used conjunctive adverbs are “consequently,” “finally,” “furthermore,” “hence,” “however,” “incidentally,” “likewise,” “meanwhile,” “nevertheless,” “next,” “nonetheless,” “otherwise,”” “then,” “therefore,” and “thus.”

English Usage  However, a conjunctive adverb is not strong enough to join two independent clauses without the aid of a semicolon.

Adjective An adjective describes, identifies, or quantifies a noun or a pronoun. An adjective usually precedes the noun or the pronoun which it modifies. Example, There goes a tall man. ‘Tall’ is an adjective describing the noun ‘man’.

Possessive Adjectives A possessive adjective (‘‘my,’’ ‘‘your,’’ ‘‘is,’’ ‘‘her,’’ ‘‘its,’’ ‘‘our,’’ ‘‘their’’) is similar to a possessive pronoun.

Demonstrative Adjectives The demonstrative adjectives ‘‘this,’’ ‘‘these,’’ ‘‘that,’’ ‘‘those,’’ and ‘‘what’’ are identical to the demonstrative pronouns.

Preposition A preposition connects nouns, pronouns and phrases to other words in a sentence. They show the position of a subject with its object. noun (s) and pronouns (s) Example—The book is on the table. The book is beneath the table. The book is leaning against the table.

  2.55

However, between may be used for more than two persons or things in order to bring each person or thing into the relation expressed. a. While packing these glass sheets, be sure to place paper between them. b. The funds were distributed between SriLanka, China, Pakistan and India. 3. At/in Both at and in are used in reference to places. Mostly in is used for larger places and at for smaller places. He lives at Patel nagar in Patna. He lives in Delhi. 4. In/into/in to In implies the position within and into implies motion within to within from one medium to another. In to is a two word phrase in which in is an adverb. The correspondence is in the file. He walked into my office/He jumped into the pool. Varun came in to see me. 5. Besides, besides Besides means in addition to; beside means by the side of.

The book is beside the table.

Beside, we also require your support for this movement.

He is at the theatre

I sat beside river Nile.

Some of the usage of prepositions are given below:

Besides being fined, he was also jailed.

1. All, of

6. On/upon/up on

Do not use of after all, unless the next word is a pronoun.

Both on and upon are interchangeable, although upon is a little more formal and emphatic. In the two word phrase up on, on is an adverb.

All the men belong to the club. All of us belong to the Club. All of us boys belong to H10. 2. Among/between Among always implies more than two; between literally implies two. Between, however, is now often used for three or more items, when each is regarded individually. The teachers distributed the sweets among the students. (more than two)

Please place the book on the table. His statements were based upon the scientific data. It will be necessary to step up on the school. 7. Some word like senior, junior, prefer, prior, superior, inferior, etc., are followed by to and not than. He was senior to me in college. Health is more preferable to wealth. This cloth is inferior to that cloth.

Distribute these sweets among the workers. (more than two)

8. Certain words are used in gerund (first form of a verb followed by-ing) along with prepositions.

The election commission is divided evenly between the two partners. (only two persons)

For example, abstain, confident, fond, insist, keen, persist, prohibit, refrain, succeed etc.

2.56 

  Verbal and Logical Reasoning

I prohibited him from parking his car near the entrance. (and not “to park”)

10. Certain words are followed by different preposition in different contexts. For example:

She is confident of speaking English within six months. (and not ‘‘to speak”)

I agree with Mr Saxena.

I abstain from drinking on Tuesday. (and not “to drink”) He worked hard and succeeded in securing good marks. (and not “to secure”)

In the above example, the word ‘agree’ is used with two different prepositions, with and to. ‘Agree with’ is used for agreement with a person, whereas ‘agree to’ is used for agreement to a plan, or proposal.

9. Certain words are used in gerund without a preposition if followed by the first form of a verb. For example, avoid, enjoy, help, dislike, help, stop, remember etc.

11. Prepositions of Time: at, on, and in

I agree to your proposal.

Similarly, we angry ‘with’ a person, however we angry ‘at’ something.

He enjoys playing cards. (and not “to play’’)

We use at to designate specific times.

Stop writing as the time is over. (and not “to stop”)

■  The train is due at 2.15 am.

I dislike playing with Raman. (and not “to play”)

We use on to designate days and dates.

Many people avoid drinking before their superiors. (and not “to drink’’)

■  Hari is coming on Monday. ■  We’re going to Mussorrie on 15th August.

Tenses  

Past Tense

Present Tense

Future Tense

Simple Form

I walked

I walk

I will walk

Continuous Form

I was walking

I am walking

I will be walking

Perfect Form

I had walked

I have walked

I will have walked

Perfect Continuous Form

I had been walking

I have been walking

I will have been walking

Subject–Verb Agreement A sentence has the following properties: it contains a subject it contains a verb it expresses a complete thought

E.g., the sentence “Japan prospers” has a subject: “Japan”; a verb: “prospers”; and it conveys a complete thought or idea that makes sense. Most sentences also have an object (receiver of the action); example, in the sentence “Ram ate a Mango,” the object is “mango.” According to the concept, the verb in a sentence should be in agreement with the subject.

Common rules and errors Rule 1:  The verb in a sentence should agree with the subject. If a subject is singular, verb should also be singular. And if the subject is plural, verb should also be plural. Let us see some of the examples:

English Usage 

  2.57

Incorrect usage

Correct usage

Explanation

There is no rooms vacant.

There are no rooms vacant.

The subject rooms is plural; therefore, the verb should be plural (i.e., are).

He like movies.

He likes movies.

The subject he is in the second person, and is singular; therefore, the verb should also be in the second person, and be singular (i.e.likes).

Neither Raman nor Harsh were there.

Neither Raman nor Harsh was there.

“Harsh” is singular, so the verb should be also.

Neither Raman nor the others was there.

Neither Raman nor the others were there.

“Others” is plural, so the verb should be also.

There are a variety of pens.

There is a variety of pens.

“Variety” is singular.

Here is wealth and beauty.

Here are wealth and beauty.

“Wealth and beauty” is plural.

He is one of the best officers who has graduated from here.

He is one of the best officers who have graduated from here.

“Doctors” is plural, so the verb should be also (i.e. “have”).

All of the team were there.

All of the team was there.

“Team” is singular, so the verb should be also.

All the players was present.

All the players were present.

“Players” is plural, so the verb should be also.

Rule 2:  Pronouns should agree with their nouns in terms of (a) number (singular or plural), (b) person (first, second, or third), and (c) gender . Incorrect usage

Correct usage

Explanation

Did everyone remember their job?

Did everyone remember his job?

Everyone is singular, so the pronoun should as well be singular.

It was them who did it.

It was they who did it.

The nominative case (I, you, he, she, it, we, you, they, who) is used following some form of the verb to be.

If I were him, I would go.

If I were he, I would go.

As above.

It is me.

It is I.

As above.

Whom will rule country?

Who will rule country?

Who did you give it to?

Whom did you give it to?

“You gave it to he” does not sound right, while “you gave it to him” does.

He was in the same school as us.

He was in the same school as we.

Expand the sentence: “He was in the same school as we were in.”

It belongs to he and I.

It belongs to him and me.

The objective case of pronoun (i.e., me, you, him, her, it, us, you, them, whom) is used as the object of a preposition, such as “to”.

Sama hired he.

Sama hired him.

The objective case of pronoun (i.e., me, you, him, her, it, us, you, them, whom) is used as the object of a verb.

He is as busy as me.

He is as busy as I.

Expand the sentence: “He is as busy as I am busy, not “he is as busy as me am busy.”

2.58 

  Verbal and Logical Reasoning

However, there are following exceptions and expansions to this basic rule. Exception 1 The rule is not applicable to the sentences in the past and future tense. It means agreement  applies only when the sentence is in present tense. Example 1(a)  He drove to Gurgaon yesterday. (Past tense) 1(b)  They drove to Gurgaon yesterday. (Past tense) It can be seen that the subject is singular in 1(a) and plural in 1(b), however the verb used in each case in same.



(b) Aerobics provides receration. (other example. athletics, olympics, etc.) (c) Mathematics is an interesting subject. (other example. politics, civics, etc.)

2. Period of time, sum of money and unit of distance is singular. Example   (a)  One lac rupee is a big amount. (b)  Five km is a long distance to be covered by foot. (c)  Two hours is a long time to wait.

2(a)  They will go to watch a movie. (Future tense)

Hundred Rupees is kept on the table – Here hundred rupees is a sum of rupees.

(b)  He will go to watch a movie. (Future tense)

Let us look at another example

It can be seen that the subject is singular in 2(b) and plural in 2(a), however the verb used in each case in same.



(a) Rupees are deteriorating. This is also correct because we are not talking about ‘a sum of rupee’, but of rupees in holistic sense.



(b)  Dollars are inferior to pounds in value.

Exception 2 No distinction is made in 1st person singular and 1st person plural. Example 1(a) I pray everyday 1(b) We pray everyday. Exception 3 Case of I and You – I and You both take a verb “don’t”(which is plural in nature) and not “doesn’t” (which is singular in nature). Example 1(a) I don’t smoke. 1(b) You don’t smoke. However, with ‘He’, which is 3rd person singular, “doesn’t” is used. 1(c ) He doesn’t smoke. Expansion 1 When two nouns or pronouns are joined with words like ‘including, as well as along with, together with, except’ etc then verb agrees to the first subject. Example (a) Sam along with his family members is going. (b) My teachers and my best friend is invited to my wedding party. Case 1  There are some nouns that might appear plural but they are actually singular, and hence verb should be used accordingly. 1. Names of diseases, sports and field of study. Example  (a) Diabetes is a common disease. (other Example, mumps, arthiritis, etc.)

Expansion 2 Collective nouns are considered singular (for example–team, family etc.) and they take singular verb. However, nouns of magnitude take plural verb. Example 1(a)  The jury was unanimous in its decision. 1(b) The jury were divided in their decision. (because it shows division.) Expansion 3 When subject contains both singular and plural noun tied by or/not, the verb should agree with the part of the subject nearer to it. Example He or his friends have done it. Has he or his friends done it? Expansion 4 When the subject of a sentence is composed of two or more nouns connected by and, we use a plural verb. Example (a)  The principal and the secretary are out of town. (b)  The principle and secretary is out of town. [Here, the absence of an article ‘the’ before ‘secretary’ tells us that it is only one person acting as a principal and secretary]

English Usage  Expansion 5 Each, each one, either, neither, everyone, everybody, anybody, nobody, somebody, someone and no one are singular and require a singular verb. Example (a)  Everybody is invited. (b)  Somebody is there. Expansion 6  When a subject consisting of two singular nouns connected by ‘and’ refers to the same idea or outcome, a singular verb is used. Example Bread and butter is what I eat. Time and tide waits for none.

Articles The three articles—a, an, the—are a kind of adjective.

Use of A and An A and An are called indefinite articles because they are used to refer to something in a less specific manner (an unspecified count noun). We use a before singular count-nouns that begins with consonants (a cow, a barn, a sheep); we use an before singular count-nouns that begin with vowels or vowel-like sounds (an apple, an urban blight, an open door). Words that begin with an h sound often require an a (as in a horse, a history book, a hotel), but if an h-word begins with an actual vowel sound, use an an (as in an hour, an honor). Examples—a useful device, a university, a European [u of these words actually sounds like yoo unlike to the u of an ugly incident). a once-in-a-lifetime experience, a one-time hero [the words once and one begin with a w sound as if they were spelled].

  2.59

• more than one snake - snakes • more than one boy - boys

1. Words that end in -ch, x, s or s-like sounds, however, will require an -es for the plural • more than one witch—witches • more than one box—boxes • more than one gas—gases • more than one bus—buses • more than one kiss—kisses Please note that some dictionaries list “busses” as an acceptable plural for “bus.” 2. There are several nouns that have irregular plural forms. Plurals formed in this way are sometimes called mutated (or mutating) plurals. Some of the examples are given below: • more than one child—children • more than one woman—women • more than one man—men • more than one person—people • more than one goose—geese • more than one mouse—mice • more than one ox—oxen 3. There are nouns that maintain their Latin or Greek form in the plural. • more than one nucleus—nuclei • more than one syllabus—syllabi • more than one focus—foci • more than one fungus—fungi • more than one thesis—theses • more than one phenomenon—phenomena

Use of ‘The’

• more than one index—indices (indexes is acceptable)

The is called the definite article because it usually precedes a specific or previously mentioned noun.

• more than one criterion—criteria

The is used with specific nouns. The is required when the noun it refers to represents something that is one of a kind The moon circles the earth.

4. A handful of nouns appear to be plural in form but take a singular verb: • The news is bad. • Gymnastics is fun to watch.

The is required when the noun it refers to represents something named earlier in the text.

• Economics/mathematics/statistics is said to be difficult. ("Economics" can sometimes be a plural concept, as in "The economics of the situation demand that . . . .")

Plural Noun Forms

5. Numerical expressions are usually singular, but can be plural if the individuals within a numerical group are acting individually:

The plural form of most nouns is created simply by adding the letter s.

2.60 

  Verbal and Logical Reasoning

• Fifty thousand dollars is a lot of money. • One-half of the faculty is retiring this summer. • Fifty per cent of the students have voted already. 6. Another set of nouns might seem to be singular in nature but take a plural form and always use a plural verb: A. •  Her scissors were stolen.

  PARALLEL STRUCTURES In parallel structures or parallelism different parts of a sentence should be in symmetry. The symmetrical order is maintained in a sentence by using the same verb form, same tense and other parts of speech should also be same, like noun or adjective. Consider the sentences below: 1. I like to play guitar and singing. (Incorrect)

•  The glasses have slipped down his nose again.

I like playing guitar and singing. (Correct)

• Other examples include tongs, spectacles, trousers, shears, phiers, shoes, pants.

2. Mansi likes to watch televisition, ice-creams and carrom. (Incorrect)

  (They are always plural unless preceded by ‘a pair of’)

Mansi likes to watch television, eat ice creams and play carrom. (Correct)

B. The use of adjectives as noun.

3. The idea is fantastic but a danger . (Incorrect)

•  The rich are arrogant.

The idea is fantastic but dangerous. (Correct)

•  The intelligent are blessed.

The concept of parallel structures is very important in the english usage section and sometimes two to three options can be eliminated because they don’t follow a parallel structure in a sentence. If you see a window in a room of which one pane is painted and the other is not. This will look non-symmetrical and to make it look symmetrical you would want to paint the other pane also. This is exactly what parallelism in language does, it makes the structure symmetrical!

7. There is a category of nouns that do not change in form. Example—cattle, sheep, police, poultry, gentry, vermin etc.,

•  The police are running after a criminal.



•  Cattle are grazing in the field.

English Usage 

  2.61

  PRACTICE EXERCISE  1 Direction for questions 1 to 10:  Each of following questions are divided into sections. Choose the section/s that has/have grammatical error.

8. A.  Whenever I felt low

1. A.  As a writer he has written B.  a short story

1.  b 3.  c

C.  A poem that is an epic

9. A.  The service at the restaurant was pathetic.

D.  and a tragic play.

B.  They served tea that was cold and

1.  b 3.  c

2.  a and d 4.  a and c

2. A.  Despite hours of deliberation B.  the jury was divided C.  over the matter. 1.  a 3.  c

2.  b 4.  b and c

3. A.  Given the shortage of time B.  The team was unable C.  To discuss the matter completely. 1.  c 3.  b

2.  c and a 4.  b and c

4. A.  It was me who supported him during crisis

B.  my friend and benefactor C.  were always there to cheer me up. 2.  a 4.  a and b

C.  hot ice cream. 1.  b and c 3.  a

2.  b 4.  b or c

10. A.  When I was in college B.  I have been a part of the dramatics team C.  but I am completely out of touch these days. 1.  a 3.  b

2.  c 4.  a, b, c

Direction for questions 11 to 20:  Choose the most appropriate way to express the following sentences. 11. 1.  For years he and me have been best friends. 2.  For years him and me have been best friends. 3.  For year I and he have been best friends.

B.  and gave him the strength

4.  For years he and I have been best friends.

C.  to strike back.

12. 1.  Rita is elder than her.

1.  a 3.  c

2.  b 4.  a and c

2.  Rita is older than she. 3.  Rita is elder than her. 4.  Rita is elder than she is.

5. A.  A city which

13. 1.  I am going to go for a movie tonight.

B.  is set on a hill C.  cannot be hidden.

2.  I am going for a movie tonight.

1.  c 3.  a and b

4.  Tonight I am going for a movie.

2.  a 4.  b

6. A.  She lives at house no. 32 B.  at park avenue 2.  b and a 4.  c

7. A.  Despite his sincere efforts B.  his knowledge of Indian Vernaculars C.  were not good. 1.  a 3.  a and c

14. 1.  The policemen, not the thief are to be blamed. 2.  The policemen are to be blamed not the thief. 3.  The policemen, not the thief is to be blamed.

C.  at New York city. 1.  a and c 3.  b and c

3.  I am tonight going for a movie.

2.  c 4.  b

4.  The policemen is to be blamed and not the thief. 15. 1.  The store sold inflatable children’s toys. 2.  The store inflatably sold children’s toys. 3.  The store sold inflatable toys for children. 4.  The children’s store sold inflatable toys. 16. 1.  Everybody in this room is attending the party. 2.  Everybody in this room are attending the party.

2.62 

  Verbal and Logical Reasoning

3.  In this room, everybody is attending the party. 4.  In this room, everybody are attending the party.

2. The old friends caught in on each other during the journey.

17. 1.  Since adolescence he is courting me. 2.  Since adolescence he was courting me. 3.  Since adolescence he has been courting me. 4.  Since adolescence he had been courting me.

4. The old friends caught down on each other during the journey.

18. 1.  I see the Taj Mahal jogging every morning. 2.  Every morning I see the Taj Mahal jogging. 3.  I see the Taj Mahal every morning while jogging. 4.  While jogging every morning, I see the Taj Mahal. 19. 1.  I have promised that this will be between she and I. 2.  I have promised that this will be between her and I. 3.  I have promised that this will be between she and me. 4.  I have promised that this will be between her and me. 2 0. 1.  The captain, along with his players is going to play. 2.  The captain, along with his players are going to play. 3.  The captain is going to play along with his players. 4.  The captain are going to play along with his players. Direction for questions 21 to 30:  Choose the sentence that best expresses the idea. 21. 1.  She backed out at the last minute. 2.  She broke out at the last minute. 3.  She bowed out at the last minute. 4.  She bloomed out at the last minute. 2 2. 1.  The car broke in during the journey. 2.  The car blew out during the journey. 3.  The car broke down during the journey. 4.  The car backed up during the journey.

3. The old friends caught up on each other during the journey.

26. 1. Her putting the blame on us for the chaos was a classic case of the pot calling the kettle black. 2. Her putting the blame on us for the chaos was a classic case of the pan falling into the fire. 3. Her putting the blame on us for the chaos was a classic case of the bucket getting kicked. 4.  Her putting the blame on us for the chaos was a classic case of the hand calling the feet dirty. 27. 1. She couldn’t choose between marriage and career as she was between the dog and the bone. 2. She couldn’t choose between marriage and career as she was between the sky and the dark mountains. 3. She couldn’t choose between marriage and career as she was between fire and the well. 4 She couldn’t choose between marriage and career as she was between the devil and the deep blue sea. 28. 1. Her presence of mind was well appreciated because a stitch in time saves nine. 2. Her presence of mind was well appreciated because a collar around the neck protects the dog. 3. Her presence of mind was well appreciated because a burnt child fears fire. 4. Her presence of mind was well appreciated because a tough egg never cracks. 29. 1. It was shameful to see the politicians fight like lions and tigers.

2 3. 1.  She was reprimanded for giving out the secret. 2.  She was reprimanded for giving away the secret. 3.  She was reprimanded for giving in the secret. 4.  She was reprimanded for giving up the secret.

2. It was shameful to see the politicians fight like cats and dogs.

24. 1. He is very cautious ever since he hurt his fingers in the share market.

4. It was shameful to see the politicians fight like cats and mice.

2. He is very cautious ever since he burnt his fingers in the share market.

30. 1. She has been on the mountains ever since she won the pageant.

3. He is very cautious ever since he broke his fingers in the share market.

2. She has been in seventh heaven ever since she won the pageant.

4. He is very cautious ever since he bit his fingers in the share market.

3. She has been on cloud eleven ever since she won the pageant.

25. 1. The old friends caught out on each other during the journey.

4. She has been over the rainbow ever since the won the pageant.

3. It was shameful to see the politicians fight like husbands and wives.

ANSWER KEYS

English Usage  Q.

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  2.63

  PRACTICE EXERCISE  2 Direction for questions 1 to 10:  Choose the sentence/s  that is/are grammatically incorrect. 1. a.  Being a rainy day the children could not go out. b.  My friend and guide plays the piano. c.  Having completed the task the book was read. d.  I enjoy hiking, biking and to watch movies. 1.  a and c 3.  a, c, d

2.  b and d 4.  b

5. a.  I hurt myself as much as I did himself b. Krishna could not make up his mind if he would agree with his teacher. c. We thought it was they who believed politics knew no better candidate than her. d. Of who are you speaking, Sudipta or I? 1.  a 3.  a, b, c

2.  a, b, d, 4.  a, c

2. a. His cattle was not fattened, so he could not sell them at the market.

6. a. I don’t care for the expensive blue jeans my son chose, but It’ll pay for them anyway.

b. Every teacher and every student was given a packet of sweets.

b.  Each of the houses were slightly different. c.  My brother had graduated before I started college.

c.  Either the woman or the men is happy.

d. I want somebody to delivery these documents with good characters.

d.  Ten million rupees is a huge amount. 1.  a and d 3.  a, c, d

2.  a, c 4.  b, d

3. a.  I am truly ashamed with my behaviour. b.  The child creeped under the table. c.  I cannot dance as I did before the war.

1.  a 3.  a, c, d

2.  b, c, d 4.  d

7. a.  Geeta is superior than Meeta in intelligence. b.  There are less than 100 different species in the area. c. She handed out brownies to the children stored in tupperwares.

d. Each of the doctors are concerned about the rising death rate from asthma.

8. a.  He deprived me of my rightful share of the property.

1.  None of these 2.  a, c 3.  b, c 4.  All of these

b. Hardly had she finished singing when she heard a loud wail.

4. a.  I hear that he is not very rich.

c.  I went to the UK last month.

b.  The messenger will arrive presently.

d.  The faithfulness of a dog is greater than that of a cat.

c.  The river had flowed over its banks.

1.  All of these 3.  d

d.  The girls beat the boys and so won the prize. 1.  None of these 2.  a 3.  d 4.  All of these

2.  None of these 4.  a, b, c

9. a.  The traveler marveled at the sceneries. b.  It is quarter to ten by my watch.

2.64 

  Verbal and Logical Reasoning

c.  He called for the menu at the swanky restaurant.

15. 1.  Ravi has decided to hand in his papers.

d. The minister as well as his team are arriving tomorrow. 2.  b, d 1.  a, 3.  a, c 4.  c

2.  Ravi has decided to hand out his papers.

10. a.  Frequent breaks affect his concentration span.

3.  Ravi has decided to hand off his papers. 4.  Ravi has decided to hand around his papers.

b.  The presentation he gave was very impressive.

16. 1. The Sharma’s have been eager to show off their new house.

c. The broker made a small fortune during the stock market bull run.

2. The Sharma’s have been eager to show up their new house.

d. His large income was not sufficient to sustain his family. 1.  d 3.  b

2.  c 4.  a

Direction for questions 11 to 20:  Choose the correct form of phrasal verbs/idioms in the following questions. 11. 1.  She has a tendency to lie at the drop of a glove. 2.  She has the tendency to lie at the sting of a bell. 3.  She has the tendency to lie at the chime of a bell.

3. The Sharma’s have been eager to show out their new house. 4. The Sharma’s have been eager to show around their new house. 17. 1. Once the public opinion was declared the politician was forced to eat humble pie. 2. Once the public opinion was declared the politician was forced to eat hand to mouth.

4.  She has the tendency to lie at the drop of a hat.

3. Once the public opinion was declared the politician was forced to eat hot potatoes.

12. 1. During the war, many families had to live from hand to mouth.

4. Once the public opinion was declared the politicians was forced to eat his own pie.

2. During the war, many families had to live from grain to morsel.

18. 1.  I have a row to pick with Ram.

3. During the war, many families had to live from foot to mouth.

3.  I have a thorn to pick with Ram.

4. During the war, many families had to live from bad to worse. 13. 1. His heart wrenching speech was enough to put the house on fire. 2. His heart wrenching speech was enough to raise the dust from the ground. 3. His heart wrenching speech was enough to bring the house down. 4. His heart wrenching speech was enough to bring the roof down. 14. 1. Sita regretted all that she had said to her mother when the iron was hot.

2.  I have a bone to pick with Ram. 4.  I have a task to pick with Ram. 19. 1. The newspaper carried sensational articles on how the actress was murdered in hot blood. 2. The newspaper carried sensational articles on how the actress was murdered in cold blood. 3. The newspaper carried sensational articles on how the actress was murdered in blue blood. 4. The newspaper carried sensational articles on how the actress was murdered in flesh and blood. 20. 1. Successive ministers have found the question of unemployment a hard nut to crack.

2. Sita regretted all that she had said to her mother when the sun shone.

2. Successive ministers have found the question of unemployment a tough nut to crack.

3. Sita regretted all that she had said to her mother in the heat of the moment.

3. Successive ministers have found the questions of unemployment a tough prize to grab.

4. Sita regretted all that she had said to her mother in the wink of an eye.

4. Successive minister have found the questions of unemployment an impossible lion to tame.

  2.65

English Usage  Direction for questions 21 to 25:  There are certain numbers of sentences in each of the passages given below. Indicate the number of correct sentences in each paragraph. 21. We do no know what to do with our knowledge. Science has given us superman powers, which we do not use properly. For example, we unable to manage our machines. Machines should be fed promptly and waited after attentively. 1.  4 3.  0

2.  3 4.  2

22. We must insist that free oratorship is only the beginning of free speech. The end is to find the truth. The practicality justification of civil liberty is not that the examination of opinion is one of necessities of man. 1.  a 3.  1

2.  0 4.  3

23. The trumpets loud candour Excites us to arms With shrink notes of anger and mortal alarms. 1.  1 3.  3

2.  2 4.  4

24. One day a wonderful plate made of gold fell from heaven into the court of the temple in Benaras. And on the plate these words were inscribed. ‘A gift from heaven who loves best.’ The priests at once made a proclamation that every day at twelve O’clock everyone who would like to claim the plate should assemble at the temple to have their kind deeds judged. 1.  0 3.  2

2.  1 4.  3

25. The best friend a man has in this world may turn against him and become his enemy. His son or his daughter that he had reared with loving care, may prove ungrateful. Those who are near and dearest to us, those who we trust with our happiness and good name may become traitors. 1.  3 3.  1

2.  2 4.  0

Direction for questions 26 to 29:  Choose the most  appropriate way to complete the following sentences. 26. I met him in New Delhi in 1996 ____________

27. Neither the teacher nor the students __________ I.  is going for the picnic. II.  are going for the picnic. 1.  I 3.  Both

2.  II 4.  Neither

28. The rise and fall of the tide __________ I.  are due to lunar influence. II.  is due to lunar influence. 1.  II 3.  Neither

2.  I 4.  both

2 9. Two third of the city: I.  is in ruins II.  are in ruins 1.  I 3.  both

2.  II 4.  neither

Direction for questions 30 to 34:  In each of the questions below, a statement is written in two different ways. Identify the correct statement. 3 0. 1.  He has wealth, reputation, and is powerful. 2.  He has wealth, reputation, and power. 31. 1. Not only did the horse lost, but the jockey broke his leg. 2. Not only did the horse lost, but the leg of the jockey was broken. 32. 1. The reason is because I don’t have enough resources. 2.  The reason is that I don’t have enough resources. 33. 1.  If I was taller, I would be richer. 2.  If I were taller, I would be richer. 3 4. 1.  After watching the movie, burger was eaten. 2.  After watching the movie, we ate burger. Direction for questions 35 to 46:  In each of the questions below, fill the appropriate preposition from the given set of prepositions.

I.  I had seen him 5 years before.

35. It’s too cold _______ winter to run outside.

II.  I had seen him 5 years ago.

1.  at

III.  I had seen him 5 years prior.

36. Mohan went _______ home.

1.  I 3.  II

1.  To 3.  In

2.  I and III 4.  None of these

2.  On

3.  In

2.  At 4.  No preposition required

2.66 

  Verbal and Logical Reasoning

3 7. He’s lived here ...... seven years. 1.  For 2.  Since

45. When the bull ran ______ me, I jumped ______ the fence.

3.  From

1.  by/on 3.  from/into

38. Most people like IPL, but ____ my opinion there is nothing Indian in it. 1.  For 2.  In 3.  On

46. Harry comes to work ______ car but I prefer to come ______ foot.

39. Are you travelling to Paris ____ business or ____ holiday? 2.  On, For 1.  For, For 3.  On, On 4.  For, On

1.  at/in 3.  At/on

2.  by/on 4.  By/in

Direction for questions 47 to 55:  In each of the questions below, fill the appropriate preposition from the given set of prepositions.

40. He made his escape by jumping ______ a window and jumping ______ a waiting car.

2.  towards/over 4.  in/next to

1.  over/into 2.  between/into 3. out of/between 4.  out of/into

47. _____ people like this area a lot. 1.  Elder 3.  Few

2.  Older 4.  After

41. I saw something about it ______ television. 1.  In 3.  At

2.  On 4.  Through

48. After visiting several galaxies, the aliens found themselves captivated by life on _____

42. I couldn’t get in ______ the door so I had to climb ______ a window.

1.  Earth 3.  Sun

1.  through/in 3. up/along

49. As soon as I picked up the packet, it _____

2.  between/into 4.  None of these

1.  came apart

43. I went ______ him and asked him the best way to get ______ town. 1.  by/on 3.  towards/over

2.  Was separated

2.  up to/out of 4.  along/up

3.  Came to be apart 50. The world needs to depend on other energy sources _____ oil and other non-renewable resources.

44. The restaurant is ______ the High Street, ______ the cinema. 2.  up/along 4.  under/around

ANSWER KEYS

1.  through/in 3.  in/next to

2.  The earth 4.  Moon



1.  Beside

2.  Besides

3.  After

4.  Before

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English Usage 

  2.67

VOCABULARY   ANTONYMS Antonyms are a part of several non-CAT exams like FMS, IIFT, JMET, XLRI etc., The antonyms are tools to test the vocabulary of a candidate, and they can be a great value addition to the score as they are big time savers. In these questions, student will be expected to choose a word or phrase that is most nearly opposite in meaning to the word. As some of the questions require you to distinguish fine shades of meaning, one has to be sure that all the choices have been considered before marking the answer. Ideally, the best way to improve antonyms is to improve the vocabulary. But there are certain techniques to ace these words. You will find three types of words in the question paper. The words you know, the words you sort of know, and the words you have never seen. The words that are totally unfamiliar should not be touched to avoid negative marking. For the words, you are comfortable with; do not look at the options in the first go. Try to think of an opposite meaning word in simple English. Look at the options and eliminate those, which do not match your shadow word. If you are not very clear about the meaning of the word: • Try to find the context in which the word is generally used like mitigating circumstances and abject poverty. You may also make a short sentence using the word. • Try to find some prefix, suffix or word root. Premeans before so precognition means awareness of events before they take place, and post- means after, so posterity means future generation. • Try to guess whether the word is positive or negative in shade. If the word is positive, all the positive and neutral and related options can be eliminated and vice versa. CENSURE a.  extol b.  impartial c.  slander d.  castigate e.  admonish The options c, d, and e can be eliminated straight away as they are also negative like censure which means to criticize. Impartial means unbiased is a neutral word, so it can also be eliminated. Therefore, we are left with extol (to praise), which is the right answer.

• Consider the secondary meanings of the words like pedestrian, august, cataract etc. PEDESTRIAN a.  Ordinary b.  Static c.  Jejune d.  Motor Car e.  Imaginative The answer is (e) Imaginative, as the secondary meaning of pedestrian is unimaginative. • Look at the answer choices to determine the part of speech of the question word. POLISH a.  Ruthless b.  Honesty c.  Indolent d.  Gaucheness e.  Complexity Here, polish has nothing to do with rubbing and shining. The noun POLISH means refinement and culture, so the opposite is gaucheness or awkwardness. • You can also eliminate the choices that don’t have opposites like chair, flower, philosophy, priority, birthright etc., You can also eliminate the answer choices that are synonyms of each other as no question can have two answers. • Looks can be deceptive, so beware! Some of the simple looking words can be really tricky and insidious. They are the land mines laid by the examiners. The word simplistic does not mean simple, and the word redoubtable has least to do with doubting again. REDOUBTABLE a.  Decisive b.  Resolved c.  Awesome d.  Formidable e.  Minnow Redoubtable means generating respect and fear or formidable, so its opposite is minnow, which means a small and unimportant person or company, so (e) is the answer.

2.68 

  Verbal and Logical Reasoning

  PRACTICE EXERCISE  1 1. Fickle 1.  aggressive 4.  hard working

2.  persistent 5.  timid

3.  miraculous

16. Condescend 1.  surrender 4.  disdain

2.  resist 5.  come down

3.  laud

17. Profound 1.  minnow 4.  petty

2.  deep 5.  excessive

3.  shallow

18. Archetype a.  unique 4.  modern

2.  quixotic 5.  ancient

3.  duplicate

2.  ugly 5.  miserly

3.  provident

2. Tranquil 1.  serene 4.  beautiful

2.  disturbed 5.  sumptuous

3.  cowardly

3. Gloomy 1.  disgusting 4.  spirited

2.  comical 5.  dark

3.  versatile

4. Cacophonous 1.  loud 4.  harsh

2.  melodious 5.  loud

3.  raucous

19. Frugal 1.  wasteful 4.  stylish

2.  coercive 5.  repulsive

3.  sensitive

2.  decipher 5.  jumble

3.  cook eggs

2 2. Elite 1.  plebeian 4.  gentry 23. Ostensible

2.  ignoble 5.  top class

3.  boring

3.  paucity

1.  crooked 4.  avian

2.  apparent 5.  equine

3.  hidden

3.  aggravate

2 4. Modest 1.  complacent 4.  barbaric

2.  haughty 5.  decent

3.  jovial

3.  sensitive

2 5. Irrevocable 1.  alterable 4.  moving

2.  ultimate 5.  permanent

3.  fixed

2.  awful 5.  somber

3.  lively

5. Zenith 1.  crest 4.  nadir

2.  pinnacle 5.  acme

3.  interior

2 0. Repugnant 1.  odious 4.  agreeable

6. Advance 1.  retreat 4.  defeat

2.  goad 5.  cash

3.  plod

21. Scramble 1.  simplify 4.  denigrate

7. Coy 1.  shy 4.  brazen 8. Dearth 1.  terror 4.  levity 9. Alleviate 1.  motivate 4.  malign 10. Callous 1.  frugal 4.  stingy

2.  reserved 5.  comely 2.  abundance 5.  life 2.  pep up 5.  godly 2.  nonchalant 5.  cellular

3.  optimistic

11. Oriental 1.  fatal 4.  actuarial

2.  occidental 5.  bank

3.  fatalistic

2 6. Ludicrous 1.  awesome 4.  grave

12. Nascent 1.  primal 4.  modish

2.  senescent 5.  modish

3.  primordial

2 7. Congenital 1.  inborn 4.  hereditary

2.  societal 5.  genetic

3.  acquired

13. Brood 1.  support 4.  fragmented

2.  exult 5.  vermin

3.  slander

2 8. Hilarious 1.  eulogistic 4.  sportive

2.  morose 5.  comical

3.  paltry

14. Blasphemy 1.  irreverence 4.  respect

2.  scandalous 5.  assail

3.  cursing

1.  affluent 4.  superficial

2.  comatose 5.  ravenous

3.  ruthless

15. Shelter 1.  pillar 4.  refuge

2.  imperil 5.  protégé

3.  security

3 0. Absolve 1.  confront 4.  confuse

2.  charge 5.  vindicate

3.  accuse

29. Impecunious

ANSWER KEYS

English Usage  Q.

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  2.69

HINTS AND EXPLANATIONS 1. Fickle means changing unpredictably and persistent means consistent, which does not change.

2. Tranquil means peaceful, so its antonym will be disturbed.

17. shallow profound means deep, so shallow. 18. Archetype means original, so duplicate.

3. Gloomy means sad and depressed, spirited means lively.

19. Frugal means economical, so wasteful.

4. Cacophonous means harsh and unpleasant.

20. Repugnant means deserving hate, so agreeable.

5. Zenith is the topmost point, and nadir is the lowest point. 6. Advance means to move ahead and retreat means to withdraw. 7. Coy means shy, brazen means rude and shameless. 8. Dearth means scarcity, so abundance is the opposite.

21. Scramble means to jumble or mix randomly, so decipher, which means to crack a code. 22. Elite, belonging to the upper class, so plebeian, pertaining to the masses.

9. Alleviate means to make the things more bearable, aggravate means to worsen.

23. Ostensible means apparent, so hidden.

10. Callous means insensitive, so sensitive is the antonym.

24. Modest means unassuming, so haughty means arrogant.

11. Oriental means pertaining to East so occidental, which means pertaining to West.

25. Irrevocable means something which can’t be undone, so alterable.

12. Nascent means new so senescent means old is the opposite.

26. Ludicrous means humorous , so grave.

13. Brood means to sulk, opposite can be exult , to praise highly.

27. Congenital means acquired by birth, so acquired.

14. Blasphemy means insulting God or religion, so respect is the opposite.

28. Hilarious means comical, so morose means sorrowful or depressive.

15. Shelter means to protect, so imperil i.e., to risk or endanger oneself is the answer.

29. Impecunious means poor, so affluent.

16. Condescend means to belittle, so laud which means to praise is the opposite.

30. Absolve, means to free from charges or blame, so accuse is the opposite.

2.70 

  Verbal and Logical Reasoning

  PRACTICE EXERCISE  2 1. Ratify 1.  abrogate 4.  competition

2.  abbreviate 5.  magnify

3.  assail

1 7. Impede 1.  tolerate 4.  bother

2.  recede 5.  cripple

3.  assist

3.  concrete

1 8. Dissent 1.  fall 4.  antagonism

2.  debacle 5.  ascent

3.  approval

2.  arbitrary 5.  objective

3.  nurtured

2.  perplexed 5.  derive

19. Reasoned

2.  messy 5.  gauche

3.  convoluted

2.  partner 5.  partner

3.  fence-sitter

1.  apparent 4.  alert

2.  unperturbed 3.  nonchalant 5.  absent minded

8. Affirmative 1.  obliging 4.  negative

2.  uncivilized 5.  approving

3.  platonic

9. Ambiguous 1.  unequivocal 4.  murky

2.  perplexing 5.  uncertain

3.  befuddled

2.  admiration 5.  loathsome

3.  animus

1.  zealous 4.  bullish

2.  fanatical 5.  spirited

3.  apathetic

2.  placatory 5.  irritable

3.  jaundiced

22. Contentious 1.  irascible 4.  myopic 1.  lively 4.  morose

2.  disinterested 3.  affable 5.  relaxed

24. Coalesce 1.  converge 4.  moderate

2.  assimilate 5.  assemble

3.  disperse

2.  antiquated 5.  lucky

3.  stylish

2.  dictatorial 5.  arrogant

3.  haughty

1.  diurnal 4.  obscure

2.  pellucid 5.  transparent

3.  indifferent

2 8. Puerile 1.  obliging 4.  mature

2.  uncivilized 5.  credulous

3.  platonic

25. Antediluvian 2.  ample 5.  scanty

3.  marginal

1 2. Analysis 1.  dissection 4.  synthesis

2.  criticize 5.  dialysis

3.  projection

1 3. Condemn 1.  penalize 4.  approve

2.  censure 5.  castigate

3.  punish

2.  ruddy 5.  apt

3.  truthful

1.  modern 4.  artistic 26. Overbearing

14. Apposite 1.  opposite 4.  inappropriate

2.  aromatic 3.  gibberish 5.  fowl smelling

23. Buoyant

10. Abhorrence

1 1. Meagre 1.  insufficient 4.  extraneous

1.  rotten 4.  bucolic 21. Ardent

7. Oblivious

1.  disgust 4.  pathos

1.  logical 4.  confused 20. Fetid

6. Ally a.  adversary 4.  almighty

3.  appreciate

3.  messy

5. Clumsy a.  adroit 4.  boorish

2.  slander 5.  downsize

2.  abortive 5.  prolific

1 6. Disparage 1.  indict 4.  honour

4. Abstract 1.  confused 4.  open

3.  amenable

3.  rat race

3. Amplify 1.  rake 4.  mark

2.  caustic 5.  infirm

2.  pass 5.  pass a law

2. Fruitful 1.  productive 4.  dingy

1 5. Inflexible 1.  rigid 4.  acrid

1.  servile 4.  irate 27. lucid

English Usage  29. Pulchritude

30. Eschew 2.  fitness 5.  charm

ANSWER KEYS

1.  ugliness 4.  robustness

  2.71

3.  daintiness

1.  taunt 4.  castigate

2.  embrace 5.  abstain

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

2

3.

2

4.

3

5.

1

6.

1

7.

4

8.

4

9.

1

10.

2

11.

2

12.

4

13.

4

14.

4

15.

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16.

3

17.

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18.

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2

20.

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21.

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22.

2

23.

4

24.

3

25.

1

26.

1

27.

4

28.

4

29.

1

30.

2

3.  possess

HINTS AND EXPLANATIONS 1. Ratify means to pass a law, so abrogate i.e., to cancel a law.

17. Impede means to hinder, so opposite is assist.

2. Fruitful means successful, so abortive which means unsuccessful.

18. Dissent means disagreement, so opposite is approval.

3. Amplify means increase, so abbreviate.

19. Arbitrary means not clear.

4. Abstract means hazy and intangible, so concrete. 5. Clumsy means awkward, so adroit which means skilled. 6. Ally means a friend and supporter, so adversary. 7. Oblivious means unaware, so alert. 8. Affirmative means positive. 9. Ambiguous means unclear, so unequivocal which means definite is the antonym. 10. Abhorrence means hatred, so admiration. 11. Meager means less. 12. Synthesis is the opposite of analysis. 13. Condemn means to criticize, so approve.

20. Fetid means rotten, so opposite is aromatic. 21. Ardent means very interested, so opposite means apathetic or insensitive. 22. Contentious means argumentative or quarrelsome, so opposite is placatory. 23. Buoyant means lively or spited, so opposite is morose. 24. Coalesce means to join, so disperse. 25. Antediluvian means very old, so modern. 26. Overbearing means haughty, so servile. 27. Lucid means easy to understand, so obscure.

14. Apposite means appropriate, so inappropriate.

28. Puerile means childish, so mature.

15. Inflexible is the opposite of amenable which means flexible.

29. Pulchritude means beauty, so ugliness.

16. Disparage means to belittle, so opposite is appreciate.

30. Eschew means to avoid, so embrace.

2.72 

  Verbal and Logical Reasoning

  PRACTICE EXERCISE  3 13. Invigorate

1. Fledgling 1.  lobbyist 4.  sapling

2.  sophomoric 3.  veteran 5.  green horn

2.  rebuttal 5.  fortune

3.  antipathy

2.  apocryphal 5.  humane

3.  carnal

2.  ignorance 5.  honour

3.  passivity

16. Diaphanous 1.  flimsy 4.  angry

2.  thin 5.  lamenting

3.  opaque

3.  pleasant

17. Facetious 1.  comical 4.  ironical

2.  grave 5.  ardent

3.  satirical

2.  loyalty 5.  agnosticism

3.  mockery

3.  exciting

18. Perfidy 1.  felony 4.  antagonism 19. Fatuous 1.  silly 4.  perplexed

2.  inane 5.  impressive

3.  sensible

2 0. Heretical 1.  heroic 4.  climactic

2.  orthodox 5.  rebellious

3.  villainous

2.  sociable e.  enlightened

3.  motivating

2.  fugitive 5.  hidden

3.  expatriate

2.  retiring 5.  bitter 2.  impervious 5.  dull

7. Ameliorate 1.  conquer 4.  exaggerated

2.  worsen 5.  better

3.  circumvent

2.  capacious 5.  garrulous

3.  fragile

2.  joining 5.  nuclear

3.  spinning

2.  glut 5.  scarcity

3.  suffering

2.  unoriginal 5.  abundance

3.  boring

8. Voluble 1.  tender 4.  taciturn

11. Platitude 1.  genuine 4.  jejune 12. Sober 1.  egalitarian 4.  inebriated

2.  gory 5.  smart

22. Furtive 1.  clandestine 4.  open

10. Paucity 1.  intricacy 4.  fastidious

21. Gregarious 1.  unsociable 4.  ecstatic

9. Fission 1.  splitting 4.  discursive

3.  morbid

1.  stellar 4.  vernal

6. Soporific 1.  mature 4.  steep

2.  sickly 5.  diseased

3.  punish

5. Vitriolic a.  humble 4.  pure

1.  pale 4.  wholesome

2.  censure 5.  rustic

4. Veneration 1.  dissuasion 4.  contempt

3.  revel

15. Spiritual

3. Bucolic 1.  penalize 4.  civic

2.  enliven 5.  animate

14. Insalubrious

2. Apathy 1.  nonchalance 4.  empathy

1.  debilitate 4.  carouse

3.  morose

23. Fleeting 1.  vanishing 4.  permanent

2.  passing 3.  affable 5.  mesmerizing

2 4. Flowery 1.  decorated 4.  fragrant

2.  magical 5.  unadorned

3.  heavenly

2 5. Fecund a.  sterile 4.  debacle

2.  poor 5.  damsel

3.  amateur

ANSWER KEYS

English Usage  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

4

3.

4

4.

4

5.

3

6.

3

7.

2

8.

4

9.

2

10.

2

11.

2

12.

4

13.

1

14.

4

15.

3

16.

3

17.

2

18.

2

19.

3

20.

2

21.

1

22.

4

23.

4

24.

5

25.

1

  2.73

HINTS AND EXPLANATIONS 1. Fledgling means young and inexperienced, so veteran.

14. Insalubrious means unhealthy, so wholesome.

2. Empathy is the opposite of apathy.

15. Carnal means showing physical desire, so carnal.

3. Bucolic means village like, so civic.

16. Diaphanous means transparent, so opaque.

4. Veneration means respect, so opposite is contempt.

17. Facetious means humorous, so grave.

5. Vitriolic means bitter and biting, so pleasant.

18. Perfidy means disloyalty, so loyalty.

6. Soporific means causing sleep, so exciting.

19. Fatuous means silly and pointless, so sensible.

7. Ameliorate means to improve, so worsen.

20. Heretical means against established religious views, so orthodox.

8. Voluble means expressing fluently, so taciturn.

21. Gregarious means group loving, so unsociable.

9. Fission means splitting, so joining. 10. Paucity means lack of, so glut which means abundance.

22. Furtive means secretive, so open.

11. Platitude means clichéd , so unoriginal.

23. Fleeting means passing and disappearing, so permanent.

12. Sober, means not drunk, so inebriated means drunken.

24. Flowery means decorated so unadorned, so unadorned.

13. Invigorate means to energize, so debilitate means to cripple.

25. Fecund means fertile, so sterile.

  PRACTICE EXERCISE  4 4. Inculpate

1. Imperious 1.  docile 4.  sloppy 2. Illustrious 1.  nasty guished

2.  unimportant 3.  pacific 5.  puerile

2.  arraign 5.  debase

3.  incarcerate

2.  respectful 5.  crazy

3.  irreverent

2.  praise 5.  divine

3.  honour

5. Impudent 2.  hazy 4.  rich

3.  undistin5.  respectful

1.  saucy 4.  onerous 6. Invective

3. Immaculate 1.  contaminated 4.  virgin

1.  exonerate 4.  indict

2.  charge 5.  germinal

3.  incarcerate

1.  humour 4.  grace

2.74 

  Verbal and Logical Reasoning

7. Indigent 1.  crooked 4.  saintly

20. Malignant 2.  reserved 5.  occidental

3.  wealthy

1.  stoic 4.  tranquil

2.  calm 5.  excitable

3.  peaceful

9. Impeach 1.  allege 4.  slander

2.  extradite 5.  vindicate

3.  invoke

10. Imminent 1.  likely 4.  remote

2.  probable 5.  inevitable

3.  possible

8. Imperturbable

11. Guileful 1.  ingenuous 4.  insidious

b.  spiteful 5.  vague

12. Intelligible 2.  insightful 1.  perceptive c.  incomprehensible 4.  sagacious

3.  malicious

5.  insipid

2.  jaded 5.  lachrymose

3.  jocular

14. Innocuous 1.  genetic 4.  malicious

2.  genuine 5.  harmful

3.  cursing

15. Indigenous 1.  crafty 4.  wicked

2.  foreign 5.  awkward

3.   crafty

2.  insular 5.  prosaic

3.  solemn

3.  expedite

1.  lenient 4.  intractable

2.  easy 5.  refractory

3.  rigorous

2.  equitable 5.  behemoth

3.  balanced

2.  lavish 5.  prudent

3.  stingy

23. Macrocosm 1.  equable 4.  microcosm

1.  generous 4.  provident 25. Benevolent 1.  cheerful 4.  edgy

2.  sporty 5.  moribund

3.  comatose

2.  optimistic 3.  malevolent 5.  bad tempered

26. Piquant 2.  racy 5.  vulgar

3.  risqué

2.  joy 5.  love

3.  harmony

2.  morose 5.  amorphous

3.  noticeable

2.  mitigate 5.  coach

3.  imperil

27. Perseverance 1.  patience 4.  inconstancy 28. Unobstrusive

17. Jaunty

1.  arcane 4.  amoral 29. Aggravate

18. Intransigent 2.  squalid 5.  prim

3.  flexible

19. Jaundiced 1.  optimistic 4.  strong

2.  ratify 5.  motivate

22. Lax

1.  tangy 4.  bland

16. Jocular

1.  rigid 4.  filthy

3.  rigid

24. Munificent

1.  energetic d.  delighted

1.  lively 4.  sedate

2.  benign 5.  impervious

21. Nullify 1.  eradicate 4.  activate

13. Languid

1.  comical 4.  dull

a.  pernicious 4.  roomy

1.  worsen 4.  redeem 30. Naive

2.  diseased 5.  meek

3.  vulnerable

1.  tyro 4.  veteran

2.  sophisticated 3.  beginner 5.  inveterate

ANSWER KEYS

English Usage  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

3

3.

1

4.

4

5.

2

6.

3

7.

3

8.

5

9.

5

10.

4

11.

1

12.

3

13.

5

14.

5

15.

2

16.

3

17.

4

18.

3

19.

1

20.

2

21.

2

22.

3

23.

4

24.

3

25.

3

26.

4

27.

4

28.

3

29.

2

30.

2

  2.75

HINTS AND EXPLANATIONS 1. Imperious means authoritative, so docile.

17. Jaunty means lively and cheerful, so sedate.

2. Undistinguished.

18. Intransigent means stubborn, so flexible.

3. Immaculate means pure, so contaminated. 4. Inculpate means to blame, so indict. 5. Impudent means showing casual disrespect, so respectful. 6. Invective means abuse or verbal insult, so praise.

19. Jaundiced means prejudiced, so optimistic. 20. Benign is the opposite of malignant. 21. Nullify means to cancel a law, so ratify.

7. Indigent means poor, so wealthy.

22. Lax means not strict.

8. Imperturbable means one who can’t be disturbed.

23. Microcosm.

9. Impeach means to charge a public official, so vindicate.

24. Munificent means generous, so stingy.

10. Imminent means likely to happen, so remote. 11. Guileful means deceptive, so ingenuous. 12. Intelligible means perceptible. 13. Languid means tired, so energetic.

25. Benevolent means kind and generous, so malevolent. 26. Piquant means sharp and biting, so bland. 27. Perseverance means consistent.

14. Innocuous means harmless.

28. Unobtrusive means something which is not very clear or distinct.

15. Indigenous means native of, so foreign.

29. Aggravate means to worse, so mitigate, means to make bearable.

16. Jocular means comical, so solemn, serious.

30. Naïve means unworldly, so sophisticated.

2.76 

  Verbal and Logical Reasoning

  SYNONYMS Direction for questions 1 to 20: In the following questions, a word is given in bold letters followed by four alternatives marked a–d. Select the alternative that conveys the same meaning as the word given in bold letters.

  PRACTICE EXERCISE  1 1. Amply 1.  sufficiently 2.  to dress 3.  prior 4.  a brief account of some interesting event or incident 2. Comport 1.  abnormal; straying from the normal or usual path 2.  fitting in 3.  too dirty or discoloured 4.  with no shape; unorganized 3. Abjure 1.  hard coal 2.  to recant, renounce, repudiate under oath 3. a book whose leaves are so made to form paper frames for holding photographs 4.  one who or that which accompanies 4. Hostility; opposition 1.  cacophonous

8. Touching; or adjoining and close, but not touching 1.  Contiguous 2.  abase 3.  antagonism 4.  apposite 9. Advent 1.  cheerful willingness 2. the coming or arrival, as of any important change, event, state, or personage 3.  a portable free-reed musical instrument 4. the act or state of lying concealed for the purpose of surprising or attacking the enemy 10. Trite; without freshness or originality 1.  baroque 2.  boor 3.  chimera 4.  banal 11. Alter 1.  flood 2. one chosen to act in place of another, in case of the absence or incapacity of that other 3.  to make change in 4.  the act of cutting off, as in a surgical operation 12. Analogy 1.  unnecessary activity or ceremony 2.  induction or elevation, as to dignity, office, or government 3. reasoning in which from certain and known relations or resemblance, others are formed 4.  that which is near or bordering upon 13. Corroborate 1.  to confirm the validity 2.  tasting sour; harsh in language or temper 3.  unselfish devotion to the welfare of others 4.  controversy; dispute

2.  comeliness 3.  bombastic 4.  antagonism 5. Alley 1.  quantity or extent of land, especially of cultivated land 2.  a narrow street, garden path, walk, or the like 3.  largeness 4.  to represent beforehand in outline or by emblem

14. Augment 1. one who is skeptical of the existence of know ability of a god or any ultimate reality 2.  urge; plead for 3.  increase 4.  pertaining to soil deposits left by running water

6. Wrong; awry 1.  contentious 3.  amiss

15. To become a semisolid, soft mass; to clot 1.  coagulate 2.  advocate 3.  copious 4.  abysmal

2.  collusion 4.  conglomeration

7. Anglophobia 1.  hatred or dread of England or of what is English 2.  having the right or privilege of entry 3. to make shorter in words, keeping the essential features, leaning out minor particles 4.  sourness, with bitterness and astringency

16. Amazement or terror that causes confusion 1.  conjure 2.  appease 3.  analogy 4.  consternation 17. To determine the quality of a substance 1.  consequential 2.  cacophonous 3.  assay 4.  agrarian

English Usage  18. A fortified place or strong defense 1.  adamant 2.  astringent 3.  bungler 4.  bastion

2 0. Airy 1.  slight sickness 2.  delicate, ethereal 3.  to hate violently 4. anything gained, or made one’s own, usually by effort or labour.

19. To go away hastily or secretly; to hide 1.  abaft 2.  abscond 3.  clemency 4.  aseptic

1NSW5R K5YS

  2.77

Q.

1ns.

Q.

1ns.

Q.

1ns.

Q.

1ns.

Q.

1ns.

1.

3

2.

2

3.

4

4.

2

5.

2

6.

3

7.

1

8.

1

9.

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12.

3

13.

1

14.

3

15.

1

16.

4

17.

3

18.

4

19.

2

20.

2

  PRACTICE EXERCISE  2 Direction for questions 1 to 20: In the following questions, a word/phrase is given in bold letters followed by four alternatives marked a–d. Select the alternative that conveys the same meaning as the word/phrase given in bold letters.

3.  the art or practice of flying aircraft. 4.  portion.

1. Eager readiness or speed 1.  cloying 2.  bode 3.  alacrity 4.  arbiter

8. Aide-de-camp

2. Acknowledgment 1.  recognition 2.  willing and ready to submit 3.  very hateful 4.  answering yes; to a question at issue 3. Of the land 1.  complacent 3.  beholden

2.  approbatory 4.  agrarian

4. Anachronism 1.  pertaining to the act or sense of hearing. 2.  anything occurring or existing out of its proper time. 3.  self denial. 4.  the entire number, sum, mass, or quantity of something.

7. To come down from one’s position or dignity 1.  adage 2.  condescend 3.  cajole 4.  abandon 1.  a white or delicately tinted fine-grained gypsum. 2.  profound devotion. 3. an officer who receives and transmits the orders of the general. 4.  good-by; farewell. 9. To move towards one point (opposite: diverge) 1.  askance 2.  converge 3.  analogy 4.  asperity 10. Annuity 1.  an annual allowance, payment, or income. 2.  the superior of a community of monks. 3.  to warn of a fault. 4.  to pile or heap together.

5. Being too long, as in a description or expression; a roundabout, indirect, or ungainly way of expressing something. 1.  abysmal 2.  circumlocutory 3.  complacent 4.  awry

11. Accede 1.  without determinate shape. 2.  misfortune. 3.  of unknown authorship. 4.  to agree.

6. Acquit 1.  able to move or act quickly, physically, or mentally. 2.  to free or clear, as from accusation.

12. To overlook; to forgive 1.  charisma 2.  condone 3.  contempt 4.  consecrate

2.78 

  Verbal and Logical Reasoning

13. Arrogant 1.  allure 3.  bumptious

2.  the entire number, sum, mass, or quantity of something. 3.  the practical unit of electric-current strength. 4.  the state of being attached or joined.

2.  cacophony 4.  conjoin

14. To forgive; to acquit 1.  chary 2.  aghast 3.  absolve 4.  accretion

18. To acknowledge; admit 1.  concede 2.  communal 3.  attenuate 4.  arrogate

15. Afoot 1.  in progress. 2.  to warn of a fault. 3.  to refer incidentally. 4.  an adulterating substance.

19. Anode 1. the point where or path by which a voltaic current enters an electrolyte. 2.  friendship. 3. of or pertaining to the times, things, events before the great flood in the days of Noah. 4.  sharpness or bitterness of speech or temper.

16. Something that is abnormal 1.  cohesion 2.  connotative 3.  atypical 4.  alacrity

2 0. With no shape; unorganized 1.  asperity 2.  amorphous 3.  conviviality 4.  constrain

ANSWER KEYS

17. Aggregate 1. a series of tables giving the days of the week together with certain astronomical information.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

1

3.

4

4.

2

5.

2

6.

2

7.

2

8.

3

9.

2

10.

1

11.

4

12.

2

13.

3

14.

3

15.

1

16.

3

17.

2

18 .

1

19.

1

20.

2

  PRACTICE EXERCISE  3 Direction for questions 1 to 20: In the following questions a word/phrase is given in bold letters followed by four alternatives marked a–d. Select the alternative that conveys the same meaning as the word/ phrase given in bold letters.

4. Abhorrent 1.  very repugnant; hateful. 2.  a member of an academy of literature, art, or science. 3.  easy to approach. 4.  profound devotion.

1. Lack of emotion or interest

5. Acrimonious 1.  full of bitterness. 2.  not conformed to the ordinary rule or standard. 3. a book whose leaves are so made to form paper frames for holding photographs or the like. 4.  to cause to appear greatly.

1.  apathy 3.  caliber

2.  complacent 4.  anecdote

2. Ailment

1.  colourless, 2.  a discharge from accusation by judicial action. 3.  slight sickness. 4.  having fi ne and penetrating discernment.

3. Changeable; fickle 1.  condescend 3.  cascade

2.  complaisance 4.  capricious

6. One who believes that a formal government is unnecessary 1.  confluence 2.  anarchist 3.  compromise 4.  aghast 7. Abdominal 1.  one who manages affairs of any kind. 2.  not mandatory.

English Usage 

  2.79

3.  a condensed form as of a book or play. 4.  of, pertaining to, or situated on the abdomen.

3.  aversion; dislike 4.  increase

8. A symbolic description 1.  conjure 2.  amiss 3.  allegory 4.  chaffing

15. Advert 1.  to speak to 2.  to make explanatory or critical notes on or upon 3.  to fight 4.  to refer incidentally

9. To lump together, causing confusion; to damn 1.  confound 2.  abbreviate 3.  arcane 4.  candid

16. Fitting in 1.  comport 3.  allure

10. Americanism 1. beginning, ending, or changing suddenly or with a break. 2.  opposing or opposed. 3.  a charge of crime, misdemeanor, or error. 4. a peculiar sense in which an English word or phrase is used in the United States.

17. Abdicate 1. an officer who receives and transmits the orders of the general. 2.  a person or thing that aids the principal agent. 3.  primitive; unsophisticated. 4.  to give up (royal power or the like).

11. Suitable (as land) for plowing 1.  amity 2.  arable 3.  adjure 4.  blatant

18. Conferring benefits; kindly 1.  beneficent 2.  amortize 3.  carte blanche 4.  audacious

12. Alabaster 1.  before noon. 2.  of, pertaining to, or involving an accusation. 3.  a white or delicately tinted fine-grained gypsum. 4.  a condensed form as of a book or play. 13. Not yielding, firm 1.  awry 3.  abase

19. Abrupt 1.  designed to excite love. 2.  beginning, ending, or changing suddenly or with a break. 3. the branch of pneumatics that treats of the equilibrium, pressure, and mechanical properties. 4.  to move faster.

2.  contrite 4.  adamant

2 0. Ablution 1.  a manually skilled worker 2.  dry; barren 3.  ash-coloured; deadly pale 4.  washing

14. Antipathy 1.  urge; plead for 2.  calm; pacify

ANSWER KEYS

2.  attenuate 4.  beholden

Q.

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Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

3

3.

4

4.

1

5.

1

6.

2

7.

4

8.

4

9.

1

10.

1

11.

2

12.

3

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  PRACTICE EXERCISE  4 Direction for questions 1 to 20: In the following questions, a word/phrase is given in bold letters followed by four alternatives marked a–d. Select the alternative that conveys the same meaning as the word/ phrase given in bold letters.

1. Abbot 1.  a discharge from accusation by judicial action. 2.  a white or delicately tinted fine-grained gypsum. 3.  the superior of a community of monks. 4.  sufficiently.

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2. Friendly; amiable 1.  affiliate 3.  affable

2.  abstemious 4.  abeyance

3. Academy 1. any institution where the higher branches of learning are taught. 2. induction or elevation, as to dignity, office, or government. 3.  the act of detesting extremely. 4.  to refer incidentally. 4. Erratic 1. irresponsible, eccentric; lacking a fixed purpose erratic behaviour. 2.  display or wave boastfully. 3.  relating to the countryside. 4.  dry; barren. 5. Affront 1. the setting forth of a subject under the guise of another subject of aptly suggestive likeness. 2. a record of events in their chronological order, year by year. 3.  the character ‘&’; and. 4.  an open insult or indignity. 6. Benevolent 1.  art authoritative statement; a saying. 2.  kindly; charitable. 3.  to pierce through with a pointed instrument. 4.  a distortion of the face to express an attitude or feeling. 7. Affix 1.  to contend angrily or zealously in words. 2. practicing an art or occupation for the love of it, but not as a profession. 3.  to stick fast or together. 4.  to fasten. 8. Expound 1.  to express sorrow or grief over. 2.  to set forth in detail; to explain. 3.  to make gestures, or indicate feelings by motions. 4.  a god. 9. Alienable 1.  occurring or existing before birth. 2.  to make inefficient or worthless; muddle. 3.  anything forbidden, as by social usage. 4.  capable of being aliened or alienated, as lands. 10. Acute 1.  historian 2.  of, pertaining to, or involving an accusation.

3.  estrangement. 4.  having fine and penetrating discernment. 11. Devout 1.  devoted to religious observances. 2.  to beg earnestly. 3.  pertaining to public discussion or law courts. 4. a picture or other description of a person which exaggerates ludicrously one or more of his distinctive features. 12. Abet 1.  to use for one’s selfish purpose. 2.  to encourage or support. 3.  origin. 4.  rudely abrupt. 13. Condole 1.  sociable, courteous, and agreeable in manner. 2.  despotic. 3. to express sympathy with another in sorrow, pain, or misfortune. 4.  inclined to believe anything; easily imposed upon. 14. Affiliate 1.  some auxiliary person or thing. 2.  of or pertaining to an academy, college, or university. 3.  to recognize (v.); to admit the genuineness or validity of. 4.  plentiful (adj). 15. Heresy 1.  despotic. 2.  historical records. 3.  an opinion held in opposition to the traditional view. 4.  coward. 16. Devoid 1.  implied but not clearly expressed; unquestioning. 2.  lacking in; not possessing. 3.  sharp or harsh in language or temper. 4. positive in expressing an opinion; asserting an opinion as though it were an undisputed fact. 17. Aggrieve 1. reasoning in which from certain and known relations or resemblance others are formed. 2.  a vehicle fitted for conveying the sick and wounded 3.  to give grief or sorrow to. 4. a volatile, inflammable, colourless liquid of a penetrating odour and burning taste. 18. Cringe 1.  self-satisfied. 2.  to shrink in fear. 3.  prejudiced. 4.  habitually fond of associating in a company or herd.

English Usage 

ANSWER KEYS

19. Acrimonious 1.  sharp or harsh in language or temper. 2.  of low morals; corrupt. 3.  to make a mistake or to do something wrong. 4.  one who denies that God exists.

  2.81

2 0. Craven 1.  implied but not clearly expressed; unquestioning. 2.  of low morals; corrupt. 3.  coward. 4.  rudely abrupt.

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  PRACTICE EXERCISE  5 Direction for questions 1 to 20: In the following questions a word/phrase is given in bold letters followed by four alternatives marked a–d. Select the alternative that conveys the same meaning as the word/phrase given in bold letters. 1. Antarctic 1.  pertaining to the south pole or the regions near it. 2. corresponding (to some other) in certain respects, as in form, proportion, relations. 3.  some auxiliary person or thing. 4.  eagerly desirous and aspiring. 2. Egregious 1.  a distortion of the face to express an attitude or feeling. 2.  conversation which is amusing and not serious. 3.  a record of a person’s or a family’s ancestors or relatives. 4.  often of mistakes, extremely and noticeably bad. 3. Adjuration 1.  to pile or heap together. 2.  to wear away the surface or some part of by friction. 3.  a vehement appeal. 4. anything gained, or made one’s own, usually by effort or labour. 4. Annuity 1.  solemn curse; someone or something that is despised. 2.  unreasonable or capricious; tyrannical 3.  preventing infection; having a cleansing effect. 4.  yearly allowance. 5. Aboriginal 1.  primitive; unsophisticated. 2.  passive consent.

3.  to assign or affix a date to earlier than the actual one. 4.  to represent beforehand in outline or by emblem. 6. Fetish 1.  a swamp. 2. something that is believed to have magical powers an object of unreasoning devotion and worship. 3.  to soil or dirty. 4.  to quicken, speed tip. 7. Anterior 1. a member of a municipal legislative body, who usually exercises also certain judicial functions. 2.  prior. 3.  having the right or privilege of entry. 4. the point where or path by which a voltaic current enters an electrolyte or the like. 8. Apathy 1.  to free from blame. 2.  to give a false idea of. 3.  lack of feeling, emotion, or interest. 4. to express sympathy with another in sorrow, pain, or misfortune. 9. Exploit 1.  spirited; ardent. 2.  a swamp. 3.  to use for one’s selfish purpose. 4.  quick to find fault about trifles. 10. Abrogate 1.  lacking in freshness, originality, or vigor. 2.  liable to make mistakes or be deceived. 3.  a public command or proclamation issued by an authority. 4.  to abolish or render void.

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11. Antithesis 1.  pertaining to the clergy or the church. 2.  to declare positively; to confirm. 3.  departure, emigration. 4.  contrast; the direct opposite.

16. Disparity 1. inequality; difference in image, quantity, character, or rank. 2.  to punish or criticize severely. 3.  to declare positively; to confirm. 4.  coarse and stupid.

12. Deluge 1.  thoughtless; taking little care. 2.  to abolish or render void. 3.  a brief summary of the main ideas of a larger work. 4.  a great flood; downpour.

17. Aggrandize 1.  having fine and penetrating discernment. 2.  to cause to appear greatly. 3.  to utter with a shout. 4. the setting forth of a subject under the guise of another subject of aptly suggestive likeness.

13. Advocate 1.  diversion. 2. one who pleads the cause of another, as in a legal or ecclesiastical court. 3. any raised place or structure on which sacrifices may be offered or incense burned. 4.  change or modification.

18. Cumbrous 1.  burdensome and clumsy. 2.  mentally distressed; distracted. 3. to express sympathy with another in sorrow, pain, or misfortune. 4.  a tombstone inscription.

14. Crass 1.  personal peculiarity. 2.  coarse and stupid. 3.  well-deserved (applied chiefly to punishment). 4.  wicked; hateful.

19. Annex 1.  to add or affix at the end. 2.  to recant, renounce, repudiate under oath. 3.  an abiding. 4.  to move faster.

ANSWER KEYS

15. Aldermanship 1.  invulnerable. 2.  the art or practice of flying aircraft. 3. the dignity, condition, office, or term of office of an alderman. 4.  to warn of a fault.

2 0. Cabal 1.  a feeling of hatred. 2.  obnoxiously conceited or self-assertive. 3.  pertaining to public discussion or law courts. 4.  a small group of persons engaged in plotting.

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English Usage 

  2.83

  FILL IN THE BLANKS The fill in the balnks or sentence completion questions on the CAT Verbal section are designed to measure your ability to understand the intended meaning of a sentence. Each question requires you to analyze the context of a sentence and determine which word or words best complete that sentence. The CAT includes both vocabulary-in-context and logic-based sentence completion questions that are designed to test your grasp of the English language. You should be able to determine which answer choice best fills the blank(s) of the given sentence. Keep in mind that a complete sentence is clear and concise, conveys a logical meaning, and is uniform in grammar and style. A strong vocabulary is the cornerstone of critical reading, and the best way to develop a large and varied vocabulary is to read extensively.

Anatomy of a CAT Sentence   Completion Question Before getting to the strategies, let us understand what a Sentence Completion question looks like. Sentence completion questions consist of an incomplete sentence that includes one or two blanks, followed by five answer choices. Consider the following example: Despite Tendulkar’s _____ efforts, the team still suffered a _____ loss. A.  complicated . . modest B.  daring . . beneficial C.  generous . . constructive D.  heroic . . devastating (Answer) E.  selfish . . desperate

General Strategies for Sentence   Completion Questions Every sentence contains hints that will help you select the correct answer. Each of the following strategies will help you decipher those hints, but remember that any given question might require you to use more than one approach: 1.  Predict the best fit for the sentence. 2. Use context, prefixes, suffixes, and cognates to define unfamiliar words. 3.  Identify “clue” words and phrases. 4.  Use connotation. 5.  Watch for idiom. 6.  Select an answer. 7.  Questions with two blanks.

1.  Predict the best fit for the sentence Before you look at the answer choices, think of a word that “Fits” the sentence. CAT sentence completion questions usually test the standard meaning of a word. Pay attention to the logic and context of the sentence. Try to predict a word to insert in the blank or blanks as you read the sentence, and then look for your word or a synonym of your word among the answer choices. A synonym is a word with the same or a similar meaning. You should also look for antonyms, which are words that have the opposite meaning of your predicted word. If you locate any words among the answer choices that have a meaning opposite to the word that you would like to insert in the blank, eliminate those answer choices. You should immediately begin to pick up on the idea the sentence is trying to convey, as well as any suggestions of tone or mood. Understanding the general meaning and nature of the sentence will help you to choose the most logical and stylistically appropriate answer.

Example Crestfallen by having done poorly on the CAT, Akansha began to question her abilities. Her self-confidence was _____ A.  appeased D.  elevated

B.  destroyed E.  sustained

C.  placated

If somebody is crestfallen (despairing) and has begun to question herself, then her self-confidence would be destroyed. Hence, the answer is (b). 2.  Use Context, Prefixes, Suffixes and Cognates to Define Unfamiliar Words Understanding the context of a sentence also helps to determine the meaning of any unfamiliar words you might encounter. Consider the following example: Although the fossils were well preserved, paleontologists were unable to _____ the identity of the mammal species. A.  display D.  embellish

B.  ascertain D.  exploit

C.  violate

The best answer is B. You might not have heard the word “paleontologists” before, but you can deduce from the context of the sentence that they are most likely the scientists who study fossils. Another hint provided by the context is the word “although,” which suggests a contrast between the condition of the fossils and the ability of the paleontologists to identify the species. Now, you can insert the words in the answer choices into the sentence to see which one best fits the context. It does not make sense that scientists would “display” or “violate” the identity of a mammal species, so eliminate answer choices A and C. Likewise, scientists might “embellish” or “exploit” certain findings, but these words do

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not accurately describe what the scientists might do with the identity of a mammal species. If you did not know the meaning of “ascertain,” you could arrive at it as the correct choice by using the context of the sentence to help you eliminate incorrect answer choices. Also, if you have trouble establishing the meaning of an unfamiliar word from the context of the sentence, you can use your knowledge of prefixes and suffixes to help you. For example, the prefix “multi-” means “many,” as in “multinational,” and the suffix “-less” means “without,” as in “careless.” Lastly, look for any recognizable cognates from French, Spanish, or Italian (the modern versions of Latin) in words that you are not familiar with. A cognate is a word that means the same or nearly the same thing in more than one language. For example, the word amigo, which means friend in Spanish, the word ami, which means friend in French, and the word amicable, which means friendly in English, all come from the Latin root word for friend, amicus. 3.  Identify “Clue” Words and Phrases/Be Alert To Transitional Words. Transitional words tell you what is coming up. They indicate that the author is now going to draw a contrast with something stated previously, or support something stated previously.

A.  Contrast Indicators To contrast two things is to point out how they differ. In this type of sentence completion problem, we look for a word that has the opposite meaning (an antonym) of some key word or phrase in the sentence. Following are some of the most common contrast indicators: But

Yet

Despite

Although

However

Nevertheless

And

Also

Furthermore

Likewise

In Addition

For

Example Harshit is an opprobrious and _____ speaker, equally caustic toward friend or foe—a true curmudgeon. A.  lofty C.  retiring

B.  vituperative C.  unstinting D.  laudatory

“And” in the sentence indicates that the missing adjective is similar in meaning to “opprobrious,” which is very negative. Now, vituperative—the only negative wordmeans “abusive.” Hence, the answer is (b).

C.  Cause and Effect Indicators These words indicate that one thing causes another to occur. Some of the most common cause and effect indicators are Because

For

Thus

Hence

Therefore

If , Then .

Example Because the House has the votes to override a presidential veto, the President has no choice but to _____ B.  abdicate E.  compromise

C.  abstain

Since the House has the votes to pass the bill or motion, the President would be wise to compromise and make the best of the situation. The answer is (E).

Although the warring parties had settled a number of disputes, past experience made them _____ to express optimism that the talks would be a success. B.  ambivalent E.  reticent

Supporting words support or further explain what has already been said. These words often introduce synonyms for words elsewhere in the sentence. Following are some common supporting words:

A.  object D.  capitulate

Example

A.  rash D.  overjoyed

B.  Support Indicators

C.  scornful

“Although” sets up a contrast between what has occurred—success on some issues—and what can be expected to occur--success for the whole talks. Hence, the parties are reluctant to express optimism. The common word “reluctant” is not offered as an answer-choice, but a synonym—reticent—is. The answer is (E).

Apposition This rather advanced grammatical structure is very common on the CAT (Don’t confuse “apposition” with “opposition”: they have opposite meanings.) Words or phrases in apposition are placed next to each other, and the second word or phrase defines, clarifies, or gives evidence to the first word or phrase. The second word or phrase will be set off from the first by a comma, semicolon, hyphen, or parentheses. Note: If a comma is not followed by a linking word—such as and, for, yet—then the following phrase is probably appositional.

English Usage  Identifying an appositional structure, can greatly simplify a sentence completion problem since the appositional word, phrase, or clause will define the missing word.

Example Man has no choice but to seek truth, he is made uncomfortable and frustrated without truth—thus, the quest for truth is part of what makes us _____ . A.  noble D.  intelligent

B.  different E.  aggressive

C.  human

Solution:  If man has no choice but to seek truth, then this is an essential characteristic of man. In other words, it is part of what makes us human. Though he claimed the business was _______, his irritability _______ that claim.

A.  sound . . belied B.  expanding . . supported C.  downsizing . . vindicated D.  static . . contradicted E.  booming. . affirmed

Solution:  If the business was not sound, his irritability would belie (contradict) his claim that the business was sound.

4.  Use Connotation Each word expresses two things: a definition and a connotation. A connotation is a positive, negative, or neutral feeling that is implied by or associated with a word. Although context is the part of a sentence that surrounds a particular word or passage and determines its meaning, connotation refers to the emotion that is suggested by the word itself. For example, the adjective “thrifty” implies a positive connotation, whereas the adjective “cheap” implies a negative connotation. Both words have similar definitions, but very different connotations. Using connotations can help you determine the correct answer or at least eliminate a few wrong answers. Here is an example of how to use connotation to select the correct answer: Because of his _____, Max’s guests felt very welcome and comfortable staying at his house for the weekend. A.  animosity B.  hospitality C.  determination D.  wittiness E.  severity

  2.85

The best answer is B. The sentence has a positive connotation—Max’s guests feel welcome and comfortable. In addition, the transition “because” indicates that something that belongs to Max has caused his guests to feel welcome and comfortable. “Animosity” and “severity” have a negative connotation and “determination” has a neutral connotation. “Hospitality” and “wittiness” both have positive connotations, but “hospitality” best fits the context of the sentence.

5.  Watch for Idiom Idiom refers to the common or everyday usage of a word or phrase. Learn to recognize idiomatic words and phrases, as they might provide additional clues regarding the intended meaning of the sentence. Idiom is part of standard written English, and must be considered when answering this type of CAT question. Ask yourself if the completed sentence “sounds” correct, and make sure that the sentence effectively combines words into phrases that express a logical idea. If any portion of the sentence becomes unclear, wordy, or awkward after you insert an answer choice, eliminate that choice.

6.  Select an Answer Before you look at the answer choices, try to predict an answer. If your predicted word or words match one of the answer choices, it is most likely the correct choice. Remember that the test writers create incorrect answers in an attempt to distract you—if you predict an answer you are less likely to get caught up on these confusing incorrect answers. Be careful to consider all of the choices before you confirm your answer, even if your predicted answer is among the choices. The difference between the best answer and the second best answer is sometimes very subtle. When you think that you have the correct answer, read the entire sentence to yourself, using your choice(s).

7.  Questions with Two Blanks If a sentence has two blanks, you can quickly eliminate incorrect answer choices if any word alone does not fit into the blank. When you select an answer choice for a two blank question, always ensure that both the words make sense in the sentence, both logically and stylistically. It helps to focus on one blank at a time. You can start with either the first or the second blank. Remember that if one word in the answer choice doesn’t fit within the context of the sentence, you can eliminate the entire answer choice. Work on both blanks together only if you have not been able to eliminate all of the incorrect answers.

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  PRACTICE EXERCISE  1 6. As the employee’s motives were found to be ______, no disciplinary action will be taken against him for the mistake.

Direction for questions 1 to 10:  The following sentences each contain one or two blanks, indicating that something has been left out of the sentence. Each answer choice contains one word or a set of words. Select the word or set of words, that, when inserted in the blank(s), best fits the context of the sentence.

1.  absurd 4.  benign

2.  rescinded 5.  belied

3.  improvised

7. Devesh loves roses for the ______ appeal of their petals and leaves, while I am most ______ by their olfactory properties.

1. Her concern for the earthquake victims _________ her reputation as a callous person. 1.  restored 4.  roved

2.  gratuitous 5.  intentional

1.  aesthetic . . enthralled

3.  created

2.  acrid . . interested 3.  nurturing . . persuaded

2. The author presumably believes that all businessmen are _________, for her main characters, whatever qualities they may lack, are virtual paragons of _________.

4.  visual . . displeased 5.  tacit . . disenchanted

1.  clever . . . ingenuity 2.  covetous . . . greed

8. His ______ for learning history should prove to be ______ during his studies to become a history teacher.

3.  virtuous . . . deceit

1.  disdain . .useful

4.  successful . . . ambition

2.  penchant . . practical

5.  cautious . . . achievement

3.  dislike . . exceptional 4.  affinity . . futile

3. Lacking sacred scriptures or __________, Shinto is more properly regarded as a legacy of traditional practices and basic values than as a formal system of belief. 1.  followers 4.  relics

2.  customs 5.  faith

3.  appreciation . . gratuitous 9. We felt ______ once the committee issued its report that ______ our actions.

3.  dogma

1.  angered . . supported

4. Male sperm whales are normally _________ creatures; however, when they are jealously guarding their territory, they have been known to _______ ships.

2.  abused . . endorsed 3.  vindicated . . authenticated 4.  helpless . . applauded

1.  docile . . . attack 2.  aggressive . . . strike

5.  ignorant . . dignified

3.  large . . . assault

10. The air in a room that contains several houseplants can be more ______ oxygen than a room that contains no plants.

4.  peaceful . . . ignore 5.  powerful . . . assail



5. Her charisma was a double-edged sword; in her friends, it aroused both admiration and __________. 2.  laudation 5.  affection

ANSWER KEYS

1.  envy 4.  obstinacy

3.  equanimity

1.  enjoyed by 2.  exhausted with 3.  obscured by 4.  saturated with 5.  complicated by

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English Usage 

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HINTS AND EXPLANATIONS 1. Callous means unfeeling, uncaring, but if this person has concern for the earthquake victims, her reputation must be an unfounded one, so the correct choice will mean contradicted or proved false. This is one of the meanings of belied, correct choice e. b, rescinded is the second best answer. It means revoked or withdrawn, but you don’t say that a reputation is rescinded. a, c, and d are the opposite of what we’re looking for—they don’t make sense in this context.



2. The author mentioned in this sentence believes that businessmen are models of some quality; whatever qualities they may lack implies that whatever bad points they possess, there’s this one particular good thing about them. All of this should lead you to a—if an author’s main characters are businessmen, and if they’re all paragons of “ingenuity” (meaning inventively talented), one could easily be led to the presumption that the author thinks all businessmen are “clever.”

5. A major sign here is the semicolon between the two clauses, signaling a continuation or consistency between the two parts. If her charisma is a double-edged sword, then it has contrasting points—good aspects and bad. The clause after the semicolon will elaborate on or give an example of these conflicting sides. In the second clause, we find that even in those who like her, her charisma arouses admiration, which would be the good side of the sword, and something else, which must be the bad side. This blank must be filled with a negative word.



    Several of the wrong answers play off your possible biases about people in the business world, B being the most blatant in that regard. That choice is tempting only because an author’s use of many “greedy” businessman characters might suggest that the author thinks all businessmen are “covetous.” But labeling businessmen as greedy contradicts the sense of “whatever qualities they may lack”—as we noted, we need a positive quality (also, paragons of greed is awkward). One who is morally upright or “virtuous” C would hardly be a paragon of “deceit” (lying, falseness). Characters possessing great “ambition”, d, wouldn’t necessarily make one presume that the author believes all such people are “successful,” since ambition and success in a field don’t always go hand in hand; and there’s even less connection between businessman characters who demonstrate great “achievement”, e, and a conclusion that, in the author’s opinion, all businessmen are “cautious.”

3. We’re looking for something that goes with sacred scriptures and implies a formal system of belief, but something whose absence doesn’t rule out a legacy of traditional religious practices and basic values. We can eliminate choices A, B, and E because if Shinto lacked followers, customs, or faith it wouldn’t be a legacy of traditional religious practices and basic values. Relics, D, are sacred objects but relics don’t make something a formal system of beliefs. The best choice is C—a dogma is a formal religious belief. 4. The first blank here will be filled with a word that describes what type of creatures male sperm whales normally are. The word “however” between these clauses indicates that a contrasting point will be made—these whales are normally something, but sometimes can be different. A clue in the second clause helps us figure this one out. In the second clause, we learn that something happens when the whales are jealously guarding their territory. They probably act aggressively or violently when guarding their territory, so the first blank will be a contrast to this. It must suggest that whales are not normally violent. The second blank will be filled with a word that tells us what the whales do to ships when are guarding their territory.

    A good prephrase for this answer would be “these whales are normally peaceful creatures; however when guarding their territory, they have been known to sink ships.

    Starting with the first blank, two choices look good right away, A and D. A also looks good for the second blank, while the second word in D is the opposite of what we need. Quickly checking the other choices, we see that B the words aren’t contradictory, and we need words that are opposite in meaning. C and E can be eliminated because each is a descriptive word that relates to the whale’s physical characteristics rather than its temperament. So the answer is a.



    A prephrase here might be: “Her charisma provoked both admiration and dislike in her friends.”



    Only two choices here have negative meanings, A and D. A makes the most sense since charisma could easily invoke envy in others. D, obstinacy, is negative as well but means stubbornness; this answer does not make sense in the sentence. The remaining choices can be ruled out because they are positive in meaning, so the answer is a.

6. The context of the sentence indicates that the employee will not be disciplined as a result of his mistake, which suggests that the error was not intentional, and that the employee meant no harm. The word “benign” means “harmless,” so it is the best choice based on the context of the sentence. 7. The best answer is a. Because the sentence indicates that Devesh “loves roses,” the word that best fits in the first blank should have a positive connotation. The first word in answer choice B has a negative connotation, and the first words in both answer choices D and E have neutral connotations, so none of those choices will be best. “Aesthetic” refers to “the appreciation of beauty,” which makes the most sense in this sentence. Likewise, “enthralled,” which means “captivated,” works well in the second blank. 8. To have a “penchant” for something means to have a fondness for it. A fondness for history would be practical or helpful for future studies in the field. Answer choices A and C are incorrect because anyone having “disdain” (hate) or “dislike” for history would certainly not study to become a history teacher. 9. “Vindicated” means “cleared of suspicion or doubt” and “authenticated” means “proved to be genuine.” The rest of the answer choices are contradictory in nature and do not fit the context of the sentence. 10. The word “saturated” most accurately indicates the density of the oxygen in the room. The other answer choices do not fit the context of the sentence.

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  PRACTICE EXERCISE  2 Direction for questions 1 to 20:  The following sentences each contain one or two blanks, indicating that something has been left out of the sentence. Each answer choice contains one word or a set of words. Select the word or set of words, that, when inserted in the blank(s), best fits the context of the sentence.

1.  thwarting

1. Because of his success as a comedian, directors were loath to consider him for ___________ roles.

7. These categories amply point out the fundamental desire that people have to express themselves and the cleverness they display in that expression; who would have believed that the drab, mundane DMV would become the ___________ such creativity?



1.  supporting 2.  leading 3.  dramatic 4.  comedic 5.  musical

2. The aspiring candidate’s performance in the debate all but __________ any hope he may have had of winning the election. 1.  nullifies 2.  encourages 3.  guarantees 4.  accentuates 5.  contains 3. She is the most ____________ person I have ever met, seemingly with an endless reserve of energy.

1.  jejune 2.  vivacious 3.  solicitous 4.  impudent 5.  indolent

4. Despite all its ___________, a stint in the diplomatic core is invariably an uplifting experience. 1.  merits 2.  compensation 3.  effectiveness 4.  rigors 5.  mediocrity 5. Liharev talks about being both a nihilist and an atheist during his life, yet he never does ___________ faith in God. 1.  affirm 2.  lose 3.  scorn 4.  aver 5.  supplicate 6. Existentialism can be used to rationalize evil: if one does not like the rules of society and has no conscience, he may use existentialism as a means of ___________ a set of beliefs that are advantageous to him but injurious to others.

2.  proving 3.  promoting 4.  justifying 5.  impugning



1.  catalyst for 2.  inhibitor of 3.  disabler of 4.  referee of 5.  censor of

8. This argues well that Chandresh exercised less free will than Ashutosh; for even though Chandresh was aware that he was misdirected, he was still unable to ______ _____ free will. 1.  defer 4.  prevent

2.  facilitate 5.  exert

3.  proscribe

9. Man has no choice but to seek truth, he is made uncomfortable and frustrated without truth—thus, the quest for truth is part of what makes us ___________. 1.  noble 4.  intelligent

2.  different 5.  aggressive

3.  human

10. Though most explicitly sexist words have been replaced by gender-neutral terms, sexism thrives in the _______ ____ of many words. 1.  indistinctness 2.  similitude 3.  loquacity 4.  implications 5.  obscurity 11. Though a small man, Abdul Kalam appeared to be much larger behind his desk; for, having skillfully designed his office, he was ___________ by the perspective. 1.  augmented 2.  comforted 3.  apprehended 4.  lessened 5.  disconcerted

English Usage  12. Man is violent and therefore any theory of conflict resolution between nations that ___________ to account for this is ___________ flawed. 1.  declines . . supposedly 2.  refuses . . pejoratively 3.  fails . . . inherently 4.  consents . . manifestly 5.  flinches . . innately



1.  a dogma 2.  a study 3.  a profession 4.  a philosophy 5.  a lifestyle

1.  impassive to 2.  indifferent to 3.  imperiled by 4.  sensitive to 5.  inured to

18. In spite of the _______ vista of the country dismantled by war and its development clogged by illiteracy, locals like to _______ their nationalism. 1.  sickening . . unveil 2.  diverse . . exhibit

14. Although the buildings and streets of this small beach town appear ______, the property values are quite ___ _________.

3.  unruly . . curb 4.  picturesque . . conceal 5.  chaotic . . flaunt

1.  expensive . . steep 2.  dilapidated . . high 3.  artistic . . pedestrian 4.  refurbished . . low 5.  quaint . . reasonable

19. The citizenry had become so __________ by the government’s ______________ that the latest financial scandal did not even make the front page of the newspapers. 1.  fascinated . . impropriety

15. Though he claimed the business was ___________, his irritability ___________ that claim.

1.  comparable 2.  menacing 3.  alternative 4.  augmented 5.  extraordinary

17. Despite its lofty goal –truth- many scholars maintain that law as ___________ is a highly regulated street fight.

13. Ironically, the foreign affairs policies of democracies are more likely to meet with protests than similar policies of totalitarian regimes because a democracy is ___ ________ protest; whereas in a totalitarian regime, no one is listening.

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2.  disgusted . . peccadilloes 3.  distraught . . magnanimity

1.  sound . . belied 2.  expanding . . supported 3.  downsizing . . vindicated 4.  static . . contradicted 5.  booming. . affirmed

4.  regretful . . personification 5.  jaded . . indiscretions 20. In these politically correct times, it has become _____ ______ to discuss certain subjects at all.

ANSWER KEYS

16. The rules of engagement for United Nations troops stationed in Bosnia prohibit deadly force unless all ________ actions have been exhausted.

1.  safe 4.  efficacious

2.  eccentric 5.  effortless

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3.  precarious

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  Verbal and Logical Reasoning

HINTS AND EXPLANATIONS 1. If the public expects a comedian to always make them laugh, then

they might not accept a comedian in a serious role. Hence, the directors would be loath (reluctant) to cast a comedian in a dramatic role. The answer is (3).

2. The phrase “all but” implies that the debate was a make-or-break event for the candidate. Suppose the candidate did well. Then his spirits would be high, and we would expect the missing word to be positive. However, a positive word in the phrase “all but _________ any hope” is awkward. Hence, the candidate must have done poorly in the debate and had his hopes for election nixed. So we turn to the answer-choices looking for “nixed.” It’s not there, but a synonym— nullifies—is. The answer is (1). 3. Since no connecting word—such as and, for ,so, etc.,—follows the comma, the phrase “seemingly with an endless reserve of energy” defines the missing word. Now, a person with an endless reserve of energy would be lively, which is the meaning of “vivacious.” The answer is (2). 4. “Despite” sets up a contrast between the key phrase “uplifting experience” and the missing word. The implication is that in spite of the rewards, the job is harsh and trying; in other words, rigorous. The answer is (4). 5. “Yet” draws a contrast between what one would expect an Atheist to do (renounce faith in God) and what Liharev did (maintained faith in God). In other words, he did not lose faith in God. The answer is (2). 6. D To rationalize evil is to make excuses for wrong doing. Now, the words following the colon explain how existentialism can be used to excuse or justify evil. The answer is (4). 7. The phrase “who would have believed” implies that the reality is the opposite of what one would expect. Now, one would not expect the drab DMV to be a catalyst for creativity. The answer is (1). 8. The sentence implies that even when Chandresh knows he is taking the wrong path in life, he still cannot stop. That is, he cannot exert free will. The answer is (5). 9. If man has no choice but to seek truth, then this is an essential characteristic of man. In other words, it is part of what makes us human. The answer is (3).

10. The sentence is saying that although a word may not be explicitly sexist it may contain sexist connotations or implications. The answer is (4). 11. The passage states that when sitting behind his desk Abdul Kalam looked larger than he actually was. So the perspective must have increased the appearance of his size. The only word that means to increase is “augmented.” The answer is (1). 12. Since man is violent, any useful theory of conflict resolution must incorporate this fact. The answer is (3). 13. The clause “whereas in a totalitarian regime, no one is listening” implies that a democracy does listen to protests. In other words, it is sensitive to protests. The answer is (4). 14. “Although” sets up a contrast between what the property values are (high) and what one would expect them to be in a dilapidated (run down) community. The answer is (2). 15. If the business was not sound, his irritability would belie (contradict) his claim that the business was sound. The answer is (1). 16. The word “exhausted” implies that all other actions (alternatives) have been tried. The answer is (3). 17. The sentence is pointing out that as a practical matter the legal profession pursues the truth through a rough and tumble path. The answer is (3). 18. The country under consideration has been dismantled by war and its development clogged by illiteracy. The author describes the overall situation of the country as “chaotic.” One would expect the citizens to feel disgrace in such a situation. But the locals still “flaunt” their nationalism. The answer is (5). 19. A financial scandal is an indiscretion; and it may not have made the front page because the public was jaded (worn out) by an excess of scandals. The answer is (5). 20. The sentence is suggesting that it is risky to discuss certain subjects regardless of what you say. The answer is (3).

  PRACTICE EXERCISE  3 Direction for questions 1 to 14:  The following sentences each contain one or two blanks, indicating that something has been left out of the sentence. Each answer choice contains one word or a set of words. Select the word or set of words, that, when inserted in the blank(s), best fits the context of the sentence. 1. By ________ celebrities from the sports, entertainment, or business arenas, the show narrates the stories of the ________ newsmakers from all walks of life.



1.  displaying . . pedestrian 2.  profiling . . influential 3.  parading . . effective 4.  narrating . . dominating 5.  setting forth . . ordinary

2. Behind their strange appearance and ________ for carrion, which has long singled them out for fear and loathing, hyenas present a ________ society in which females dominate.

English Usage 

1.  longing . . contrastive 2.  penchant . . realistic 3.  proclivity . . virtual 4.  appetite . . matriarchal 5.  yearning . . monarchal

3. At the cutting edge of research, scientists are developing new sunscreens of both ________ and internal varieties. 1.  polar 2.  tropical 3.  territorial 4.  atmospheric 5.  regional 4. Although the AIDS epidemic is in the limelight, there is a silent killer _______ through India, killing more people than AIDS itself. The _______ is that, unlike AIDS, this disease is easily cured. 1.  storming . . satire 2.  flaming . . ridicule 3.  raging . . parody 4.  rampaging . . irony 5.  traducing . . sarcasm 5. Knowing Hrithik was overshadowed by many other actors, she knew she was indulging in a bit of _______ when she wondered whether Hrithik was the greatest living actor ever. 1.  irony 2.  overemphasis 3.  understatement 4.  hyperbole 5.  injustice 6. Their courage is only _______, and a small show of strength is enough to call their bluff. 1.  ostentation 2.  fortitude 3.  temperament 4.  exhibition 5.  bravado 7. Life, as the film demonstrates, is too complex for _______ endings. 1.  facile 2.  intricate 3.  straight 4.  occult 5.  recognizable 8. Today, plastic has proved to be a _______ to the environment; the world over, steps are being taken to ban the _______ and non-recyclable material, which has silently taken over our lives. 1.  boon . . ominous 2.  threat . . jeopardizing

  2.91

3.  menace . . non-eco-friendly 4.  inauspicious . . disastrous 5.  perquisite . . deleterious 9. While environmentalists and NGO’s have welcomed the move, there has been strong _______ from many a quarter.

1.  opposition 2.  rivalry 3.  approval 4.  defiance 5.  acceptance

10. Suicide is the outcome of man’s difficulty to _______ himself in society, so he does not feel isolated.

1.  materialize 2.  isolate 3.  homogenize 4.  secure 5.  integrate

11. Some are born with a _______ to commit suicide, whereas some commit suicide because they are unable to bear _______ changes in their lives.

1.  sentiment . . inimical 2.  resolution. . adverse 3.  predisposition. . cataclysmic 4.  prognosis. . miserable 5.  prodigy. . abrupt

12. It is a situation with a hard, practical edge which raises issues of life-threatening _______ and therefore demands to be addressed with cool, clear-headed _______.

1.  existence . . involvement 2.  incidents . . erudition 3.  evidence . . cognizance 4.  illustrations . . expedience 5.  immediacy . . pragmatism

13. We landed at the airport with _______ notions of the country as _______ country where many parents are alleged to have sold their children in exchange for food.

1.  paradoxical . . an abounding 2.  incongruous . . an opulent 3.  preconceived . . an impoverished 4.  unwarranted . . an impotent 5.  germane . . a prolific

14. Located amidst the colossal green hills, what might have otherwise been _______ airfield in _______ part of the North assumed the overtones of the battlefield.

1.  an impressive . . an alien 2.  a blood-shattered . . an estranged 3.  a combatant . . a war torn 4.  a picturesque . . an exquisite 5.  a reposeful . . a hostile

  Verbal and Logical Reasoning

ANSWER KEYS

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2

2.

4

3.

2

4.

4

5.

4

6.

5

7.

1

8.

3

9.

1

10.

5

11.

3

12.

5

13.

3

14.

4

HINTS AND EXPLANATIONS 1. The show was organized to tell the stories of successful celebrities. By “profiling” these celebrities, the show narrates the stories of the “influential” newsmakers from all walks of life. The answer is (2). 2. Since hyenas eat carrion (decaying flesh), they have an “appetite” for it. A society ruled by females is called “matriarchal.” The answer is (4). 3. The word “both” in the statement implies there are two different types of sunscreen. Since one is internal, the other one should be external or at least of a different type. The choices “territorial,” “atmospheric,” and “regional” do not imply the opposite of internal. “Polar” and “tropical” may indicate other varieties. Sunscreens are not used in polar regions; they are used in tropical regions. Hence, the answer is (2). 4. The first sentence describes AIDS as a big threat; it also describes another disease that is unreported and is on a greater rampage. Yet, the author says there is a cure for this silent killer. It is ironic that the silent killer causes more harm than AIDS, yet it is curable. The answer is (4). 5. The statement implies that Hrithik is certainly not the greatest Indian actor. To believe him to be the greatest actor would be to indulge in “hyperbole.” The answer is (4). 6. The word “only” in the first clause limits the meaning of courage: They have courage, but only to a point. The word “bluff ” in the second clause indicates that their courage is merely bluster. This is the meaning of “bravado.” The answer is (5). 7. The phrase “too complex for” indicates that the missing word should have the opposite meaning of the word “complex.” The opposite of complex is simple. Now, “facile” means simplistic, superficial. The answer is (1). 8. The second clause states that worldwide steps are being taken to ban plastic. The word “and” joining the two clauses of the sentence indicates that the first clause should provide a reason for the worldwide ban of plastic. The reason is that plastic is proving to be

a menace to the environment. The second blank needs to be filled by a word that supports the statement and shows the negative consequences of plastic usage. The suitable word is “non-eco-friendly.” The answer is (3). 9. The word “while” indicates a contrast between what is expressed in the first clause (welcoming the move) and what is expressed in the second clause (opposing the move). The answer is (1). 10. Man is a social being; and to function properly, he needs to be an integral part of society. When a person fails to integrate himself into society, he often feels alienated and incomplete, which, without a social support system, can lead to suicide. The author believes that those who commit suicide do so because they are unable to integrate themselves into the society. The answer is (5). 11. The author states that some people are born with an inclination to commit suicide. Though the remaining people who have committed suicide do not have such a predisposition, they commit it because they are unable to bear sudden cataclysmic changes that occur in their lives. The answer is (3). 12. According to the author, the core issue involves a hard, practical point that is to be dealt with a pragmatic approach. Pragmatism means “practical approach.” The author stresses the immediacy of the situation since it is raising life threatening issues. The answer is (5). 13. One would reasonably assume (preconceive) that a state where parents are alleged to have sold their children in exchange for food is an “impoverished” state. The answer is (3). Note, (4) is the secondbest choice. Although an impoverished state is probably impotent, impoverished describes the situation better. Further, the sentence does not imply that the preconceived notions of the state were unwarranted (not justified). 14. The sentence implies that the location, though having splendid natural settings, is distressed by the ongoing battle. We can observe from the structure of the sentence that both blanks explain the natural beauty of the location. The author implies that if the location had no overtones of the battlefield, it would have been a “picturesque” airfield in an “exquisite” part of the North. The answer is (4).

  PRACTICE EXERCISE  4 Direction for questions 1 to 13:  Choose the option that fills the maximum number of blanks. The world may need some change of form. 1. A. I jumped up too quickly and got a ________on

the head. B. He had a big ___________ for his twenty -first birthday.

C. Learning Russian is very interesting, why don’t you have a ______at it? D. Oh well, that’s enough chatting, I suppose I’d better ________on with this essay. 1.  bash

2.  bang

3.  work

4.  get

English Usage  2. A.  A _______of experts is going to study the case. B.  The torch failed to work as it ran out of _____

  2.93

C. Since he had nothing worthwhile to do for the rest of the afternoon, he had to _______off.

C.  They refused to eat eggs laid by _______hens

D.  Never ______when an insomniac can hear you.

D.  The shore _______opened fire.

1.  rest

1.  battery

2.  group

3.  power

4.  artillery

3. A.  We sailed into a beautiful and secluded _____ B.  A frightened animal at _____can turn violent. C.  Exercise can help keep fat at_______ D. Mom added some ___leaves to the Rasam to improve its flavour. 1.  rest

2.  bay

3.  edge

4.  shore

4. A. We could just pick out the path in the weak _____ of the torch. B. If you’re on your ______ends you have little or no money left.

2.  sleep

3.  doze

4.  snore

8. A. The government must _______ahead with reforms at a greater pace. B.  The fiscal ______initiated the recession of 1992. C. If proper simulation of working conditions is done, it will be easy to _______the correct panic buttons when required. D. The officer will ______ you from seeking greener pastures abroad. 1.  squeeze

2.  press

3.  prohibit

4.  pull

9. A. Restructuring the PSU management is a _____ task indeed. B.  To be _____, he did not really try hard enough.

C. You could see his face ______with joy on hearing the news of his selection to IIM-A.

C. Be clear about your goals and even the most _____ __challenges will look like child’s play.

D.  Syringes are sterilized using election _____

D. To attain exceptional heights, you ought to be ____ ___and honest.

1.  beam

2.  fag

3.  suffuse

4.  ray

5. A.  This product has made its own ______on the market.

1.  daunting

B. The forging machine has to _______the steel blocks to smaller shapes.

10. A.  She trains guide dogs for the ________

C. This document requires the official ______ of the collector. D. Please affix the ________properly otherwise it may fall from the envelope. 1.  mark

2.  stamp

3.  cachet

4.  seal

6. A. Never _____excessively greasy food—it is bad for the heart. B. He had to _____the whole cup of wine in one go as the train was about to leave. C. The emergency button in the cockpit should theoretically _____the pilot in the desired direction. D. The authorities were forced to _________humble pie when their blunder was highlighted by the newspaper. 1.  drink

2.  gulp

3.  eat

4.  eject

7. A. ‘Do not __________on your oars,’ warned the teacher. B. The ______of the document should be checked by a senior.

2.  arduous 3.  upright 4.  honest

B.  A Venetian ______covers the window. C.  He was ______ drunk. D.  It can be very dangerous if there is a vehicle in your _______spot. 1.  deaf

2.  window

3.  blind

4.  rough

11. A. Please print your name and address in ______in letters. B.  My friend and I live on the same ______ C.  I’m not going to put my head on the ______for you. D.  Every autumn dead leaves _______the drains. 1.  capital

2.  block

3.  stop

4.  range

12. A.  My nose is choked, I need to _______it B.  He lifts weights after work to ______off steam. C. My father will ______his top when he sees what happened to the car.

2.94 

  Verbal and Logical Reasoning

D.  Her death at twenty came as a _______to her parents. 1.  blow

2.  feed

3.  rough

B. He’s been feeling really _______since he failed his exams. C.  ______collar jobs are on the rise.

4.  smash

D.  He has a bath once in a ______moon.

ANSWER KEYS

13. A. His type of humour is a bit too ______for my tastes.

1.  full

2.  pleasant

3.  rare

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4.  blue

HINTS AND EXPLANATIONS 1. ‘Bash’ fills the blanks, in A, B and C (maximum number). In

8. The word ‘press;’ fills the blanks in A and C (maximum number). The word ‘squeeze’ (1) fills the blank only in B. The word ‘prohibit’ (3) fills the blank only in D. The word ‘pull’ (4) fills no blank. Hence, option (2) is the correct option.

2. ‘Battery’ fills the blanks in A, B and C (maximum number). In options (2), (3), (4), ‘group’ and ‘power’ fill no blanks , ‘artillery’ fills the blanks only in D all the three options are wrong.

9. The word ‘daunting’ (1) fills the blanks in A and C (maximum number). The word ‘arduous’ (2) fills no blank. The word ‘upright’ (3) fills the blank only in D. The word ‘honest’ (4) fills the blank only in B. Hence, option (1) is the correct option.

options (2), (3), (4), ‘bang’ fills the blanks in only A, ‘work’ does not fill any blank, and ‘get’ fills the blank in only D, so these three options are wrong.

3. ‘Bay’ fills the blanks in A, C and D (maximum number). In options (1), (3), (4), ‘rest’ fills the blank in only B, ‘edge’ and ‘shore’ fill no blank thus they are wrong. 4. ‘Beam’ fills the blanks in A, C and D (maximum number). In options (2), (3) and (4) ‘fag’ fills the blank in only B, ‘suffuse’ and ‘ray’ fill no blank, so the three options are wrong. 5. The word ‘stamp’ (2) fills the blanks in C and D (maximum number) ‘Mark (1) fills the blank only in A. No word fills the blanks in B. The words ‘cachet’ (3) (distinguishing mark or seal) and ‘seal’ (4) fill no blank. Hence, option (2) is the correct option.

10. The word ‘blind’ fills the blanks in A, B, C (‘blind drunk’, means ‘extremely drunk’). The words ‘deaf ’ (1) ‘window’ (2) and ‘rough’ (4) fill no blanks. So options (1), (2) are wrong. 11. The word ‘block’ fills the blanks in A (‘block letters mean capital letter)’ B (‘block means ‘a large building’ especially when subdivided into flats), C (‘put the head on the block’ means ‘risking reputation or position by taking particular course of action) and D (‘block’ means to obstruct a passage etc.,) Words ‘capital’ (1), stop (3) and ‘range (4) fill no blank, options (1), (3), (4) are wrong.

6. The word ‘eat’ (3) fill the blank in A and D (maximum number) (‘eat humble pie’ means ‘make a humble apology, accept humiliation’). The word ‘drink (1) fills no blank. the word ‘gulp’ (2) fills the blank only B. The word ‘eject’ (4) fills (4) fills the blank only C. Hence, option (3) is correct option.

12. The word ‘blow’ fills the blanks in A (‘blow’ means ‘clear the nose of mucus by blowing) , B (‘blow off ’ means ‘to remove the pent up steam’), C (‘blow, one’s top’ means ‘explode in ranger’) and D(‘blow’ means ‘a sudden shock or misfortune’). Words ‘feed (2) ‘rough’ (3) and ‘smash’ (4) fill no blanks. So options (2), (3), (4) are wrong.

7. The word ‘rest’ (1) fills the blanks in A and B (maximum number) (‘rest on your oars’ means ‘relax one’s efforts’). The word ‘sleep’ (2) fills no blank. The word ‘doze’ (3) fills the blank in C (‘doze off mans ‘fall lightly asleep’). The word ‘snore’ (4) fills the blank in (D). Hence, option (1) is the correct option.

13. The word ‘blue’ fills the blank in A (‘blue’ means ‘ depressed’; gloomy dismal, sad’) b (‘blue’ means ‘sad, gloomy ) C( ‘blue collar jobs’ means manual or industrial jobs’). And D (‘blue moon’ means ‘very rarely ‘). The word ‘full’ (1), ‘pleasant’ (2) and ‘rare’ (3) fill no blanks.

English Usage 

  2.95

  PRACTICE EXERCISE  5 Direction for questions 1 to 9:  Each sentence below has three blanks, each blank indicating a missing set of words. Four numbered sets of words follow each sentence. Choose the option that fits each blank in the context of the whole sentence. 1. The ______difficulties produced by the marriage

_______ prompted some intense ________in Eliot’s poetry.

3.  blindly, profit, management 4.  recently, durability, experts. 6. Then in 1856, a similar skull, __________ in the Neander Valley outside the German city of Düsseldorf, showed that at least one man’s __________ ancestors, later named Neanderthal man, had a low sloping forehead, a receding chin, and thick ridges __________ his eye sockets.

1.  sentimental, clearly, mistakes

1.  found, possible, in

2.  adjustment, obviously, remarks

2.  stalked, surmized, above

3.  emotional, evidently, passages

3.  unearthed, probable, on

4.  familial, glaringly, smiles

4.  stumbled, closest, around

2. Economists engage in ________ enquiry into the effects of those human ________which are grouped under three broad headings: production, ________, and consumption.

7. But five years ago, it could hardly have been _______ ____ that a master’s thesis ____________ this recondite subject, published under the conservative imprint of the University of California Press, would become one of the ________ books of the early `70s.

1.  scientific, acts, redemption 2.  methodical, attitudes, supply 3.  systematic, activities, exchange 4.  pragmatic , function, exchange 3. Taipei is the capital, largest city , and _________, ___ _______, and industrial centre of _______

1.  thought, upon, great 2.  guessed, on, bestselling 3.  considered, about, masterpiece 4.  surmized, over, bestseller

3.  educational, commerce, Taiwan

8. But it’s there too—in the meetings the priests _____ ____ to schedule their planting dates and combat the problem of crop pests; in the plans they _________ up to maintain aqueducts and police conduits; _________ the irrigation proposals they consider and approve, the dam proposals they reject or amend.

4.  educational, commercial, Taiwan

1.  call, set, of

4. Eclecticism from the Greek ‘eklektikos’ (“selective”), is the practice of ________elements _______ in style in a ______ work of art.

3.  preside, step, with

1.  agricultural, educational, world 2.  educational, frugal, Taiwan

1.  compost, different , vague 2.  uniting, several , solid 3.  mixing , diverse, single 4.  converging , unlike, likely 5. It is a _________held belief that ________and productivity are a function of ________or a set of new equipment.

2.  conduct, summon, for 4.  convene, draw, in 9. The ape-like part was above the waist, including the skull—more like a chimp in size than a human—and the arms, with _________ shoulders and long, curving fingers, well __________ to climbing, although is isn’t clear whether they actually did climb ______ ___ this point, or merely retained a more primitive feature. 1.  rounded, adapted, at 2.  moulded, built, around

1.  closely, inefficiency, technology

3.  contoured, grounded, on

2.  commonly, quality, technology

4.  hefty, groomed, within

2.96 

  Verbal and Logical Reasoning

11. Earlier contributors to this discussion have adequately made the _____ point that in the Indian media, over recent years, ______ commercial considerations have increasingly ______ journalistic ethics and editorial ______. spurious, crass, transcended, authority, corruption, maneuvered.

10. The poisoned chalice, as Shakespeare says, will return to_____ its inventor and propagating a culture of compassion and fellow feeling that _______ all barriers and religious labels is ______ and spiritual duty. transcends, dominates, an enunciating, buttress, plague.

12. Is this metamorphosis of the gentleman’s game into a _____ sport deplorable? Not at all, never mind the purists. There is more emotion that will ______ the stars. Despite the tag of being a team game there will be the clash of the ______. frenzy, midgets, glorified, gladiatorial, proscribe, contaminate.

ANSWER KEYS

Direction for questions 10 to 12:  Each question is a sentence that contains blank spaces to be filled in from the words that are given below. The answer would be the number of blanks that get contextually and correctly filled in, with 1, 2, 3 and 4 standing respectively for the number of blanks that are correctly filled in.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

3

3.

4

4.

3

5.

2

6.

3

7.

2

8.

4

9.

1

10.

3

11.

3

12.

1

HINTS AND EXPLANATIONS 1. The words ‘mistakes’, ‘remarks’, and ‘smiles’ in options (1), (2), (4) respectively, are wrong contextually for the third blank. the words ‘sentimental’, adjustment ‘ and ‘familial’ of the same options are not proper for the first blank. The word ‘evidently’ in option (3) has to be preferred to ‘clearly’ , obviously’ and ‘glaringly’ in options (1), (2), (4) respectively .Thus the words ‘emotional ‘ evidently’ and passages in option (3) are correct for the three blanks and options (1), (2) and (4) are wrong. 2. The word ‘redemption’ in option (1) for the third blank is contextually wrong (redemption’ means ‘returns or recovery’). The word ‘attitudes’ in option (2) for the second blank is wrong in the context of ‘economists ‘Supply’ in option (2) will not be proper for the third blank contextually without its counterpart, ‘demand’. The word ‘pragmatic’ in option (4) is not proper contextually for the first blank as an ‘enquiry’ need not be ‘pragmatic’. ‘Function’ in the same option will be grammatically wrong for the second blank in the context of ‘which are’ succeeding it. Thus words ‘systematic’, ‘activities’ and ‘exchange’ in option (3) are correct and options (1), (2) and (4) are wrong. 3. The word ‘World’ in option (1) is wrong grammatically for the third blank. (‘the’ should precede it). ‘Frugal’ of option (2) is inappropriate as it means ‘sparing’. Finally, ‘commerce’ is incorrect in option (3) it should have been ‘commercial’ to fit in. Thus ‘educational’, ‘commercial’ and ‘Taiwan’, in option (4) are correct for the three blanks and options (1), (2) and (3) are wrong. 4. The words ‘compost’ (mixed manure) and ‘vague’ in option (1) for the first and third blanks respectively are wrong contextually

(‘compost’ is wrong grammatically also, following ‘practice of ’). The word ‘likely’ in option (4) is wrong contextually for the third blank as ‘likely work of art’ means ‘nothing’. The word ‘solid’ in option (2) is wrong for the third blank in the context of ‘work of art’. Thus, ‘mixing ‘, ‘diverse’ and ‘single’ in option (3) are correct for the three blanks and options (1), (2) and (4) are wrong. 5. ‘Closely and inefficiency’ in option (1) for the first and second blanks respectively are wrong contextually. The words ‘belief ’ not to be held ‘closely’ are in the context of production. ‘Inefficiency’, preceding ‘productively’ is wrong in the given context. ‘Blindly’ and ‘profit’ in option (3) for the first and second blanks respectively are wrong contextually as ‘belief ’ need not be ‘held’ blindly and ‘profit’ comes in after successfully marketing etc., It is the end-result of all the elements alongside ‘productivity’. Also, in ‘management’ in option (3) for the third blank is not proper because it is a very broad term. ‘Recently’ in option (4) is also wrong for the first blank with ‘held’. Also ‘experts’ doesn’t fit in the third blank. Thus, ‘commonly’, ‘quality’ and ‘technology’ in option (2) are correct as ‘commonly’ is the most appropriate option preceding ‘held belief ’ for the first blank and ‘quality’ and ‘technology’ are the most correct option for the second and third blank respectively. Options (1), (3) and (4) are incorrect in their respective combinations. 6. The expression ‘unearthed’ (discovered by searching or rummaging) has to be preferred for the first blank to any of ‘found’ (1), ‘stalked’ (pursue or approach stealthily), (2) and ‘stumbled’ (found or encountered by chance) (4), ‘stumbled’ also needing a preposition ‘on’ or ‘upon’; ‘probable’ is also apt for the second; preposition ‘on’ has to be preferred to other prepositions, options for

English Usage 

  2.97

the third blank, being correct both grammatically and contextually, ‘above’ (2) and ‘around’ (4) being wrong contextually, ‘over’, (2) and ‘around’ (4) being wrong contextually, ‘over’ evoking a connotation of above, in or to a position higher than what is conceived.

(3); ‘convene’ (summon or arrange) (4) is also appropriate for the first blank following ‘in the meetings the priests’; in (4) is also the most suitable preposition for the third blank in the context of or preceding the ‘irrigation proposals’, hence (4))

7. In the context of or following ‘could hardly have been’ expression, ‘guessed’ has to be preferred for the first blank to any of ‘thought’ (1), ‘considered’ (3) and ‘surmised’ (conjectured about, or suspected the existence of truth of something); preposition ‘on’ is the most suitable, for the second, both grammatically and contextually i.e., preceding ‘this recondite subject’, compared to any of ‘upon’ (up + on) (1), ‘about’ (3) and ‘over’ (4); adjective ‘bestselling’ is also appropriate grammatically and contextually, for the third, compared to ‘great’ (1) ‘masterpiece’ (3) or ‘bestseller’.

9. Adjective ‘rounded’ (given a round shape) (1) is most suitable for the first blank, in the context of preceding ‘shoulders and long, curving fingers’; verb ‘adapted’ (2) is also grammatically suitable for the second blank, preceding ‘well’ and following ‘to climbing’; similarly, preposition ‘at’ is most suitable, for the third blank both grammatically and contextually preceding ‘this point’.

8. In the context of following ‘in the plans they’, verb ‘draw’ (compose or draft) is most suitable both grammatically and contextually and has to be preferred for the second blank to any of ‘set’ (1), ‘summon’ (call upon to appear) (2) and ‘step’ (increase, intensify)

10. All the blanks in the sentence can be correctly filled in. ‘plague’ fills in the first blank, ‘transcends’ the second, and ‘an enunciating’ fills the third. Hence (3). 11. ‘Crass’ fills in the second blank, ‘transcends’ the third and ‘authority’, the fourth, hence (3). 12. Only ‘gladiatorial’ fills in the first blank, hence (1).

  PRACTICE EXERCISE  6 Direction for questions 1 to 20:  Each sentence below contains either one or two blanks. A blank indicates that a word or brief phrase has been omitted. Select among the five choices the word or phrase for each blank that best fits the meaning of the sentence as a whole. 1. Corruption is ________ in our society; the integrity of even senior officials is _______.

1.  growing ... unquestioned 2.  endangered ... disputed 3.  pervasive ... intact 4.  rare ... corrupted 5.  rife ... suspect

3.  reactionary ... admiration 4.  rigid ... support 5.  accommodating ... annoyance 4. Our grandfather was an entertaining ____; he used to ____ us with marvelous anecdotes that we, in our childlike simplicity, accepted unquestioningly. 1.  rascal ... bore 2.  orator ... intimidate 3.  raconteur ... regale 4.  curmudgeon ... surprise 5.  tyrant ... stupefy

2. In their day to day decision making, many senior managers do not follow the rational model favored by orthodox management experts, but rather rely on intuitive processes that often appear _______ and _______.

5. Members of the research team were initially so adversarial that ___________ seemed impossible; the project’s inauspicious start made its final success all the more ___________.

1.  cerebral ... considered

1.  concentration . . incidental

2.  heretical ... judgmental

2.  disagreement . . incongruous

3.  conscientious ... logical

3.  collaboration . . predictable

4.  irrational ... iconoclastic 5.  capricious ... deliberate 3. His characteristically ____ views on examination methods at university level have aroused ____ in those who want to introduce innovative and flexible patterns of assessment.

4.  hostility . . dazzling 5.  cooperation . . remarkable 6. Charu had never visited Kempty Falls, but she could appreciate their splendor _________ through the descriptions of others.

1.  hidebound ... antagonism

1.  vicariously

2.  moderate ... anger

2.  heedlessly

2.98 

  Verbal and Logical Reasoning

3.  innocuously 4.  mystically 5.  voluminously 7. Dependence by primitive humans on their environment would not have permitted them to be ________ the effects of the surrounding world on them.



2.  relatively rare…..certain 3.  very serious…..most 4.  clinically acceptable….. younger 5.  commonly misunderstood…..older

3.  indifferent about

12. Paradoxically, industrialist Sunil Mittal gained his reputation for ________at the expense of his own factory workers, who were oppressed by the ________ steel magnate to an extent that would be considered by today’s standards of labour practice to be unconscionable.

4.  surprised by

1.  efficiency…..affluent

5.  knowledgeable about

2.  innovation…..benevolent

8. We live in a ____ age; everyone thinks that maximizing pleasure is the point of life.

3.  stinginess…...entrepreneurial

1.  intrigued by 2.  protected from



1.  ubiquitous 2.  propitious 3.  sporadic 4.  corrupt 5.  hedonistic

9. When listening to a medieval religious chant, the listener does not encounter the composer’s individual personality; ________, the chant merely ________both the musical and religious rules of the period.

4.  ruthlessness…..shrewd 5.  philanthropy…..cost-conscious 13. The fossil record reveals innumerable instances of environmental _______ by which one can draw an analogy between the evolution of life on Earth and the branches of a bush, a few of which ________ but most of which branch again and again. 1.  calamities…..end abruptly 2.  adaptations…..progress linearly 3.  safeguards…..wither and die

1.  rather….embodies

4.  events…..intertwine

2.  in addition….conveys

5.  changes…..produce leaves

3.  instead….belies

14. In India, the development of the field of sociology was not ________ controversies; rather, it burgeoned from social experience, which explains the relatively ________ approach among Indian sociologists to identifying and solving social problems.

4.  in other words….repudiates 5.  moreover….reflects 10. Even detractors who warn of its potential for abuse by powerful despots agree that genetic engineering, if used _________, can reduce the incidence of the sort of physical and mental deformities that any society would want to eliminate. 1.  premeditatedly 2.  biologically 3.  recklessly 4.  discriminately 5.  illicitly 11. The high incidence of speech articulation disorders among young children suggests that such «disorders» are ________ developmental phenomena, since they generally occur less frequently among _________ age groups. 1.  actually normal…..other



1.  impeded by political…..academic 2.  challenged by academic…..theoretical 3.  hindered by petty…...controversial 4.  stimulated by ideological…..empirical 5.  sparked by social…..experimental

15. The government’s _______ clinical study requirements for approval of new drugs do not _______ pharmaceutical firms when it comes to research and development, chiefly because of the profit potential afforded by patent protection.

1.  official…..permit 2.  onerous…..dissuade 3.  extensive…..motivate 4.  unenforceable…..favour 5.  vague…..prejudice

ANSWER KEYS

English Usage  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

5

2.

4

3.

1

4.

3

5.

5

6.

1

7.

3

8.

1

9.

1

10.

4

11.

1

12.

5

13

2

14

4

15

2

  2.99

HINTS AND EXPLANATIONS 1. The semicolon suggests that the second part expands upon the first part. The word “even” also sets up a contrast. So, if corruption is rife (common), then we will doubt the integrity of the officials. Their integrity will be suspect (doubtful).

(pervasive = spreading everywhere; rife = common)

2. The ‘but rather’ construction indicates an opposite. Since they do not follow a rational model, we infer that they must seem irrational. Also, since they do not follow the orthodox, they must be unorthodox (iconoclastic). Note that ‘and’ usually links words with similar values (both positive or both negative etc.,)

(cerebral = concerned with thinking; heretical = opposed to orthodoxy = iconoclastic; capricious = whimsical, fickle)

3. Clue: Follow the logic. If his views are flexible the people who want flexible methods will approve. But, if his views are rigid thee same people will oppose them. Hence, the best fit comes with hidebound (rigid) and antagonism (hostility).

(reactionary = ultraconservative; accommodating = flexible).

4. Clue: Grandfather used to tell stories (anecdotes). He was also entertaining. So, the best answer will be that he was a raconteur (teller of stories) who regaled (entertained) the children.

(orator = good speaker; curmudgeon = grumpy person; tyrant = harsh ruler)

5. Choice (5) is the only pair of words that logically completes this sentence. The “adversarial” attitude of the team members would suggest that working together would be quite difficult, or that “cooperation” would be “impossible”; given the project’s bad start, its ultimate success would be “remarkable” because nobody would have expected it. 6. Charu hadn’t visited Kempty Falls but “could appreciate their splendor,” so the word that fills the blank must be an adverb whose definition has to do with appreciating something indirectly, “through the descriptions of others” (based on their experiences). Choice (1) is correct because to experience something “vicariously” is to experience it through imaginative participation in the actual experience of someone else. 7. The correct response is (3). Dependence on one’s environment would in all likelihood make one concerned about it. Version (3) makes sense; primitive humans would surely not have been indifferent (unconcerned) about how the environment might affect them. 8. The part after the semicolon explains what kind of age we are talking about. So, since we are told that maximizing pleasure is the point, the word we need is hedonistic (pleasure seeking).

(ubiquitous = found everywhere; propitious = favourable; sporadic = intermittent, not continuous)

9. The operative word in this sentence is merely, which calls for a contrast between the first and second clause. The first missing word

should set up that contrast. Only (1) and (3) accomplish this. Of these two choices, only (1) makes complete sense. (The word belies means “misleads or deceives” and makes no sense here in tandem with the word merely.) 10. The correct response is (4). The missing word must contrast with the notion of abuse of genetic engineering, while at the same time be consistent with the desirable goal of reducing the incidence of deformities. Only (4) accomplishes both. To use the technology “discriminately” would be to conscientiously apply it only toward certain ends (such as reducing deformities) and not toward others (such as creating a master race that dominates others). 11. The first operative word in the sentence is since, which means “because” here. The fact that the disorders appear frequently only among young children would explain the conclusion that these “disorders” are not disorders at all, but rather normal developmental phenomena that children grow out of. Version (1) conveys this idea. The second operative word is disorders (in quotes). The fact that the word appears in quotes provides a clue that the term might be a misnomer—an inappropriate label. Again, version (1) conveys this idea. 12. The operative word in this sentence is paradoxically. A paradox is an apparent contradiction. So the sentence intends to point out two contradictory traits of Mittal. (5) accomplishes this. Philanthropy literally means “love of humankind” and is usually used to describe generous charitable giving by wealthy individuals. Mittal’s cost-cutting business practices and oppressive treatment of his labor force would seem paradoxical, given his reputation as a philanthropist. 13. The operative phrase in this sentence is by which. What precedes this key phrase must adequately explain the analogy that follows it. Version (2) fits the bill. In the context of evolution, many organisms have continually adapted to environmental changes, resulting in a large variety of species (in a continual branching manner); in other words, for most organisms evolution is not linear. 14. The first operative word in the sentence is rather, which sets up a contrast between what precedes it and what follows it. So the first clause must run contrary to the phrase “it burgeoned [grew] from social experience.” Only (1), (2), and (4) fit the bill. Of these, three choices, (4) establishes the clearest contrast--between ideology and experience. A second operative term in the sentence is which explains. What follows this phrase must be consistent with what precedes it. Version (4) accomplishes just that. The word empirical means “based on observation or experience (as opposed to theory).” 15. The operative word in this sentence is because, which requires that what follows it must explain what precedes it. Profit potential would explain why drug companies persist in developing new drugs despite onerous (burdensome) government regulations. Version (2) expresses this idea. (The word dissuade means “discourage or persuade not to.”)

2.100 

  Verbal and Logical Reasoning

  PRACTICE EXERCISE  7 Direction for questions 1 to 20:  Choose the best alternative that can fill in the spaces in the following passages. It is clean, smooth, fast and ___(1)___. At every station stroll uniformed guards, truncheons in hand, deterring muggers and graffiti artists. Teams of moppers and sweepers keep platforms ___ (2) ___. Air-conditioning chills the carriages and a soothing voice, in English and Thai, tells passengers where they are. Compared with the ___ (3) ___, overcrowded underground systems of London, Paris and New York, Bangkok’s train on stilts is a ___ (4) ___ success. Launched a year ago, after five years of building-and many more before that of ___ (5) ___ dealings over contracts-the train is supposed to help cure the Thai capital’s ___(6)___ traffic congestion. ___ (7) ___ and thick with exhaust fumes; Bangkok is one of the most difficult cities in which to get around. But with 600,000 people tempted on to the Skytrain each day, said the Bangkok Transit System Corporation (BTSC), the Skytrain’s ___ (8) ____, Bangkok might “breathe again”. Not yet, though. Despite the distribution of 1m leaflets and much ___ (9) ___, only 170,000 passengers are thought to take the train each day. Its 25 stations and 23 km (15 miles) of track, running along two lines, serve only part of the capital and stretch only some of the way to the city’s airport. Most people seem to find it too __ (10) __: a short trip costs the same as a taxi and up to three times as much as a bus.

One of the most famous, __ (11) __ and influential African-American writers of this century, James Baldwin spent his life battling against a __ (12) __ enemy: racism. His sensitive and intelligent __ (13) __ helped to lay the groundwork for the black liberation movement in the 1950s and 1960s. Growing up as a young black man in Harlem in the 1920s and 30s, James faced __ (14) __ and hatred every day. Finally, he snapped. When he was 18, he __ (15) __ a pitcher of water at a waitress who had refused to serve him. She ducked in time and the pitcher ___ (16) ___ a mirror on the wall behind her. When he later described this __ (17) __, he said, “My life, my real life, was in danger, and not from anything other people might do but from the hatred I carried in my own heart.” From then on he channeled his anger, frustration and __ (18) __ into his art. He __ (19) __ racism in classic novels and essay collections including Notes of A Native Son, Go Tell It On The Mountain, and Nobody Knows My Name. For his literary __(20)__, Baldwin received a host of honors, including a Guggenheim Literary Fellowship, a Ford Foundation grant-in-aid, a Partisan Review Fellowship and a National Institute of Arts and Letters Award in 1956. 11. 1.  profound 3.  bizarre

2.  violent 4.  prolific

1. 1.  frequent 3.  fashionable

2.  vapid 4.  sluggish

12. 1.  docile 3.  dreadful

2.  savage 4.  insipid

2. 1.  unkempt 3.  pristine

2.  appealing 4.  befouled

13. 1.  prose 3.  sketch

2.  depiction 4.  portrait

3. 1.  convenient 3.  sanitary

2.  grubby 4.  brand-new

4. 1.  ludicrous 3.  desolate

2.  cloudy 4.  sparkling

14. 1.  decency 3.  propriety

2.  prejudice 4.  integrity

15. 1.  fractured 3.  hurled

2.  punctured 4.  uplifted

16. 1.  scattered 3.  scraped

2.  penetrated 4.  shattered

17. 1.  incident 3.  nightmare

2.  memory 4.  episode

18. 1.  anguish 3.  rage

2.  anxiety 4.  felicity

19. 1.  compliments 3.  engages in

2.  compromises 4.  rails against

2 0. 1.  revenges 3.  fiasco

2.  triumphs 4.  collapse

5. 1.  servile 2.  murky 3.  straightforward 4.  understandable 6. 1.  fantastic 3.  notorious

2.  famous 4.  noted

7. 1.  Deadlocked 3.  Confined

2.  Gridlocked 4.  Detained

8. 1.  staff 3.  officials

2.  advocates 4.  authorities

9. 1.  publicity 3.  commercial

2.  propaganda 4.  broadcasting

10. 1.  unsafe 3.  onerous

2.  pricey 4.  confusing

ANSWER KEYS

English Usage  Q.

Ans.

Q.

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Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

3

3.

2

4.

4

5.

2

6.

3

7.

2

8.

4

9.

1

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2

11.

4

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2

13.

1

14.

2

15.

3

16.

4

17.

1

18.

3

19.

4

20.

2

  2.101

HINTS AND EXPLANATIONS Vocab

Vocab

Vapid = lacking spirit or liveliness

Profound = marked by intellectual depth or insight

Sluggish = slow

Bizarre = strange

Unkempt = lacking order or neatness

Prolific = productive

Pristine = unspoiled

Docile = easily taught, led, or managed; tractable

Befouled = made dirty

Savage = cruel, fierce

Grubby = dirty = slovenly Sanitary = free from filth or infective matter Ludicrous = laughable, ridiculous Desolate = deserted, abandoned Sparkling = brilliant Servile = befitting a slave or servant

Insipid = lacking taste or savor Prose = t he ordinary language people use in speaking or writing Puncture = to make a hole in : pierce Hurl = to throw down with violence Uplift = to lift or raise up; elevate

Murky = dark

Scrape = to damage or injure the surface of by contact with something rough

Notorious = widely and unfavorably known

Shatter = to dash or burst into fragments

Deadlock = a stoppage of action because neither faction in a struggle will give in

Episode = an incident in a course of events; occurrence

Gridlock = a traffic jam in which an intersection is so blocked that vehicles cannot move

Anguish = extreme pain or distress esp. of mind Rage = violent and uncontrolled anger

Publicity = public attention or acclaim

Felicity = the quality or state of being happy

Pricey = expensive

Rail against = to complain angrily

Onerous = imposing or constituting a burden; troublesome

Fiasco = a complete failure

2.102 

  Verbal and Logical Reasoning

  ANALOGIES EXERCISE  1 1.  grass 3.  paper

Direction for questions 1 to 20: In each question below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

11. scissors : paper : : axe : 1.  wood 2.  canvas 3.  wall 4.  spices

1. bountiful : scant : : generous :: ___________. 1.  magnanimous 3.  prodigal

12. lighter : burner : : screw driver : 1.  paper 2.  car 3.  screw 4.  pipe

2.  munificent 4.  stingy

2. naive : experienced : : : migrant : ___________. 1.  native 3.  flamboyant

13. needle : wool : : fork : 1.  spices 2.  hair 3.  food 4.  knife

2.  inherent 4.  aureate

3. solicitude : calmness : : : immorality : ___________. 1.  habits 3.  ethicality

14. brush : canvas : : : cloth 1.  needle 2.  pen 3.  marker 4.  paint

2.  cheating 4.  honour

4. dynamic : static : : : whole : ___________. 1.  strenuous 3.  partial

15. wrench : pipe : : lawn mower : 1.  tennis 2.  grass 3.  paper 4.  plants

2.  biased 4.  vigorous

5. sluggish : energetic : : forward : ___________. 1.  rearward 3.  bold

16. floss : teeth : : needle : 1.  thread 2.  nurse 3.  cloth 4.  sew

2.  ahead 4.  developing

6. comicality : seriousness : : disagreement _________. 1.  coherence 3.  harmony

17. sunshine : light : : push : 1.  movement 2.  tired 3.  sluggish 4.  lethargy

2.  accord 4.  treaty

7. hammer : nail : : stick : ___________. 1.  carpet 3.  bamboo

18. friction : heat : : deforestation : 1.  soil erosion 2.  earthquake 3.  tremor 4.  wind

2.  drums 4.  table

8. needle : cloth : : scissors : ___________. 1.  carpet 3.  screw

19. stabbing : injury : : hitting :

2.  paper 4.  vegetables

1.  bruise 3.  noise

9. stick : drums : : wrench : ___________. 1.  wood 3.  paper

2.  pipe 4.  table

2.  idea 4.  heat

2 0. friction : heat : : combustion : 1.  cloud 2.  smoke 3.  air 4.  wet

10. vacuum cleaner : carpet : : lawn mower : __________.

ANSWER KEYS

2.  hair 4.  dry

Q.

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Q.

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Q.

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Q.

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1.

4

2.

1

3.

3

4.

3

5.

1

6.

1

7.

2

8.

2

9.

2

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1

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1

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3

13.

3

14.

1

15.

2

16.

3

17.

1

18.

1

19.

1

20.

2

English Usage 

EXERCISE  2 Direction for questions 1 to 20: In each question  below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

10. thieves : gang : : drawers :

1. overeating : obesity : : thunder :

1.  dust 3.  suite

1.  noise 3.  heat

1.  chest 3.  clothes

11. puppies : litter : : furniture :

2.  clouds 4.  waves

2.  carving 4.  durability

12. people : crowd : : flower : 1.  garden 3.  leaves

2. democracy : freedom : : aging : 1.  pride 3.  maturity

2.  wood 4.  wardrobe

2.  self-esteem 4.  prestige

2.  bouquet 4.  flowerbed

13. thieves : gang : : trees :

3. shower : wet : : hard work :

1.  clump 3.  branches

1.  success 3.  topper

14. furniture : suite : : ships :

2.  maturity 4.  fatigue

1.  transport 3.  fleet

4. combustion : smoke : : fire : 1.  wind 3.  heat

1.  sea 3.  food 1.  collection 3.  bunch 1.  group 3.  herd

2.  animals 4.  graze

18. singers : choir : : chocolate :

2.  accomplishment 4.  noise

1.  sweet 3.  dessert

8. medicine : healing : : carelessness : 1.  mistakes 3.  prudence

2.  ring 4.  lock

17. flowers : bouquet : : cattle :

2.  beauty 4.  praise

7. aging : maturity : : sluggishness : 1.  non success 3.  cowardice

2.  aquarium 4.  shoal

16. grapes : bunch : : keys :

2.  healing 4.  weakness

6. thunder : noise : : filth : 1.  uncleanliness 3.  corrupt

2.  harbour 4.  sailor

15. puppies : litter : : fish :

2.  forest 4.  matchstick

5. admiration : happiness : : medicine : 1.  treatment 3.  therapy

2.  forest 4.  swings

2.  bar 4.  children

19. cards : pack : : sheep :

2.  confidence 4.  intelligence

1.  wool 3.  herd

2.  flock 4.  group

9. soldier : regiment : : star :

20. tutor : governess : : fox :

1.  group 3.  galaxy

1.  vixen 3.  animal

ANSWER KEYS

2.  night 4.  bunch

2.  foxes 4.  boar

Q.

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Q.

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Q.

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Q.

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Q.

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1.

1

2.

3

3.

1

4.

3

5.

2

6.

1

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1

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1

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3

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4

16.

3

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3

18.

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19.

2

20.

1

  2.103

2.104 

  Verbal and Logical Reasoning

EXERCISE  3 Direction for questions 1 to 20: In each question below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

1.  intimacy 3.  sea shore

2.  resurrection 4.  jewels

11. roses : innocence : : griffin :

1. heir : heiress : : drone :

1.  power 3.  symbol

1.  master 3.  bat

12. compass : architect : : spiral :

2.  bee 4.  lass

2.  scavengers 4.  university

2. steward : stewardess : : stag :

1.  hairdresser 3.  progress

1.  blind 3.  hind

13. circle : endlessness : : ring :

2.  ewe 4.  squaw

2.  book seller 4.  electrician

3. monk : nun : : bullock :

1.  failure 3.  engagement

1.  cow 3.  cart

14. obelisk : eternity : : oak tree :

2.  bull 4.  heifer

2.  playfulness 4.  completeness

4. czar : czarina : : duke :

1.  shade 3.  friendship

1.  duck 3.  bee

2.  duchess 4.  holland

15. scythe : death : : sun dial :

2.  dusk 4.  dawn

16. angel : spiritual aspiration : : crown :

2.  geese 4.  goes

17. fern : New Zealand : : dove :

2.  calf 4.  cow

18. book : learning : : cenotaph : 1.  weather 2.  excelling 3.  mourning 4.  divinity

1.  heat 3.  warmth

5. boar : sow : : ram : 1.  eve 3.  ewe 1.  gender 3.  goose

8. heir : heiress : : wizard : 1.  vixen 3.  ditch

2.  witch 4.  wasp

2.  revolution 4.  justice

19. griffin : power : : ferns : 1.  trinity 3.  humility

9. anchor : safety : : yin yang : 1.  birth and death 2.  darkness and light 3.  young and old 4.  peace and prosperity

2.  aspiration 4.  mourning

20. shell : resurrection : : spire : 1.  tranquility 3.  religious aspiration

10. spire : religious aspiration : : shell :

ANSWER KEYS

2.  wisdom 4.  sovereignty

1.  London 3.  peace

7. horse : mare : : colt : 1.  cuddle 3.  filly

2.  money 4.  time

1.  king 3.  dynasty

6. bull : cow : : gander :

2.  harmony 4.  strength

2.  rigidity 4.  destination

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English Usage 

  2.105

EXERCISE  4 Direction for questions 1 to 20: In each question below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

10. bird : sparrow : : homosapien :

1. yin yang : darkness and light : : lamb :

1.  refined flour 3.  sugar

1.  timid 3.  calm

1.  squirrel 2.  hen 3.  man 4.  mammal 11. insect : fly : : bakery products :

2.  innocence 4.  peace and prosperity

12. cosmetics : nail paint : : mammal : 1.  bat 2.  child 3.  offspring 4.  class 13. electrical appliance : washing machine : : clothes :

2. mindless : unimaginative : : superfluous : 1.  abounding 3.  necessary

2.  compatible 4.  essential

1.  pullover 2.  clothesline 3.  detergent 4.  iron 14. jewellery : earring : : medicine :

3. dearth : absence : : exiguousness : 1.  scantiness 3.  sufficiency

2.  excess 4.  weakness

4. fate : fortune : : chance : 1.  accident 3.  consequence

2.  consequence 4.  circumstance

5. victorian : conservative : : stuffy : 1.  confined 3.  clear

2.  airy 4.  middle

6. conceited : big headed : : puffed up : 1.  self effacing 3.  conscious

2.  chesty 4.  meek

1.  antiseptic 3.  doctor 15. he : she : : drake :

2.  treatment 4.  healing

1.  drone 3.  duchess 16. he : buys : : they :

2.  duke 4.  duck

1.  were buying 3.  buy 17. lost : lose : : cost :

2.  bought 4.  buys

1.  cost 2.  cast 3.  costed 4.  cause 18. drove : driven : : worst :

7. guilty : accusable : : convicted : 1.  innocent 3.  fragile

2.  biscuits 4.  eggs

2.  delighted 4.  delinquent

8. disinclined : hesitant : : eager :

1.  worsten 2.  worst 3.  worst 4.  worse 19. he : himself : : they :

1.  alcholic 3.  wild

1.  herself 3.  themselves

2.  luke warm 4.  acquisitive

2.  themself 4.  itself

20. forget : forgotten : : bet :

1.  indistinguishable 2.  diverse 3.  biased 4.  variable

1.  bet 3.  beaten

ANSWER KEYS

9. competent : adequate : : equal :

2.  beat 4.  beet

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2.106 

  Verbal and Logical Reasoning

EXERCISE  5 10. cowboy : rope : : cobbler: 1.  mend 2.  goblet 3.  shoes 4.  leather cutter

Direction for questions 1 to 20: In each question below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

11. farmer : plough : : gardner: 1.  plants 2.  spade 3.  trees 4.  lawn

1. Asian : an : : European: 1.  the 3.  a

2.  an 4.  none

12. butcher : knife : : baker: 1.  knead 2.  bakery 3.  dough 4.  kneader

2. fast : faster : : good: 1.  smart 3.  clever

2.  intelligent 4.  better

13. tailor : sewing machine : : jeweller: 1.  jewels 2.  necklace 3.  gold 4.  setter

3. box : in : : pond: 1.  under 3.  inside

2.  into 4.  over

14. surgeon : scalpel : : teacher: 1.  duster 2.  chalk 3.  register 4.  chart

4. can : could : : may: 1.  shan’t 3.  might

2.  ought to 4.  would

15. farmer : plough : : butcher: 1.  slaughter 2.  flesh 3.  knife 4.  animals

5. sherrifs : sheriffs : : ox: 1.  cow 3.  oxen

16. cleaner : duster : : sweeper: 1.  sweep 2.  bin 3.  garbage 4.  broom

2.  oxes 4.  heifer

6. rahul : is : : children: 1.  is 3.  are

17. plumber : wrench : : craftsmen: 1.  tool 2.  raw material 3.  skill 4.  master piece

2.  was 4.  were

7. Taj Mahal : the : : Statue of Liberty: 1.  is 3.  the

18. teacher : chalk : : painter: 1.  canvas 2.  brush 3.  paint 4.  sketch

2.  a 4.  has

8. dangerous : dangerously : : horrible: 1.  horribly 3.  horrible

19. fisherman : fishing rod : : plumber: 1.  pipe 2.  fittings 3.  wrench 4.  tap

2.  horribaly 4.  hurably

9. fisherman : fishing rod : : cowboy: 2.  rope 4.  cowshed

ANSWER KEYS

1.  net 3.  bucket

20. writer : pen : : woodcutter: 1.  trees 3.  scissors

2.  axe 4.  wood

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English Usage 

EXERCISE  6 Direction for questions 1 to 20: In each question below, you are given a related pair of words or phrases. Select the lettered word that best expresses a relationship similar to that in the original pair of words.

10. director : films : : composer : 1.  instruments 2.  medicine 3.  symphony 4.  phoenix 11. tailor : dress : : painter : 1.  canvas 2.  brush 3.  paintings 4.  colours

1. diabetic : sweets : : drop out : 1.  careless 3.  school

2.  road 4.  pack

12. carpenter : furniture : : mason : 1.  rooms 2.  car wash 3.  house 4.  animals

2. healthy person : medicine : : bright student : 1.  sickness 3.  serious

2.  studies 4.  rote learning

13. baker : bread : : tailor : 1.  cloth 2.  needle 3.  dress 4.  wardrobe

3. nun : wedlock : : sportsman : 1.  games 3.  steroids

2.  jogging 4.  diet

14. weaver : cloth : : potter : 1.  pot 2.  clay 3.  mud 4.  harry

4. hydrophobic : water : : child : 1.  play 3.  noise

2.  fire 4.  swimming

15. pharmacist : medicines : : weaver : 1.  cloth 3.  animal

5. cleaner : dust : : orthodox : 1.  generation gap 3.  thinking

2.  aged 4.  enlightenment

16. farmer : crops : : craftsman : 1.  exhibition 3.  raw material

6. drop out : school : : hydrophobic : 1.  colours 3.  water

2.  animals 4.  light

18. lyricist : lyrics : : cobbler : 1.  shoes 2.  leather 3.  worker 4.  mending

2.  allergen 4.  infection

8. bright student : rote learning : : convict : 1.  crime 3.  police

19. architect : plans : : baker : 1.  bakery 2.  cakes 3.  sugar 4.  fruits

2.  carelessness 4.  delinquency

9. baker : cakes : : architect :

2 0. mason : house : : jeweller : 1.  diamonds 2.  gold 3.  ornaments 4.  gold smith

2.  plan 4.  building

ANSWER KEYS

1.  site 3.  fittings

2.  things 4.  handicrafts

17. potter : pots : : pharmacist : 1.  pharmacy 2.  doctor 3.  chemist 4.  medicines

7. player : foul : : asthmatic : 1.  weather 3.  lungs

2.  bird 4.  weave

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  2.107

2.108 

  Verbal and Logical Reasoning

  MODIFIERS A modifier is a word or a phrase that describes another word or phrase. The most familiar examples are adjectives and adverbs.

3. I eat only pizzas and burgers

Errors in Modifiers

1. 1st sentence conveys that all I do 24 hours is to eat pizzas and burgers. 2. 2nd sentence conveys that only I (and nobody else on the earth) eat pizzas and burger. 3. 3rd sentence conveys that I eat nothing except pizzas and burgers. 4. 4th sentence means that I eat only pizzas and burgers.

Normally, errors in modifier are not the grammatical error; rather they are the error of English usage giving an altogether different meaning than what they are supposed to. For example, consider the statement:

Example  1 A signboard at a restaurant says: We provide restrooms for the ladies that are clean and comfortable. ⇒ Analyzing this sentence, there is no grammatical error, but the phrase is wrongly, placed giving rise to ambiguity in the meaning. Restaurant meant to propagate the message that they provide clean and comfortable restrooms for the ladies, but what is conveyed is entirely different message – that they provide the restrooms only to clean and comfortable ladies. So the correct message should be—We provide clean and comfortable restrooms for ladies.

Example  2 Incorrect usage—Walking back from the village my wallet was lost. In the given sentence it appears that the wallet lost itself —which cannot happen.

Correct usage a. While ‘I’ was walking back from the village my wallet was lost. b. Walking back from the village, I lost my wallet.

Example  3 Incorrect usage—Blinded by the storm, the car was steered in the wrong direction. In this sentence, there is no clarity as to who steered the car. Incorrect usage—Blinded by the storm, I or the driver steered the car in the wrong direction.

Example  4 Read the following sentences and identify which one is correct: 1. I only eat pizzas and burgers 2. Only I eat pizzas and burgers

4. I eat pizzas and burgers only. Solution—Grammatically, all the four sentences are correct.

So, it is important to choose the sentence that imparts logical and sensible meaning. Care should be taken to choose the most appropriate option as the answer. Types of modifier errors: There are two types of modifier errors: Misplaced Modifier Error • There may be an adjective, an adverb or a phrase which is inappropriately placed in a sentence causing a mismatch between the intended and perceived meaning of the sentence. There can be various ways to correct the sentence.

Dangling Modifier Error • As name suggests, this type of moditier “hangs” without a subject. The word or phrase that modifies a word is not clearly stated in the sentence. To make such sentences sensible we need to insert a subject.

Misplaced Modifiers Incorrect   usage

Correct   usage

Explanation

I could almost run all the way up the hill.

I could run almost all the way up the hill.

The first sentence does not mean what it is intended to mean. The modifier “almost” is misplaced.

I only want one. I want only one.

Same as given above.

Dangling Modifiers Incorrect   usage

Correct usage

While walking While I was in the garden, walking in the Ravi arrived. garden, Ravi arrived.

Explanation The modifying phrase “while walking in the garden” does not refer to a particular noun or pronoun (i.e., it dangles).

English Usage 

  2.109

How to approach modifier question

2. Driving over the hill, the river came into view.

1. Objective is to make the meaning clear.

3. Crowded in the train, the trip was uncomfortable.

2. First step to identify the modifier whether its a phrase, adjective or adverb.

4. The results will only be known after all the votes have been counted.

3. Analyse the meaning intended to be conveyed.

5. A fish was found in the Ocean that had been considered extinct.

4. Modify the sentence by placing the modifier next to what it is modifying. 5. Check if the ambiguity has been done away with (making meaning clear).

  PRACTICE EXERCISE Each of the sentences given below has a modifier error. Rewrite the sentence after correcting that error. 1. Earning only minimum wage, nearly I made Rs 20,000 last year.

6. The palace was located by a pond which was made of red brick. 7. Chunu was thinking about Munu walking down the Hall. 8. They finally found a petrol pump driving around in their van. 9. He almost watched television all night. 10. Annoyed at the delay, my patience was running out.

HINTS AND EXPLANATIONS (Please note that the following sentences are not the only way of correcting the wrong sentences given):

5. A fish that was considered extinct was found in the Ocean.

1. Earning only minimum wage, I made nearly Rs 20,000 last year.

7. While walking down the hallway, Chunu was thinking about Munu.

2. When we drove over the hill, the river came into view.

8. They finally found a petrol pump while they were driving around in their van.

3. Crowded in the train, we were uncomfortable during the trip. 4. The results will be known only after all the votes have been counted.

6. The palace which was made of red brick was located by a pond.

9. He watched television almost all night. 10. Annoyed at the delay, I was losing my patience.

2.110 

  Verbal and Logical Reasoning

  SENTENCE ARRANGEMENT   (PARA JUMBLE) Jumbled paragraphs are common test item at all competitive examinations through which an examiner can assess an examinee’s reading skills as well as his reasoning prowess. Basically, you are given a paragraph—but the sentences are not in the right order. It’s up to you to untie the knot and rearrange the sentence so that they logically make sense. Since the agenda in para jumble questions is to restore the original order, it is not at all necessary to read the entire paragraph. Rather, what is more important is to look out for any piece of information that can help you connect the sentences together, and this information is limited to a surprising 15-20 per cent of the entire paragraph. Thus, if you become adept at locating this information, you can also reduce your attempt time for such questions.

Question Patterns While creating a jumble, the examiners have four basic question patterns in mind. However, management entrance tests are dynamic in nature and the examiners can of course think of other innovative question patterns. But, be confident that if you practice on the four basic question types, given below, then you will be able to develop the general skills to handle other innovative question patterns. In pattern one, the examiner conforms to the example above. There are no fixed sentences; the whole paragraph is jumbled up, and the examinee has to unjumble the lot. This is the pattern favoured by the makers of the CAT and proves to be the toughest for the examinee to handle because there are no fixed sentences that the examinee can use as an anchor to help him/her get started. In pattern two, the examiner gives the examinee the first sentence in its proper position, and then jumbles the subsequent sentences. The examinee now has one anchor instead of two, but can still manage to find a link. An example of this type follows: 1. To read the characters or the letters of the text does not mean reading in the true sense of the term. A. This mere mechanism of reading becomes altogether automatic at an early period of life. B. You will often find yourself reading words or characters automatically, while your mind is occupied with a totally different subject. C. This can be performed irrespective of attention. D. Neither can I call it reading when it is just to extract the narrative portion of a text from the rest simply for one’s personal amusement.

1.  BACD 4.  CBDA

2.  DCBA

3.  ADCB

Pattern three is a variation on Pattern Two. In this pattern, the examiner gives the last sentence as an anchor, and jumbles the preceding sentences. An example of this type follows: A. The recovery of faith is a crucial problem of our age. B. The deepest of them is the conflict of faith and unbelief. C. With it we are destined to enjoy triumphant and splendid advance, and without it we suffer failure and ignominy. D. Those ages in which faith prevails, in whatever form, are noble and fruitful for the present and the future. 5. All ages in which unbelief, in whatever form, wins an unhappy victory vanish and are forgotten by posterity. 1.  ABCD 4.  ACBD

2.  CDBA

3.  BCAD

In pattern four, the examiner gives the examinee the first and the last sentence as anchors, and jumbles the sentences in the middle. This type of jumble is considered to be the easiest because the examinee has two fixed points to guide him/her. An example of this type follows: 1. An important tenet is that managements must not confuse awards with salaries. A. An award is a one-time payment and could be anything up to 25 per cent of the annual salary. B. These can never be retrieved if performance is not stable throughout. C. It would be better to introduce an increment-cumaward system based on the results. D. Some companies give enormous salary hikes for excellent performance in a particular year. 5. In this system, the compensation becomes the hygiene factor, and the award, the motivator. 1.  DBCA 4.  BCDA

2.  ABCD

3.  CDBA

Approaches for unjumbling a jumble Most of the information given in parajumbles is unnecessary for the purpose at hand, i.e., sorting the sentences. In essence what we are looking for are things that can help us in connecting the sentences. Some approaches are given below to

English Usage  help identify the sequence of sentences. Generally, in a given parajumble more than one approach will be applicable at the same time, therefore practices identifying which approach/ approaches apply to the parajumbles you have to solve. 1. Noun-Pronoun relationship approach: In noun/ pronoun relationships, we know that the noun will come first and will be referred to later using suitable pronouns. Study the following example: A. People can get infected by handling reptiles and then touching their mouths or an open cut. B. At first they look the perfect pets: exotic, quiet and tidy. C. A study estimates that in 1995, there were as many as 6,700 reptile-caused salmonella infections. D. But lizards and other pets can harbor a salmonella bacterium that makes people sick. 1.  BCAD 4.  BDCA

2.  BCDA

3.  ACDB

Read sentences C and D carefully. Sentence D contains the noun phrase “a salmonella bacterium” and Sentence C contains the noun phrase “salmonella infections”. What is the relationship between the two? Since the phrase “a salmonella bacterium” introduces the bacterium, it should logically precede the phrase “salmonella infections”. Therefore, the sentence that contains the phrase “a salmonella bacterium” should come before the sentence that contains the phrase “salmonella infections”. So, Sentence D should precede Sentence C! Once you have a link between two sentences, look at the answer choices to see if you are on the right track. If you are, then you have the right answer (Answer 4. BDCA) and it is time to move on to the next exercise.

Try this example 1. These enormous “rivers”—quite inconstant, sometimes shifting, often branching and eddying in manners that defy explanation and prediction—occasionally cause disastrous results. A. One example is El Nino, the periodic catastrophe that plagues the West Coast of America. B.  It is rich in life. C. This coast is normally caressed by the cold, rich Humboldt Current. D. Usually the Humboldt hugs the shore and extends 200 to 300 miles out to sea. 6. It fosters the largest commercial fishery in the world and is the home of one of the mightiest game fish on record, the black marlin.

1.  ABCD 4.  CBAD

2.  DCAB

  2.111

3.  ACDB

Read sentences A and C carefully. Notice the noun/pronoun relationship between the two. Sentence A refers to “the West Coast of America” and Sentence C talks about “this coast”. Which coast? Obviously “the West Coast of America”! Therefore, Sentences A and C are related and Sentence A must come before Sentence C. Now look again. Sentence C talks about “the cold, rich Humboldt Current” and Sentence D refers to “the Humboldt” obviously these two sentences are also related. Which one should come first? Once you have decided, check the answer choices to see if you are correct. (Answer 3 ACDB) 1. Acronym Approach—Full Form vs Short Form: When we introduce someone or something, we use the complete name or title. When we refer to the same someone or something later in the paragraph, we use just the surname or the first name if we are on familiar terms with the person being discussed. If we are discussing an object, we remove the modifiers and just use the noun or a pronoun to refer to it. In Parajumbles, we encounter full and short names or sometimes acronyms of some term or institution. Example: World Trade Organisation—WTO, Dr Manmohan Singh—Dr Singh, Karl Marx—Marx, President George W. Bush—President Bush or The President. The rule is that if both full form as well as short form is present in different sentences, then the sentence containing full form will come before the sentence containing short form. Let’s see this technique at work through an example. A. If you are used to having your stimulation come in from outside, your mind never develops its own habits of thinking and reflecting. B. Marx thought that religion was the opiate, because it soothed people’s pain and suffering and prevented them from rising in rebellion. C. If Karl Marx was alive today, he would say that television is the opiate of the people. D. Television and similar entertainments are even more of an opiate because of their addictive tendencies. 1.  BACD 4.  CBDA

2.  ADBC

3.  BCDA

Sentence B has Marx (short form) and sentence C has Karl Marx (full form). So C will come before B. Now look at the options. In 1, 2 and 3 B is placed before C—hence rejected. 4 is the right answer.

2.112 

  Verbal and Logical Reasoning

3. Time Sequence Approach (TSA)—either dates or time sequence indicating words:  In a given parajumble, there may be a time indication given, either by giving years—or by using time indicating words. This provides a way for us to identify the correct sequence of the sentences by arranging the sentences using their proper time sequence. Some words through which a time sequence may be indicated are—Before, after, later, when etc.,

1.  CDAB 4.  BADC

Let’s see an example illustrating this technique.

4. Structure Approach:  In order to unjumble a group of sentences quickly, it is essential for us to understand how language sticks together to form a cohesive unit. English provides certain sequencing words—firstly, secondly, then, however, consequently, on the other hand, etc.,—which writers use to join sentences or ideas together and to provide a smooth flow from one idea to the next. It is essential to learn how to spot these words and learn how to use them correctly. Parajumble sentences often contain several signal words, combining them in complex ways.

A. Then two astronomers—the German, Johannes Kepler, and the Italian, Galileo Galilei—started publicly to support the Copernican theory, despite the fact that the orbits it predicted did not quite match the ones observed. B. His idea was that the sun was stationary at the centre and that the earth and the planets move in circular orbits around the sun. C. A simple model was proposed in 1514 by a Polish priest, Nicholas Copernicus. D. Nearly a century passed before this idea was taken seriously. 1.  CADB 4.  CDBA

2.  BCAD

3.  CBDA

In the above example, you will observe that the flow of logic is in the form of a time sequence which flows from the oldest time period to a more contemporary time period. Therefore, Sentence C will be the first sentence. Sentence B expands upon the “simple model” proposed, hence it will be the sentence following C. The next sentence in order of chronology is C—nearly a century passed, while the last sentence will be A which completes the sequence from older time to contemporary time thus giving us the answer as CBDA Let us look at another example: A. By the time he got to Linjeflug four years later, he had learned many lessons, in fact, he began his second stint as top dog by calling the entire company together in a hanger and asking for help, a far cry from his barking out commands just 48 months back. B.  At SAS, he arrived at a time crisis. C. This book is chock-a-block full of intrusive stories and practical advice, describing Carton’s activities at Vingresor (where he assumed his first presidency at age 32), Linjeflug, and SAS in particular. D. He began at Vingresor as an order giver, not a listener—neither to his people nor to his customers and made every mistake in the book.

2.  CBAD

3.  BACD

Observe the ��������������������������������������������� given ��������������������������������������� sequence. Again, you will see a chronological order in the parajumble. Sentence C gives us a clear indication that the book is being talked about in current times. Sentence D then starts tracing Carton’s career path from the beginning, thus leading us to the correct sequence of CDAB.

Cause and Effect Signals: Look for words or phrases explicitly indicating that one thing causes another or logically determines another. Some examples of such words are: Accordingly

in order to

because

so...that

consequently

Therefore

given

thus

Hence

when...then

if...then

Support Signal Words: Look for the words or phrases supporting a given sentence. Sentences containing these words will generally not be the opening sentence. These sentences will follow immediately the sentence supported. Some examples of such words are: Furthermore

additionally

also

and

indeed

besides

as well

too

likewise

moreover

Contrast Signals: Look for function words or phrases (conjunctions, sentence adverbs, etc.,) that indicate a contrast between one idea and another, setting up a reversal of a thought. on the contrary

notwith- and standing

even though Instead of

despite

In spite of while

In contrast

however

nevertheless

nonetheless Although

English Usage  Let us put into practice what we have discussed so far. Here is a typical example, combining all the points discussed above. A. When conclusions are carefully excluded, however, and observed facts are given instead, there is never any trouble about the length of the papers. B. The reason for this is that those early paragraphs contain judgments that there is little left to be said. C. A judgment (“He is a boy”, “She is an awful bore”) is a conclusion, summing up a large number of previously observed facts. D. In fact, they tend to become too long, since inexperienced writers, when told to give facts, often give more than are necessary, because they lack discrimination between the important and the trivial. E. It is a common observation among teachers that students almost always have difficulty in writing themes of the required length because their ideas give out after a paragraph or two. 1.  ECDAB 4.  EBCAD

2.  CEBAD

3.  EACBD

Sentence E states the situation in general and gives us information about why students have problems “in writing themes of the required length”. Sentence B goes on to tell us “the reason for this”, so the two sentences must be related. Similarly, Sentence C is related to Sentence B because both sentences contain the word “judgment”, with Sentence C explaining what the word

  2.113

means. Once a link of this nature is established, go to the answer choices to see if you are on the right track. D any of the answer choices offer our line of reasoning? Answer 4 does. In the above jumble, the word “however” in Sentence A suggests a contrast to something mentioned previously. In situations of this kind, it is always a good idea to separate the argument clearly. Sentences A and D, therefore, should come together. Now you try. 1. To read the characters or the letters of the text does not mean reading in the true sense of the word. A. This mere mechanism of reading becomes altogether automatic at an early period of life. B. You will often find yourself reading words or characters automatically, while your mind is concerned with a totally different subject. C.  This can be performed irrespective of attention. D. Neither can I call it reading when it is just to extract the narrative portion of a text from the rest simply for one’s personal amusement. 1.  BACD 4.  CBDA

2.  DCBA

3.  ADCB

The word “neither” in Sentence D will tell you that there is something additional that the writer wishes to discuss. Sentences 1, A, B and C all talk about the same idea. Therefore, Sentence D should be the last sentence. Any answers? (Answer 1)

  PRACTICE EXERCISE  1 Direction for questions 1 to 15:  The first and the last parts of the sentence are marked 1 and 6. The rest of the sentence is split into four parts and marked P, Q, R and S. These four parts are not given in their proper order. Read the sentences and find out which of the five combinations is correct. 1. 1.  It depends upon the P.  a new heaven on earth or to destroy Q.  user, whether science will be used to create

1.  PQRS 4.  SQRP

2.  SPQR 5.  SQPR

2. 1.  The English P.  plundered the country Q.  and raw materials, R.  as a result, the Company became rich S.  of precious mineral wealth

R.  the world in a

6.  and the Indian people became poor.

S.  outlook and mentality of the

1.  PQSR 4.  PSQR

6.  common conflagration.

3.  QPRS

2.  SQPR 5.  PSRQ

3.  SRQP

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  Verbal and Logical Reasoning

3. 1.  The power and pride

8. 1.  The need of administration

P.  for in the courage

P.  which could bring together

Q.  of Sparta was above all

Q.  language of the rulers, should be the one link

R.  discipline and skill of these troops

R.  apart from those of liberal education

S.  in its army,

S.  render it necessary that English, as the

6.  it found its security and its ideal.

6.  linguistic areas.

1.  SPRQ 4.  PRQS

2.  PQRS 5.  QSRP

3.  QSPR

1.  RSQP 4.  QSPR

2.  SRQP 5.  RSPQ

9. 1.  Economic domination

4. 1.  It is the

P.  anger and

P.  the careful observer

Q.  a different language

Q.  apparently trivial phenomena R.  which gives even the

R.  of persons speaking

S.  intelligent eye of

S.  often causes

6.  their value.

6.  a sense of revolt.

1.  SPRQ 4.  PRQS

2.  PQRS 5.  SPQR

3.  QSPR

1.  PSRQ 4.  SPQR

2.  QRPS 5.  RQSP

P.  of comparatively little consequence

P.  food as well as

Q.  whilst everything depends upon

Q.  present and future generations

R.  how a man is governed from outside

R.  directly injuring the S.  take place, contaminating air and water and

S.  how he governs

6.  of mankind.

6.  himself from within. 2.  PSQR 5.  SQRS

3.  SPRQ

1.  SPRQ 4.  RQPS

2.  QSPR 5.  PRSQ

3.  PRQS

11. 1.  What usually happens

6. 1.  The club is an P.  nearby municipal school, for the children Q.  proper and healthy functioning of a

Q.  organize a collection S.  and find a suitable occasion

S.  intolerable nuisance to the

6.  for presenting them.

6.  bizarre activities. 2.  SQPR 5.  SQRP

P.  and then choose the gifts R.  is that two or three persons

R.  are constantly disturbed by its

1.  QSRP 4.  RPSQ

3.  RQPS

10. 1.  It may be

5. 1.  Nuclear test explosions

1.  RQSP 4.  PQRS

3.  PQRS

3.  PQRS

1.  PQRS 4.  QRPS

2.  RQSP 5.  RQPS

3.  SRQP

12. 1.  Apart from these dangers

7. 1.  What the country needs

P.  years of human efforts have built up is

P.  and change tactics

Q.  hatred, and will progressively wither away if

Q.  who would encourage players R.  are coaches and officials

R.  ahead, the civilization which thousands of

S.  to read the game as it progresses

S.  being corroded and undermined by fear and

6.  accordingly.

6.  these trends continue

1.  RQPS 4.  RQSP

2.  SPRQ 5.  RSPQ

3.  QSPR

1.  PRSQ 4.  QSPR

2.  PQRS 5.  RPQS

3.  RPSQ

English Usage  13. 1.  A consideration for the

S.  in the size of their investment

P.  for his inferiors and dependents

6.  of their profitability.

Q.  and respect for their self-respect R.  feelings of others,

1.  PQSR 4.  PRQS

S.  as well as his equals

15. 1.  Sri Aurobindo studied

6.  pervade the true gentleman’s whole conduct.

P.  the country

1.  RPSQ 4.  SPRQ

Q.  judge, more maturely what

2.  PSQR 5.  RQPS

3.  PRSQ

2.  QSPR 5.  RQSP

3.  QSRP

R.  the conditions of S.  so that he might be able to

14. 1.  Public sector companies P.  and scale of operations

6.  could be done.

Q.  take a peculiar pride



R.  without talking

ANSWER KEYS

  2.115

1.  QSRP 4.  PQRS

2.  PSQR 5.  RPSQ

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

5

2.

4

3.

3

4.

1

5.

3

6.

2

7.

4

8.

1

9.

5

10.

3

11.

5

12.

3

13.

1

14.

2

15.

5

3.  RSQP

  PRACTICE EXERCISE  2 Direction for questions 1 to 6:  In each of the following questions, four sentences are given which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most  logical order of sentences from among the given  choices to construct a coherent paragraph. 1. A. So Iraq and Afghanistan are now sun-drenched lands enjoying liberty and freedom, overflowing with joy and prosperity? B. Yet in a new campaign ad, Republican Party strategists shamelessly take credit for “two more free nations” and “two less terrorist regimes,” using footage of the Iraqi and Afghan Olympic teams. C. The bylaws of the International Olympic Committee and the US Olympic Committee strictly prohibit the use of the word “Olympic” and related symbols for political ends. D. The US Congress stipulates that the USOC “shall be nonpolitical and may not promote the candidacy of any individual seeking public office.”

1.  CDBA 4.  ACDB

2.  CDAB 5.  CABD

3.  DABC

2. A. He is the faceless man who is nowhere and everywhere. B. He will live on bread and water, sleep on the streets, move from house to house. C. It is impossible for the political leaders of a tame western world that wages its wars by remote control to understand the power of the marginal man, who has been deprived, stripped of his right and driven back to the wall. D. This is a man who has lost everything, his home, his family, his country, even his personal history. 1.  CDAB 4.  CDBA

2.  DABC 5.  ABDC

3.  CABD

3. A.  The first vision is cyclical and millennial. B. It sees man originating from the greater anthropoid apes, climbing slowly through tribal groups, via the

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  Verbal and Logical Reasoning

Renaissance and the early Industrial Age, into modern technological man.

1.  CBDA 4.  CDBA

2.  DACB 5.  ABDC

3.  BDCA

C. The second is linear and utopian. D. It sees man originating from a divine source, a fall, exile, a final battle, the regeneration of the world by a Divine Saviour and the foundation of the Kingdom of God on earth. 1.  ABCD 4.  ADCB

2.  CBAD 5.  ACDB

3.  ACBD

4. A. One may disagree with some of his contentions, but in the aftermath of September 11, one must give credence to his central point: that in the post-Cold War world, the critical distinctions between people are not ideological or economic—they are cultural. B. Samuel P Huntington’s book The Clash of Civilizations and The Remaking of World Order is very topical these days. C. Religious, ethnic and racial strands that constitute cultural identity are the central factors shaping associations and antagonisms. D.  Thus, cultural communities are replacing Cold War blocs and the fault-lines between civilisations are becoming the nerve-centres of conflicts in the world. 1.  BADC 4.  DBAC

2.  CBAD 5.  BCAD

3.  BACD

5. A. Even when it is self-willed, migration causes dislocation and alienation, creating the need for meaningful identities at the individual level. B. The root cause is modernisation that has spurred migration in large numbers. C. Simultaneously, education and development within non-western societies stimulates the revitalization of indigenous identities and culture. D. Huntington’s analysis explains why we are witnessing this surging antagonism among Indian and Pakistani youth and expatriates. 1.  DBCA 4.  BADC

2.  BCDA 5.  BDCA

3.  DBAC

6. A. Not too far from the bright lights of Mumbai, a silent scourge is killing thousands of young children. B. Their ill-fed bodies vulnerable to infection, most succumbed to ailments as minor as diarrhoea. C. Stalked by chronic hunger and disease, nearly 30,000 children below the age of six have died in the last year alone in the state’s rural belt. D. It may be considered the country’s dollar magnet and envied for its robust industrial base but this image of Maharashtra cloaks a macabre reality.

Direction for questions 7 to 11:  Given below are five sentences S1, P, Q, R and S that make a paragraph. The sentences making the paragraph have been jumbled randomly, only the first sentence S1 is at its right place. Find out the correct sequence in which P, Q, R and S should follow after S1 so that a coherent and meaningful paragraph is made. 7. S 1.  There was a time Egypt faced economic crisis. P.  Cotton is the chief export commodity of Egypt. Q. Foreign trade depends on cultivation of cotton on large scale. R. It became necessary for Egypt to boost cotton crops. S. Only by means of increasing foreign trade Egypt could survive. 1.  PQRS 4.  SRQP

2.  QRPS 5.  SQRP

3.  RPSQ

8. S 1. While crossing a busy road we should obey the policeman on duty. P.  We should always cross the road at the zebra crossing. Q. We must look to the signal lights and cross the road only when the road is clear. R. If there are no signal lights at the crossing, we should look to the right, then to the left and again to the right before crossing the road. S.  If the road is not clear we should wait. 1.  PQRS 4.  RQSP

2.  PSRQ 5.  QRSP

3.  QRPS

9. S 1. Urban problems differ from state to state and city to city. P. Most of the cities have neither water nor the required pipelines. Q. The population in these cities has grown beyond the planners’ imagination. R. However, certain basic problems are common to all cities. S. Only broad macro-planning was done for such cities, without envisaging the future growth, and this has failed to meet the requirements. 1.  PQSR 4.  RSQP

2.  QPSR 5.  RQPS

3.  RQSP

English Usage  10. S 1.  Satyajit Ray made several films for children.

P. Luckily, there is no link between the amount of money spent and beneficent exercise, else the poor would have creaking bodies.

P.  Later film-makers have followed his lead. Q. Today other nations are making children’s films in a big way.

Q. While some cost you nothing, others may require the investment of some amount of money.

R. This was at a time when no director considered children as potential audience.

R. However, it is important to remember that exercises should not be overdone.

S.  Ray was, thus, a pioneer in the field. 1.  SQRP 4.  PSRQ

2.  RSQP 5.  RSPQ

S. It can take any form from sedentary ones like walking to vigorous work-outs like a game of squash.

3.  PSQR

1.  PQSR 4.  SQPR

11. S 1 Exercising daily is a must for good health.

ANSWER KEYS

  2.117

2.  QPRS 5.  SQRP

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

1

3.

4

4.

3

5.

3

6.

2

7.

4

8.

5

9.

5

10.

5

11.

4

3.  RSQP

HINTS AND EXPLANATIONS 1. Short and perhaps therefore easy! 3 is the opening sentence. 4

elaborates it further. 2 gives a turn to the para. And 1 comes as the conclusion.

2. The only independent sentence is (3) and it should therefore come at the beginning. Don’t be confused by “it” at the beginning: it is an indefinite pronoun here. The passage is about “the marginal man” talked about in (3). And then there is a gradual sequencing: the marginal man, this is a man, he. So either (1) or (4). But (1) is a better arrangement as far as tense is concerned.

3. Easy one! The clue lies in the words “cyclical” and “linear”. 4. Clearly, (2) is the initial sentence and (4) the conclusion. 5. We begin with (4), the only independent sentence. Also, BA is a sequence. 6. (4) is the first sentence as it outlines the paradoxical situation. The rest of the passage goes on to delineate the second part of the paradox.

2.118 

  Verbal and Logical Reasoning

  PRACTICE EXERCISE  3 Direction for questions 1 to 10:  Sentences given in each question, when properly sequenced, form a coherent paragraph. The first and last sentences are 1 and 6, and the four in between are labelled A, B, C and D. Choose the most logical order of these four sentences from among the five given choices to construct a coherent paragraph from sentences 1 to 6. 1. 1. Ever since Pakistan signed on as an ally in the war on terror, human rights advocates have voiced concerns that innocent people would be caught up in the net. A. Roughly half of the youths held are from families deemed uncooperative in the anti-terror fight. B. Seven women and at least 54 children under the age of 18 are languishing in prisons in the tribal areas of the NWFP under the so-called collective responsibility clause, which permits imprisonment of a person for crimes committed by a relative, clan or tribe. C. The decree has most recently been wielded to force tribal leaders to reveal the whereabouts of Qaeda and Taliban suspects. D. Now they’re pointing to evidence. 6. The rest were imprisoned for the alleged crimes of their fathers. 1.  BACD 4.  DBAC

2.  DBCA 5.  BDCA

3.  BCDA

2. 1. The smaller mobile phones get; the more functions they seem to acquire. A. Beginning early next year, TU Media, a consortium of SK Telecom and other Korean companies, will begin beaming television programmes via satellite to special Digital Multimedia Broadcasting phones. B. The phones, made by Samsung, have 5.5 centimetre screens and cost $700. C. Now a South Korean firm is rolling out mobiles that double as televisions—and high-definition ones, at that. D. Based on early tests, executives at TU Media think that the new service will improve on SK’s existing cellular-based television phone service, which has 3 million subscribers but is often interrupted due to poor transmission.

3. 1. Although Maradona recounts his life with neither explanation for his actions (save his love of football) nor fluid penmanship, his story is gripping. A. Maradona blames everyone but himself: luck, the media, managers, football executives—you name it, they did it. B. And, ironically, the book’s omissions are its most revealing element. C. In passing the buck, El Diego reveals who he really is—a man accountable to no one. D. It’s a tale of cataclysmic ups and downs as he hopskotches from the junior leagues of Argentina to four World Cups with the national side, from solidarity with the people of Naples to seeking solace from that other fallen idol, Fidel Castro. 6. I now believe that Maradona truly is a god and that’s why I am an atheist. 1.  CDAB 4.  CBDA

2.  DABC 5.  DBAC

3.  DBCA

4. 1.  The journalists have all but left Haiti. A. The suffering caused by the floods is no longer news, and we now work far from the headlines. B. Perhaps I have spent so much time in the Third World that I’m immune to it; one develops a thick skin, if only as a defense mechanism. C. Some of the aid workers are going as well, myself among them. D.  How do I feel about the misery I’ve seen? 6.  Otherwise you would be unable to do your job. 1.  CBAD 4.  ACDB

2.  ACBD 5.  ADCB

3.  BCDA

5. 1. Many space enthusiasts now warn that only private enterprise will truly drive human expansion into space, and yet America’s government keeps ignoring them. A. It may seem surprising, but there are large numbers of people who would spend hundreds of thousands of dollars on a trip into space. B.  Tourism and entertainment are both possibilities. C. Two people, so far, have spent $ 20 m, and another two are on their way.

6. The biggest problem, though, is coming up with programming.

D. What might cause market forces to take up the mission?

1.  BDAC 4.  CBAD

6. Film and television companies would also spend tens of millions if they could.

2.  BADC 5.  CADB

3.  CABD

English Usage  1.  DCAB 4.  ACBD

2.  BACD 5.  DACB

3.  DBAC

6. 1. Zimbabwe provides a dramatic illustration of how stagy economic policies, corruptly enforced, swiftly impoverish. A. The main reason the continent is so poor today is that Mugabe-style incompetent tyranny has been common since independence. B.  But Zimbabwe’s curse is also Africa’s. C. The most important question for Africans now is whether Mr Mugabe represents not only their past, but their future as well. D. In the past five years, Mr Mugabe’s contempt for property rights has made half the population dependent on food aid, while his cronies help themselves to other people’s land and savings, and build helipads for their own mansions.

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D. But both governments are worryingly dependent on a single source of revenue: oil, in Nigeria’s case, and white taxpayers, in South Africa’s. 6. It is a daunting challenge, but the alternative is likely to be worse. 1.  CDAB 4.  DBAC

2.  DCAB 5.  CDBA

3.  CBDA

9. 1. The truth is that traditional economic labels are less and less useful. A. Different organizations and banks use different groupings. B. The old “third world” label has been replaced by “developing” or “emerging” economies to portray a more positive image.

6.  There are encouraging signs that he does not.

C. “Industrial economies”, the old name used for rich countries, is now meaningless: industry accounts for only 16% of jobs in America.

1.  DBCA 4.  DBAC

3.  DCAB

D. But the breakdown of old categories has bred confusion.

7. 1. If Africans are to have a chance of pulling themselves out of penury, they need governments that do not stand in their way.

6. For instance, the United Nations and JP Morgan Chase count Hong Kong, Singapore, South Korea and Taiwan as developing (or emerging) economies.

A. Fiscal realism is more common now than a decade ago, as the continent’s generally lower inflation rates attest.

1.  ADBC 4.  CBDA

B. They need leaders who uphold the law impartially, but otherwise let people do what they wish.

10. 1.  Jane Austen died and came back as a fantasy writer.

2.  CDBA 5.  DABC

C.  But graft is still widespread. D. They need governments that pass sensible budgets and stick to them.

2.  CBAD 5.  DBCA

3.  ABCD

A. The book itself has been called, by a media ever eager to summarise even 800-page hardcover tomes into a snappy catchphrase, “Harry Potter for adults”.

3.  DACB

B. Unlike her previous avatar, the 21st-century Ms Clarke (nee Austen) seems to be enjoying the attention showered upon her and far from publishing her first book under a pseudonym, has been a central performer at her own media circus.

8. 1. Africa’s two most important countries—Nigeria and South Africa—are doing several things right.

C. The book, which she now calls her “debut”, began attracting media attention long before publication and on release it’s been universally lauded.

6. Angola’s rulers were accused of having wasted or misappropriated $ 4 billion in five years—more than 9 percent of GDP each year. 1.  BADC 4.  DBAC

2.  BDAC 5.  DBAC

A. If Africa as a whole is to prosper, the majority of its citizens will have to produce more, fashioning goods or providing services that the rest of the world wants to buy. B. Given that most Africans are subsistence farmers, that will not be possible without a vast social upheaval, with unpredictable consequences. C. Both have swapped tyranny for democracy, and both are using their diplomatic and military muscle to end some of their neighbours’ wars.

D. In her new avatar, she calls herself Susanna Clarke, lives in Cambridge, and has authored a fat historical fantasy novel set in the year 1860. 6. It’s also been praised by perhaps the best living author of British fantasy novels, Neil Gaiman, as “unquestionably the finest English novel of the fantastic written in the past seventy years.” 1.  BADC 4.  BDCA

2.  DBCA 5.  DCBA

3.  DCAB

  Verbal and Logical Reasoning

ANSWER KEYS

2.120 

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

3

3.

5

4.

4

5.

3

6.

4

7.

2

8.

1

9.

4

10.

5

HINTS AND EXPLANATIONS 1. “They” in D refers to “human rights advocates” in 1. Hence 1D is a sequence. Thus 1 and 3 are ruled out. Again, “the rest” in 6 is obviously a sequel to “half of the youths” in A. Which means A6 is a sequence. Hence 4 is ruled out. 2. C tells us about “the more functions” in 1. Hence 1C is a sequence. Thus 1 and 2 are ruled out. And “the phones” in B refers to the “special Digital Multimedia Broadcasting phones” in A. Thus AB is a sequence. Hence 4 is ruled out.

5. B is the answer to D. Hence DB is a sequence. Besides, C6 is another sequence. 6. 6 is the answer to the question raised in C. Thus C6 is an obvious sequence. Enough for our answer! 7. 6 is an example of what is mentioned in C. Again, we get C6 as a sequence. A goes best with D, thus giving us DA as another sequence. 8. Note the pronoun both in C and D. It refers to “Nigeria and South Africa” mentioned in 1. But D should come later because it is a sentence that begins with But.

3. Look at the first word It’s (focus on it) in D. It refers to “his story” in 1. Thus 1D is a sequence. Hence 1 and 4 are ruled out. And what is one of “the book’s omissions”? That Maradona does not blame himself. In other words, A is an explanation of B. Thus BA is a sequence. Hence 2 is ruled out.

9. Here 6 is an elaboration of A. We thus get A6. Enough for our answer!

4. The clue lies in “otherwise” in 6, which here means “if you do not develop a thick skin”. Obviously, B6 is a sequence. Now, 4 is the only such choice where B can precede 6.

10. Can B come before D? No. Because “Ms Clarke” in B can come only after “Susanna Clarke” in D. Hence 1 and 4 are ruled out. Again, note that “the book” in C refers to “a fat historical fantasy novel” in D. Hence DC is a sequence. Thus 2 is ruled out.

  PRACTICE EXERCISE  4 Direction for question 1 to 11:  Sentences given in each question, when properly sequenced, form a coherent paragraph. The first and last sentences are  1 and 6, and the four in between are labelled A, B, C and D. Choose the most logical order of these four sentences from among the five given choices to construct a coherent paragraph from sentences 1 to 6. 1. 1. It’s the technology equivalent of the tail wagging the dog. A. The $250 mobile phone comes with a 5-megapixel camera and an enhanced liquid crystal screen capable of handling 16 million colours—compared to the average phone screen’s quarter million. B. But this week’s announcement by Korea-based Samsung has turned the entire business of cameras latched on to cell phone, upside down.

C. A year ago, the cameras that came bundled with mobile phones were mostly low-resolution accessories whose pictures were okay for posting on website—and little else. D. Serious shooters—even the average amateur who wanted to have postcard-sized photos for the album—found the camera-phones virtually useless for printed output. 6. The number of pixels makes the camera better than almost all digital cameras available today—up to semi-professional standard. 1.  ACDB 4.  DCAB

2.  CDBA 5.  BCDA

3.  BACD

2. 1. The Prime Minister spent 2 hours and 45 minutes on the Kalpakkam campus.

English Usage 

  2.121

A. Another plant, which will produce 45 lakh litres of potable water a day using the multi-stage flash method, will be operational in some months.

B. There are some batsmen who feel that such acts only neutralise things like the umpire’s decision going against the batsman when he is not out.

B. He went round an exhibition, which featured the PFBR’s massive components such as the reactor vessel, steam generator tubes, and so on.

C. In contemporary cricket, Adam Gilchrist is perhaps the only batsman who would be half way to the pavilion even before the dreaded finger is raised.

C. After inaugurating the PFBR construction, he saw the massive work under way there.

D. When retirement was enforced on the great wicketkeeper Ian Healy in both versions of the game, we saw a smooth transition with yet another gentleman cricketer Adam Gilchrist taking over.

D. He visited the MAPS, and the nearby Nuclear Desalination Demonstration Project, where a desalination plant, using the reverse osmosis method, is producing 18 lakh litres of potable water a day from sea water.

6. This sincere cricketer, who brutalizes opponent bowlers, is one player who upholds strong values both on and off the field.

6. T  he Prime Minister went to the Fast Breeder Test Reactor, which is a forerunner to the present PFBR.

1.  DCAB 4.  ABCD

1.  BCDA 4.  BADC

5. 1.  Nobody can please everybody.

2.  BDAC 5.  CBDA

3.  CDBA

3. 1. The outcome of the Maharashtra Assembly elections defies the familiar pattern of state elections. A. None of these applies to the incumbent government in Maharashtra that has won another term for itself. B. The pattern seen in more than a hundred Assembly elections all over the country in the last decade is fairly simple: three out of four incumbent governments lose. C. Its record was a source of embarrassment for the Congress; its own leaders would fight shy of claiming that the Government was imaginatively administered. D. Those who survive do so for very special and very apparent reasons: exceptionally good governance, emotive appeal along caste-community lines, sheer organisational might or a combination of these. 6. Those at the helm lacked the “liberalization initiative” of a Chandrababu Naidu or a SM Krishna or the manipulative wiliness of a Digvijay Singh. 1.  DCBA 4.  DBAC

2.  BDAC 5.  BDCA

3.  CADB

4. 1. A batsman walking back to the pavilion before the umpire has given his verdict is a rare sight these days. A. Even when batsmen know there was a faint nick to the wicket-keeper or the bat-pad catch has gone to the close-in fielders, they would hardly walk and try to thrive on umpires’ errors.

2.  CBAD 5.  ABDC

3.  DABC

A. It’s the kind of innovative approach you can expect from NEC for your business. B.  It takes a network to do that. C. They empower massive hotels to track individual preferences while enabling a wide range of guest services and administrative functions. D. More specifically, a sophisticated platform that integrates advanced computing and networking technologies combined with highly reliable servers from NEC. 6. And it’s how we continue to deliver on our promise of empowering people through innovation. 1.  BDCA 4.  CDAB

2.  CDBA 5.  BACD

3.  BADC

6. 1. A cliche of business, these days, is that a good reputation takes years to build up but can be lost in an instant. A. That mantra has surely been doing the rounds of the BBC, a prestigious, highly respected organisation which took a real battering from Lord Hutton. B. Contrary to what Mr Gilligan said, the government did not insert a claim that Iraq could deploy weapons of mass destruction within 45 minutes knowing that it was false, nor did it do so against the wishes of its own spies. C. The report by Andrew Gilligan, defence correspondent of the “Today” programme on Radio Four, which in May 2003 incensed the government, was unfounded. D.  That battering was justified.

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  Verbal and Logical Reasoning

6. Sad to say, this report was typical of much of modern British journalism: twisting or falsifying the supposed news to fit a journalist’s opinion about where the truth really lies.

9. 1. Last year Mexico deported 147,000 illegal immigrants in all, some 20% more than in 2007.

3.  ACBD

A. In Tapachula, immigration officials concede that the higher figure represents not their success in stemming the flow, but evidence that more are making the journey.

7. 1. Corporate tax receipts as a share of GDP, never very high, have been falling.

B. Many gather in the seedy, menacing border village of Tecum Unam, whence they cross the Suchiate river to Mexico.

1.  CDBA 4.  ADCB

2.  BCAD 5.  ADBC

A. The exceptions have mainly been those countries, such as Ireland, that have sensibly lowered corporate taxes to attract new firms and investments. B. In America, corporate tax revenues have fallen from 4 percent of GDP in 1965 to barely 1 percent of GDP now.

C. Certainly, the would-be migrants on the Guatemalan side of the frontier do not seem to be deterred by any bureaucratic obstacles.

C.  This has increased their tax take.

D. Over 90 percent came from just three Central American countries (Honduras, Guatemala and Nicaragua), almost all of whom are likely to have entered through the southern border.

D. Indeed, they have been falling for years in just about every big industrial country.

6. The river bank is a medieval scene of hawkers, migrants, smugglers and even the occasional policeman.

6. As firms run themselves more globally, there is less to stop them moving.

1.  BDAC 4.  DACB

1.  BDAC 4.  ADCB

10. 1.  Recovery is indeed under way.

2.  CADB 5.  ABDC

3.  BACD

2.  ABDC 5.  DABC

3.  CDBA

A. And sustaining the growth will require substantial new investment this year.

8. 1.  It all sounds horribly familiar. A. The victims and the investigating police force may be different, but the perpetrator, murder weapon (Windows) and modus operandi are identical.

B.  The stock market is booming. C. But all this makes it harder for the government to remain so unbending towards its creditors.

B. Once again, Microsoft has fallen foul of regulators who accuse it of exploiting the monopoly of Windows, its desktop operating-system software, in order to dominate adjacent markets.

D. GDP grew by perhaps 8 per cent in 2003 and this year’s growth may be almost as strong.

C. This time around, its opponent is the European Commission, which is soon expected to issue a ruling that Microsoft has done the same thing again with its media-player software, and is using the dominance of Windows to monopolize the market for software on bigger “server” computers as well.

1.  DBAC 4.  DABC

D. Four years ago, American trustbusters argued that Microsoft had crushed makers of rival web-browsers by building its own browser into Windows, thus ensuring its ubiquity, since Windows is installed on over 95 per cent of PCs.

B.  That is starting to change.

6. The European case is, in effect, a re-run of the American case in which Microsoft was found guilty four years ago. 1.  DACB 4.  BDCA

2.  CBDA 5.  BDAC

3.  CBAD

6. This is not likely to arrive while the country remains at war with the financial world. 2.  CABD 5.  DBCA

3.  BDCA

11. 1. In a poor country like Peru, food has traditionally been robust, spicy but lacking in sophistication. A.  A decade ago, Lima had no cookery schools. C. Today, there are 14, including a joint venture with France’s Cordon Bleu. D. Mr Acurio, the son of a politician, trained in Paris while pretending to study law. 6. Now, cooking has become an acceptable profession for the children of the elite. 1.  ADBC 4.  DBCA

2.  DCBA 5.  BADC

3.  BACD

ANSWER KEYS

English Usage  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

5

3.

2

4.

4

5.

1

6.

4

7.

1

8.

4

9.

4

10.

5

11.

3

  2.123

HINTS AND EXPLANATIONS 1. Here “the number of pixels” in 6 is an obvious reference to “a 5megapixel camera” in A. Thus A6 is a sequence. 2. Note the words “another plant” in A. Thus A comes after D, where we have the mention of “a desalination plant”. Hence 1, 3, and 4 are ruled out. Again, B is an elaboration of “he saw the massive work” in C. Thus CB is a sequence. Hence 2 is ruled out. 3. “None of these” in A is a reference to the reasons talked about in D. Thus DA is a sequence. 4. “This sincere cricketer” in 6 is a reference to Adam Gilchrist, who has been mentioned in C and D. So it should be either C6 or D6. Hence 1 is ruled out. Now, if you read carefully, you find there are two sections in the paragraph: (i) batsman ethics in 1, A and B and (ii) Adam Gilchrist in C, D and 6. Hence, 4. 5. “Nobody” in the first sentence means “no single person”. This contrasts with “network” in B—that is, a group of persons. Hence 1B is a sequence. Thus 2 and 4 are ruled out. And this network is further specified—note “more specifically”—in D. Thus BD is a sequence and 3 is ruled out. 6. What does “that mantra” in A refer to? That “a good reputation takes years to build up but can be lost in an instant.” Thus 1A is a sequence. Hence 1 and 2 are ruled out. Again, “that battering” in D refers to “a real battering” in A. Thus AD is a sequence. Hence 3 is ruled out.

7. Sentences B and D continue the idea of “falling” talked about in 1. So it should be followed either by BD or DB. The only such possibility lies in choice 1 and 5. AC is logically correct rather than DC, hence 1. 8. You can clearly see a pattern in the key phrases: “It ... sounds ... familiar” in 1 because “once again” something similar has happened in B. And then comes the contrast: “Four years ago” in D and “this time around” in C. 9. Very easy if you note the words “the river bank” in 6. Obviously, it refers to “the Suchiate river” in B. Hence B6 is a sequence. Only 4 offers us this possibility. 10. Note the word “this” in 6. Obviously, it is a reference to “substantial new investment” in A. Thus A6 is a sequence. Hence 1, 2 and 4 are ruled out easily. But after that it’s a tough choice. Both B and D continue the idea of “recovery” in 1. But which of these should be placed first? We prefer D because when we talk about “recovery”, the main thing is GDP growth. Stock market plays only a subsidiary role. Hence we go for 5. 11. Again, an easy one! Read sentence C: “Today, there are 14 ....” 14 what? Obviously, “cookery schools”. Thus AC is a sequence and this we find only in 3.

  PRACTICE EXERCISE  5 Direction for questions 1 to 10:  A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the five given choices to construct a coherent paragraph.

in tourism, at a huge salary, ostensibly to help with the project. C. The main charge concerns a tourism project that Mr Appel tried to launch in 1999-2000 on a Greek island.

1. A. Gilad was to pocket $ 3 m if the project got off the ground.

D. But he also allegedly provided each of them with logistical help in primary-election campaigns in this period.

B. More controversially, Mr Appel hired Mr Sharon’s farmer son, Gilad, who had no experience

E. He sought the help of the then foreign minister, Mr Sharon, and the then Mayor of Jerusalem, Mr

2.124 

  Verbal and Logical Reasoning

Olmert, to persuade Greek officials to give the go-ahead.

5. A. Cases can be heard up to three times before final sentencing.

3.  CADBE

B. Perhaps oddly, the bill does little to tackle the biggest defect in Italian justice: its slowness.

2. A. This would let the Kurds keep a wide measure of autonomy in the three provinces north of Kirkuk, but not Kirkuk itself, pending a new Iraqi constitution due to come into force next year.

C. Might the hope be to make them more susceptible to government control?

B. He favours a return to the status quo that prevailed before the American invasion.

E. Might this be because the prime minister has been a prime beneficiary of delay, several charges against him having run beyond a statute of limitations?

1.  CEDBA 4.  BDEAC

2.  ECBDA 5.  CDEBA

C. The Kurds suspect Mr Bremer of betraying their war-time alliance by seeking to re-impose rule from Baghdad. D. Down in Baghdad, Paul Bremer, Iraq’s American proconsul, is in a bind. E. But that, at present, satisfies no one—and all sides blame the Americans. 1.  DAEBC 4.  CBDAE

2.  DBAEC 5.  DBACE

3.  CBADE

3. A. This may seem unlikely as southern Sudan is the scene of Africa’s longest-burning civil war. B. If Jerome K Jerome were alive today, he would be proud. C. Over a century after he wrote it, There Men in a Boat, his quintessentially English comic novel about accident-prone Victorian gentlemen paddling down the river Thames, is a bestseller in southern Sudan. D. How could they relate to a comedy about chaps in red-and-orange blazers sculling to Hampton Court and getting lost in the hedge maze there? E. Its people have for decades lived in fear of death or enslavement at the hands of mounted militiamen.

D. Likewise, the bill proposes a more hierarchical structure for prosecutors.

1.  EACDB 4.  BDCAE

2.  BAEDC 5.  ABEDC

3.  ACDBE

6. A.  But that conceals some wide differences. B. Slovenia’s GDP per head rises to more than 70 percent of the EU average. C. The eight newcomers to the EU have an average GDP per head of about one-quarter of today’s EU average. D. However, measured by purchasing-power parity, which takes prices into account and so gives a better indication of local living standards, the whole region looks better off. E. Incomes in the richest country, Slovenia, are three times those in the poorest, Latvia—a far greater gap than exists inside the EU now. 1.  CDAEB 4.  ECABD

2.  ECDAB 5.  CAEBD

3.  CAEDB

7. A. Today’s 15 EU countries make do with 11 national languages among them, or one for every 34 m people.

3.  BCEAD

B. Half of central Europe’s national languages are Slavic in origin.

4. A.  “Never been to school,” he explained. B. There are few jobs in Liberia, and the ex-fighters are among the least employable people anywhere.

C. Each has a different national language (if one accepts Czech and Slovak as separate languages), or roughly one for every 6 m people, not counting Russian and the Romany dialects spoken by the region’s largest minorities.

1.  DCAEB 4.  BCAED

2.  CBDAE 5.  CBDEA

C. This muscular 15-year-old can wield an AK-47 with considerable expertise, but he cannot read, write, or even spell his own name. D. Even if the gunmen are disarmed, rehabilitating them will be hard. E.  Take Boima Dagosary. 1.  EBDAC 4.  BECAD

2.  DAEBC 5.  DBEAC

3.  DBECA

D. Linguistically, the central Europeans are more diverse than the Union they join. E. Latvian and Lithuanian stem from the Baltic branch of the Indo-European tree. 1.  ABCED 4.  BADEC

2.  DCAEB 5.  DCABE

3.  BECDA

English Usage  8. A. A second view was that Dr Kelly may have been at fault for speaking too freely to an untrustworthy journalist, but that the government had exposed him when they should have shielded him.

D. The movement should not be seen to be worthless or to have achieved nothing. E. No one who remembers Iran before Mr Khatami was elected would dispute that it has changed.

B.  When the news came out, many thought so.

1.  BAECD 4.  DECBA

C.  Did governments ill-treatment drive David Kelly to suicide?

3.  EDCBA

B. Many people scoffed when the city announced plans in 1990 to develop what was then just an expanse of marsh land, villages and old factories into its new financial district.

E. Some saw Dr Kelly as a whistle-blower, a publicspirited civil servant who had exposed official deceit. 2.  CBEDA 5.  CEBAD

2.  CBEAD 5.  DECAB

10. A.  Cynics should perhaps beware.

D. The third and mildest critique was that although it might have been necessary to release his name, the government did it in a shabby, underhand way, thus contributing to his suicide.

1.  CBEAD 4.  EACDB

  2.125

C. The “build it and they will come” mentality of Shanghai has, after all, paid off handsomely before.

3.  EACBD

D. Last year, it is reckoned, it sucked in just under $ 6 billion, more than a tenth of the total for the entire country.

9. A. These activities are still crimes, but the authorities now turn a blind eye.

E. Today Pudong, as the area is called, is a stunning conglomeration of soaring office towers and hitech factories that has attracted tens of billions of dollars in foreign investment.

C. Since 1997, Tehran has become a more humane, even permissive, place.

1.  CBEAD 4.  ACBDE

ANSWER KEYS

B. Seven years ago, anyone taking a drive with a member of the opposite sex, or wearing make-up, was punished by jail or a lashing.

2.  ECDBA 5.  ECDAB

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

1

2.

2

3.

4

4.

3

5.

2

6.

3

7.

5

8.

1

9.

4

10.

3

3.  ACBED

HINTS AND EXPLANATIONS 1. Only two sentences—A and C—appear to be independent. Fortunately, no choice begins with A. So, we come to the conclusion that C is the first sentence. This rules out choices 2 and 4. Now, look at D, which mentions “each of them”. This refers to “Mr Sharon” and “Mra Olmert” in E. Thus ED is a sequence. This rules out 3. 2. Both C and D are independent sentences. And so it seems the paragraph may begin with either of them. But there is a subtle clue: D gives the full name “Paul Bremer” but C mentions him as only “Mr Bremer”. On this basis alone, D seems to be better poised for the first sentence. Thus 3 and 4 are ruled out. Again, the “he” in B refers to “Paul Bremer” in D. Also, the “this” in A refers to the action in B. Thus DBA emerges as a sequence. Hence, rule out 1 and go for 2.

3. Being the only independent sentence, B qualifies as the first in the paragraph. Thus 1 and 2 are ruled out. Next, look at E. Clearly, it elaborates A. Thus AE is a sequence, which rules out 3. 4. A is an explanation for C: why “he cannot read, write, or even spell his own name.” And “this muscular 15-year-old” in C refers to Boima Dagosary” in E. Thus ECA is a sequence. Hence 1 and 2 are easily ruled out. Again, ECA tries to substantiate D. Therefore, D can’t come after ECA. This rules out 4. 5. Only A and B qualify as independent sentences. Thus 1 is ruled out. Again, if you look carefully, A is an elaboration of the “slowness” mentioned in B. Thus BA is a sequence, which leads us to 2.

2.126 

  Verbal and Logical Reasoning

6. If you go through the sentences, it becomes clear that the passage is about “the eight newcomers to the EU”. Hence C is the first sentence and this rules out 2 and 4. Note the word “rises” in B. This is a consequence of “measuring by purchasing-power parity”, mentioned in D. Thus DB is a sequence. Hence rule out 1. 7. “Each” in C refers to the central European countries mentioned in D. Hence DC is a sequence which eliminates 1, 3 and 4. B continues the theme of language referred to in A, hence DCAB is better than DCAE, hence option 5 DCABE. 8. This one is clearly connected. C raises the issue and B refers to C. This is followed by the three views: the first (though the word

“first” has not been mentioned) in E, the “second view” in A and the “third ... critique” in D. 9. Note the words “these activities” in A. Obviously, they refer to the activities in B. Hence BA is a sequence. Thus 2 is ruled out. Now, note the sentence D. What do the words “the movement” refer to? Certainly, nothing in the paragraph. Which implies D should be the first sentence referring to some movement in an earlier paragraph. 10. What does “the city” in B refer to? “Shanghai” in sentence C. Hence CB is a sequence. Again, in D we are told in “it sucked in just under $6 billion ....” Which is a continuation of E, which tells us about the foreign investment Pudong attracts. Hence ED is a sequence.

  PRACTICE EXERCISE  6 Direction for questions 1 to 12: A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the five given choices to construct a coherent paragraph. 1. A. Says one recent North Korean defector: “While one-third of the population can eat rice and meat soup and one-third can manage to eat corn, the remaining one-third is waiting to die with waterthin porridge.” B. By cutting state subsidies and freeing prices, Kim has sent inflation through the roof—making basic foodstuffs catastrophically expensive. C.  For Kim, the next few months could be critical. D. Domestically, he must deal with the short-term fallout from the limited economic reforms he introduced two years ago. E. A recent report by the World Food Programme states that they have caused even more problems for North Korea’s people. 1.  BDEAC 4.  BAEDC

2.  CEDBA 5.  BADEC

3.  CDEBA

2. A. Arturo Fernandez Lopez, a midlevel accountant in a division of Mexico’s Interior Ministry, got a lump in his stomach two years ago as he was crunching numbers. B. On July 2 that year, Fernandez presented an official complaint to his office comptroller. C. Disaster-relief material and money destined for the coasts had somehow wound up in Mexico’s interior without sufficient explanation

D. The 55-year-old bureaucrat began to notice what he calls “irregularities” in the office accounts—overly expensive purchases and what appeared to be evidence of no-bid contracts. E. But 17 days later, when he showed up for work, armed policemen outside the office stopped him at the door. 1.  CEABD 4.  ADCBE

2.  ACDBE 5) ADCEB

3.  DEBAC

3. A. Recently, Elizabeth showed me a gorgeous scarf she’d made. B. When she brings her clients to doctors’ appointments, she knits while she waits. C. Knitting is a passion for my friend Elizabeth, who is a caregiver for the elderly. D. “How long does something like that take?” I asked. E. “About one stress test and one colonoscopy,” she estimated. 1.  DECBA 4.  ADCEB

2.  CEBAD 5.  CBADE

3.  ADECB

4. A. Their parents are offered a few thousand rupees in the first few months after which payment is stopped. B. Hundreds of children are taken by agents to Kerala to be employed as domestic helps. C. Worse is the plight of children in the 10-14 age group who are taken to Maharashtra and Gujarat to be employed under excruciating conditions in sweet-making units.

English Usage 

  2.127

D. Police and NGOs confide that a number of scams work overtime in the poverty-stricken pockets of Villupuram, Theni, Kambam, Madurai, Thenkasi and Chennai.

C. Today, offices are equipped with an array of technological features and come loaded with satellite phones, desktop computers, printers, copiers, fax machines and other items of advanced electronic gadgetry.

E.  Child trafficking across state borders is rampant.

D. Till just over a decade ago, virtually the only assets administrative personnel had to keep track of were company vehicles.

1.  EDBAC 4.  DBACE

2.  BACED 5.  DBAEC

3.  BCDAE

5. A. Anyone who invested in the IPO for brokerage firm Indiabulls in September 2004 and is still holding the shares must be a very happy person. B. Therefore, the Rs 200 crore in wealth created by Indiabulls is dwarfed by the estimated Rs 2,200 crore created by the IPO of software giant TCS.

E. But that was before the technological revolution hit the world of business. 1.  BCDEA 4.  DAEBC

2.  DEABC 5.  DECAB

3.  DECBA

8. A. But though an ideal family help, she has been unable to cope with her own family.

D. In the eight months since the Indiabulls public issue, an investment of Rs 20,000 is now worth almost Rs 1 lakh.

B. She has so mastered the art of looking after a house, preparing and serving meals, that all overburdened mothers who catch a glimpse of her and who can afford to, have the same thought: how can they persuade this paragon to work for them?

E. But Indiabulls’ issue was small in size—Rs 52 crore.

C. Juliette is fifty-one, and has been a domestic servant since the age of sixteen.

1.  ABCED 4.  DCEBA

D. At work she is wholly reliable, taking endless care with every detail; but in her own home those qualities have never been sufficient.

C.  Happy and rich.

2.  DBACE 5.  DBAEC

3.  ACDEB

6. A. Beijing gave no sign it intended to change the policy in the near term, which was bad news for the world’s automakers. B. A 30 per cent sales increase in the first half of the year dipped to a meagre 6.8 per cent in July. C. The August forecast was worse: a minuscule 0.1 per cent.

E.  Has she a few hours to spare? 1.  CBAED 4.  BCDAE

2.  CDBEA 5.  CEBAD

3.  CBEAD

9. A. But neither he nor Jinnah nor Patel fully saw the strategic consequences a divided sub-continent would hold for their peoples.

D. The main reason for the slowdown was the government’s new policy of tightening credit rules to slow an overheating economy.

B. Alone among Indian political leaders, Nehru had some sense of the stakes of these conflicts and of the need for an independent India to position itself advantageously in relation to them.

E. After racing along at a 62 per cent growth rate in 2002 and 76 per cent in 2003, car sales in China hit a speed bump in 2004.

C. The theatre of the great war of the 20th century was perhaps not—as we usually think of it—in Europe, but in Asia.

1.  AEBCD 4.  ECBDA

D. For over two decades, from the Japanese invasion of Manchuria in 1931 to the end of the Korean War in 1953, Asia was plunged in swirling conflicts and almost continuous war.

2.  EBCDA 5.  ECDAB

3.  DAEBC

7. A. Today, in addition to the company cars, a host of other things have moved centre-stage, that are deemed no less important and valuable to the smooth and well-oiled working and functioning of a modern, efficient organization. B. From the firms’ simplistic concerns for keeping their fleet in a proper trim, organisations now have their hands full taking deft care and proper management of their gizmo-laden and automated offices.

E. Partition has undoubtedly been a bonanza for international arms dealers—but overall, it created two weakened successor states to the departing Raj, much diminished as Asian powers—and it left all residents of the region more vulnerable, and open to outside influence. 1.  CEDBA 4.  EADCB

2.  DCBAE 5.  CDBEA

3.  CDBAE

2.128 

  Verbal and Logical Reasoning

10. A. The captions that attend these pictures are no doubt somewhat unhistorically drawn from the period when he had become Qaid, and they stand in tension to the images.

goods, services and people, would be a first and important step in trying, in our own lifetimes, to improve on those negative consequences of Partition which are part of our inheritance.

B. In Pakistan itself, a new image of Jinnah is being propagated, apparently in order to make him more attractive to the young.

D. The politics that resulted in Partition not only broke families and cultural connections. E. It disrupted the economic and trading rhythms of the subcontinent.

C. But, they may serve to stimulate the young in Pakistan to look anew at their founder, to ask different questions of him.

1.  DEABC 4.  CDEAB

D. This is not the skeletal, sherwani-clad Jinnah most Pakistanis have seen in some form or other virtually every day of their lives.

2.  EACBD 5.  BEDCA

B. Jinnah would be dismayed among other things to learn churches have been bombed and a bishop shot himself in despair in Pakistan; that a young American journalist had his throat slit and was forced to say: “I am a Jew.”

3.  EDABC

C. Both would be broken-hearted at the endless cycle of violence in Kashmir.

11. A. That is something that human ingenuity has shown a capacity to fix.

D. But not only are non-Muslims targets of hate: Muslims are too frequently killed in a mosque in Pakistan.

B. If Europe, after centuries of war and animosity, and after the greatest bloodletting in human history, could, in just 60 years, devise a complex, pragmatic unity— one which respects the basic sovereignty and integrity of its member states—this can serve us as a lesson.

E. Gandhi would be broken-hearted to confront the rape, murder and arson of Muslims in Gujarat, his own home state. 1.  BDECA 4.  AEBDC

C. The creation on the sub-continent of an institutional framework which can allow the open exchange of

ANSWER KEYS

3.  DCBAE

12. A. If they were looking down at South Asia, I am sure both Jinnah and the Mahatma would be pained at the turn of events.

E. As the Pakistani scholar Akbar Zaidi has pointed out, billboards have appeared in Karachi, Lahore and Islamabad, sponsored by an Internet company, which show the Qaid-e-Azam before he became Qaid—the young, dashingly handsome man about town, in wingcollar and sporting a diamond tie-stud. 1.  BEDAC 4.  BDEAC

2.  DEACB 5.  DAECB

2.  ADBEC 5.  ABDEC

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

4

3.

5

4.

1

5.

3

6.

2

7.

2

8.

3

9.

3

10.

1

11.

2

12.

5

3.  ECBDA

English Usage 

  2.129

HINTS AND EXPLANATIONS 1. If you go through the sentences, you find that they are an explanation of why “the next few months could be critical for Kim.” Hence C should be the first sentence. Which rules out 1 and 4. Again, note the pronoun “he” in D, which is a reference to “Kim” in C. Which gives CD as a sequence. So reject 2 and select 3.

7. The passage seems to be chronological to some extent. So only D qualifies as the first sentence. Hence 1 is ruled out. And E can refer only to D. Now, DE rules out 4. Again, “satellite phones, ... electronic gadgetry” in C refer to the “gizmo-laden and automated offices” in B. Thus we get BC as a sequence and 3 is ruled out.

2. Note the phrase “17 days later” in E. This is an obvious sequence to a sentence containing some date/day. Which we find in B— “on July 2”. Thus BE is a sequence. Which rules out 1 and 3. Again, look at “the 55-year-old bureaucrat” in D. This refers to “Arturo Fernandez Lopez” in A. Thus AD is a sequence. Which rules out 2.

8. 4 is ruled out because C is the only independent sentence that talks about “Juliette”; the rest use “she”. Again, BE describes how she is an “ideal family help” and should therefore come before A. This rules out 1. Besides, D is an elaboration of A. Hence we get AD and 2 is ruled out.

3. Again, two sequences. CB tells us what Elizabeth regularly does. ADE tells us about a particular incident related to this habit. And normally we first mention the general and then the particular. Hence CBADE.

9. The “he” in A is a reference to “Nehru” in B. Hence we get BA as a sequence. This rules out 4. Again, D is an explanation of C. Which gives us CD. Hence 1 and 2 are ruled out.

4. “Their” in A refers to “hundreds of children” in B. Thus BA is a sequence and 3 gets eliminated. Again, if you read the sentences carefully, E is the theme sentence of the paragraph and deserves a place at the beginning. Thus 2 and 4 get eliminated. 5. Note the short sentence C. It goes with “a very happy person” in A. Thus AC is a sequence. Which rules out 1 and 4. Again, B is a consequence of E. Thus EB is a sequence. Which rules out 2. 6. Read all the sentences and you will find E to be the only independent one. Thus 1 and 3 are eliminated. Now the problem, if you observe the remaining choices, has narrowed down to establishing whether B comes first or C. The clue lies in “worse” in C: it is a comparison to B. Hence it should be BC. Which eliminates 4.

10. E talks about the “Qaid-e-Azam”, which is a reference to Jinnah. Hence E can’t be the first sentence. This rules out 2 and 3. Between D and E, clearly D refers to E. Which gives us ED and rules out 4. 11. C talks of “those negative consequences” and therefore can’t be the first sentence. This rules out 4. Also, D should immediately be followed by E (assume “not only ... but also ...” structure). Hence 3 is ruled out. Now, apply trial and error. 12. Sentence A serves as the introductory one and introduces “Jinnah” and the “Mahatma”. We will take the first of these two—as they appear in the sentence—first. Hence, A is followed by BD for Jinnah, and then E for the Mahatma. Finally, C refers to both.

  PRACTICE EXERCISE  7 Direction for questions 1 to 11:  The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 1. A. I can still remember arriving at the Malayan internment camp. B. Packed tightly together in compartments, we had been forced to sit on each other’s knees. C. One woman became hysterical and a Japanese guard came in and slapped her several times on the face, hard. D. It had been a nightmarish trip: a train journey which had started in the afternoon and finished in the heat of the next day. E.  The air was dank and claustrophobic. F.  Children began vomitting. 1.  DBEFCA 4.  DEFBCA

2.  ADBEFC 5.  ADBECF

3.  ABCEFD

2. A.  In his place came Takashi, small and insignificant. B. Every day we worked until lunchtime while a Japanese soldier lay down in the shade of a tree, making sure we were not idle. C. One day the latrines at the camp broke down and the “strong girls”—those aged between 15 and 25 and considered healthy enough to do the backbreaking jobs—were ordered to dig trenches to be used as an alternative. D.  For months we laboured in the trenches. E. It was hard work in the tropical sun, especially for girls who had never done manual work and were malnourished. F.  Then one day our usual guard did not turn up. 1.  CBDEFA 4.  BDFCAE

2.  DFEABC 5.  DCEBFA

3.  CDEBFA

3. A. I had returned from a trip to Scotland and was eager to give the gifts I’d chosen to my husband and children.

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B. Finally, one Sunday morning, I convinced him to come and let me put it on. C. As I attached the tie to his collar, his tense shoulders relaxed and he heaved a sigh of relief. D. I had brought a tartan bow tie for four-year-old Tommy, who had never seen one before. E. “Oh Mum,” he said, “I thought you were going to put it in my hair.”

6. A. Leaving Aileen Wuornos and her murderously unglamorous ways far behind, Charlize Theron dons 1930’s garb and vamps her way through her new movie Head in the Clouds as a French-American heiress, bohemian and international heartbreaker named Gilda Besse. B. Reality intrudes in the form of the Spanish Civil War, followed by World War II.

F. He was normally obedient, but resisted my efforts to put it on him.

C. Gilda’s supposedly irresistible charms leave every man and woman prostrate at her feet.

1.  ADEFBC 4.  ADFBCE

D. While conscience calls Guy and Mia to the battlefront, the hedonistic Gilda proclaims them all party poopers and stays behind to await her darkly ironic fate.

2.  DAFCEB 5.  DAFBCE

3.  DCEBFA

4. A. Her husband was employed outside Rajasthan and she had chosen Barmer to provide a good education to her children. B. In a rare case of migration from a city to a village, Teeja Jakhar shifted to Chokhla from Barmer city along with her two daughters last year. C. The British exploration company Cairn Energy PLC promised to pay her Rs 3 lakh per year for three years for rights to her land. D. She earns Rs 6,000 per month by selling water drawn by her tubewell to Cairn.

E. Her foremost devotee is the Irish-born Guy, who falls under her spell as an undergrad at Cambridge and later rekindles his flaming devotion in Paris, where Gilda, now a photographer, shares a flat with Mia, a Spanish model-stripper-nurse-activist with a limp. F. Soon all three are happily living together in what may or may not be a menage a trios (the movie is coy). 1.  ACEDFB 4.  AEFBDC

2.  BDFECA 5.  ACEFDB

3.  ACEFBD

7. A.  They were playing golf.

E. She bought a diesel-run tubewell with the first instalment and plans to grow at least one crop on her 40-acre plot.

B. A couple of my South Korean friends called me recently, a few weeks apart, from obscure towns in Japan.

F. But Mangla near Barmer, since January last year the site of India’s biggest oil discovery in 22 years, changed all that.

C. Neither was attending a business conference or scholarly seminar.

1.  CEABFD 4.  BACFED

2.  BCAFDE 5.  BAFCED

3.  BCEAFD

5. A. The economy earlier rested on land and cattle, both depending upon scarce and unpredictable rain to generate a sustainable income. B. But Bhatt says Barmer has improved from a sick district two years ago to a developing one. C. “While earlier there were no avenues to expand economic activities, now there are options to supplement one’s income.” D. “It is no longer a place for punishment postings,” says AC Bhatt, district collector, Barmer. E.  Oil exploration has created jobs in a big way. F. Liquid gold has made a godforsaken place like Barmer glitter. 1.  ACDBFE 4.  EABCDF

2.  FEACBD 5.  FDCBAE

3.  FDCABE

D. I called a golfer friend in Seoul to ask what was going on. E. He told me that in recent months thousands of South Koreans had been flying to Japan to play. F. Both had flown directly from Inchon Airport to Japanese regional airports and proceeded directly to the course. 1.  DEABCF 4.  AFBCDE

2.  BCAFDE 5.  BACFDE

3.  BACDEF

8. A. Men who smoked this amount were almost three times as likely to be killed by lung cancer. B. Compared with those who had never smoked, the men and women who smoked between one and four cigarettes a day were almost three times as likely to die of coronary artery disease, it was found. C.  There is no safe level of smoking, the study said. D. The so-called light smokers also had significantly higher death rates—1.5 times higher generally— than those who had never smoked.

English Usage  E. Chain smokers risk developing heart disease, but a new study has revealed that those who smoke just one to four cigarettes a day also face a similar threat.

B.  Gentlemen, by nature, prefer blondes. C. But the Indian government would like our very own magnificent men to be ungentlemanly and ‘keep off ’ the blondes, brunettes and redheads too, both in and out of their flying machines.

F. Among women, smoking one to four cigarettes daily increased the chance of dying from lung cancer almost five times. 1.  ECBFAD 4.  EDCBFA

2.  FCDEBA 5.  EBFCDA

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D. The IAF officers involved in a joint exercise with the men—and the women—of the US air force in Agra had to undergo a special briefing on behavioural codes even before the yanks arrived.

3.  EBFACD

9. A. The pass/fail concept creates a lot of pressure on students; but it has a positive aspect, too.

E. More importantly, this attitude speaks of the difference in gender stereotyping between developed and developing nations.

B. It’s a barometer of teachers’ performance in government schools, especially in rural and suburban India, and should be retained till alternative mechanisms of teacher accountability are devised. C. The spirit behind the decision not to carry “pass” or “fail” on mark-sheets and, more importantly, replace marks with a nine-point grading scale for class 10 examinations from 2008 is beyond reproach.

F. The official fatwa that bars them from ‘messing’ and ‘spending evenings’ with American women officers stands out in stark contrast to the free-wheeling attitude of the foreigners, who face no official dos and don’ts, in or outside the cockpit. 1.  DEFBCA 4.  BEDFCA

D. That the CBSE has woken up to the urgent need for reforming its class 10 and class 12 board examinations is welcome.

2.  DFAEBC 5.  BCDFEA

3.  BCDFAE

11. A.  Why not earlier?

E. While the grading system may not be a bad idea in itself, doing away with the pass/fail concept could have serious implications for school education in the absence of equally emphatic reform in other related areas.

B.  I was apprehensive: would a Muslim be welcome? C. Contrary to my fears, the experience turned out to be a happy one.

F. The board would, however, do well to re-examine the shape of its reformist intent.

D. Last spring, I visited a gurdwara for the first time in my life.

1.  ABDCFE 4.  EABDCF

E.  It was so peaceful and tranquil in the gurdwara.

2.  DCEFAB 5.  DCFEAB

3.  CFEABD

F.  I was there for an hour with Sikh friends.

ANSWER KEYS

10. A. Hence, they are more liberal with their compliments, punctuating the airborne callisthenics with unbridled ‘wows’ and ‘whoos’.

1.  DABCEF 4.  DBCEFA

2.  DEFCAB 5.  DBACEF

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3

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5

3.

1

4.

5

5.

3

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3

7.

5

8.

5

9.

5

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2

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1

3.  EFDABC

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HINTS AND EXPLANATIONS 1. Clearly, the para gives a picture of how the author and others had

arrived at the Malayan internment camp. Hence it begins with A. Which rules out 1 and 4. We are told about the trip in D and its details in the remaining sentences. So it should be AD.... This rules out 3.

2. The “his” in sentence A can refer either to “a Japanese soldier” in B or to “our usual guard” in F. But FA makes logical sense while BA does not. Hence we get FA, which rules out 2 and 4. Again, note how the word “trenches” establishes a CD connection. Hence we prefer 3 to 1 and 5. 3. Since A is the only independent sentence, it should come first. Hence 2 and 3 are ruled out. Now, look at what Tommy says in E. This is an expression of relief and hence best fits after “a sigh of relief ” in C. Thus CE is a sequence. Which rules out 1. 4. B is the only independent sentence. Hence 1 is ruled out. And F is the tone-changer (“But ....”). Now, if you watch carefully, A can be grouped with B and the rest of the sentences with F. So, we get BAF _ _ _. And this combination is available only in 5. 5. Note the word “earlier” in A. Which means it can’t be the first sentence. Hence 1 is ruled out. Again, the sentences with inverted commas provide you an intelligent clue. Clearly, DC is a sequence. This establishes 3 as the only correct choice. 6. If you go through the sentences carefully, you will make out that A is the only independent sentence. Thus 2 is eliminated. Now, the

“her” in E refers to “Gilda” in C, establishing CE as a sequence. Which eliminates 4. Now, F is a sequence to E; and D is a consequence of B. Thus we obtain EF and BD. Which means 3, not 1. 7. The paragraph cannot begin abruptly with “They”. Hence 4 is ruled out. Now, F can’t come after E because of the usage of “Both”. Thus 3 is ruled out. This leaves us with two choices and we can go by trial and error. 1 is rejected because in this arrangement there is a sudden shift from A to B. 8. The use of “this amount” in A is a clear reference to F—“smoking one to four cigarettes daily”. And FA rules out 2. Also, FA is an elaboration of B. But BFA does not lead us any further. Is there any relationship between C and D? Yes CD because D explains C. Which means 1 and 4 are ruled out (5). 9. If you go through all the sentences, it is clear that board examination reforms are being talked about. Hence D serves as the introductory sentence. Hence 1, 3 and 4 are ruled out. EF is an incorrect contrast statement. FE is the correct combination, hence 2 is eliminated and 5 is the answer. 10. Beware of (1) and (4)! Don’t get blinded by the “Hence” in A! 11. A has to come just after D. So (2) and (4) are ruled out. But (3) is ruled out because D must serve as the introductory sentence.

  PRACTICE EXERCISE  8 Direction for questions 1 to 10:  In each question below five sentences lettered A, B, C, D, E are given, followed by four options each indicating two sentences, which when interchanged, create a logical sequence of five sentences.

E. In fact, the Association is confident that modern retail would have a beneficial trickle-down effect on sectors such as steel, cement and glass, bring larger revenues for the state governments and boost sectors such as tourism and hotels.

1. A. The Indian retail sector is on the threshold of something big.

1.  A and B 4.  B and D

B. The Retailer’s Association of India, formed recently by the top 25 modern retailers in the country, estimates that the annual retail consumption in the country is around Rs 9 lakh crores, but with value addition, could be scaled upto Rs12 lakh crores. C. With the total retail trade estimated at 200 billion dollars and the organised segment accounting for a mere 2 percent of this, almost all the organised players have in place, aggressive expansion plans, spreading either to more cities or to larger towns. D. Also, the development of modern retail in India could enable enhanced productivity, employment and economic growth.

2.  B and C

3.  A and C

2. A. Sadruddin insisted that he had equal sympathy for eastern and western people. B. He seemed the favourite to become the UN’s Secretary General in 1981, but the Soviet Union vetoed his candidature, claiming he was too pro-western, and vetoed him again in 1991. C. Around that time, stories circulated that the prince was a secret agent for the British, using his job as a cover for intelligence gathering. D. It was almost certainly nonsense, but the Russians may have believed it. E. Sadruddin stepped down after 12 years, the longest any refugee chief has held the job, but returned to

English Usage  the UN at times of crisis to give help, notably in Afghanistan, during the Soviet occupation and in Iraq, after the first Gulf War. 1.  A and E 4.  B and C

2.  B and D

3.  D and E

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C. Fiscal soundness is not a question of mere numerical deficit targets. D. The figures for October show further deterioration with revenue deficit at 83.9 per cent and fiscal deficit at 45.2 per cent.

3. A. In the maze of India’s twisted economic policies, it is difficult to find a more complex bundle of contradictions than the aviation policy.

E.  The deficit targets have been exceeded.

B. While the government is omnipresent in the closely guarded sector, a whiff of fresh air has started blowing in the form of ‘open skies’ agreements with Thailand, some South Asian countries and Sri Lanka.

6. A. But drug company executives have insisted that their industry is fundamentally healthy and their expensive research efforts will pay off.

C. Piecemeal liberalization would only harm the sector rather than encourage growth, and it will put both passengers and the industry at a disadvantage. D.  While implementation of the ‘open skies’ agreements will take time, these pacts indicate the hurry to put the horse before the cart. E. Much more is on the cards, if senior bureaucrats are to be taken, at face value, but concerns have cropped up. since the current trend indicates the lack of a ‘wholesome’ strategy. 1.  A and C 4.  C and D

2.  B and C

3.  B and D

4. A. That is, availability of a service, which can throw some light on the possible search terms specific to one’s subject will certainly be useful. B. Refining the search query through trial and error process is obviously a labourious exercise. C. Let us have a look at some services that can be used for this purpose. D. As Google churns out one service after another with amazing regularity, of late users find it difficult to pass even one week without reference to it. E. Recently, Google has rolled out another service for helping its users utilize its search service a little more efficiently. 1.  B and D 4.  A and C

2.  A and B

3.  C and D

5. A. The fiscal picture at the end of September reveals a revenue deficit of 79 per cent of budget estimate and a fiscal deficit of 39 per cent. B. Deficit reduction is to ensure that government borrowings are within sustainable limits and the borrowed funds are used productively for development and creation of capital assets.

1.  A and B 4.  C and D

2.  A and C

3.  B and D

B. Three major companies disclosed serious problems with important medicines. C. This has thrown the spotlight on the fact that the drug industry is failing in its core business of finding new medicines. D. The decline in drug research and development has been an open secret among analysts and scientists for years. E. Worldwide drug industry is clearly ailing. 1.  B and E 4.  C and E

2.  A and E

3.  C and D

7. A. To say that not all is well with higher education will be something of an understatement. B. Problems relating to higher education—privatization and commercialization, political interference and corruption, mismanagement and agitations, falling standards and irrelevance—are topics of public discussion almost on a day-to-day basis. C. Is it possible to locate some key factors that can explain the mess that higher education in the country finds itself in? D. The prolific and unplanned expansion of higher education since independence is undoubtedly a major factor responsible for this malaise. E. That is the question that Dr Mutton, a former professor, vice-chancellor and secretary of the association of Asian Universities and one still actively engaged in matters relating to higher education, discusses in his latest book. 1.  D and E 4.  D and C

2.  A and D

3.  B and D

8. A. The sunshine days are there again for the Indian steel industry.

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B. In the emerging global scene, experts predict a shift in steel use away from the developed world towards nations like China and India.

D. In addition, the unleashing of so called incentives to this sector by state governments is boosting their growth.

C. A combination of factors appears to be working to push it on to a higher orbit.

E. This supersonic trajectory is fuelled by the eco-

nomic compulsions of North American and European corporations to shift their low-end jobs to countries like India. 1.  D and E 2.  B and D 3.  C and D 4.  C and E

D. If the steel producers are grinning, consumers at large are wearing a grim look. E. The way the industry is slowly moving into a new era, chances are that prices will head only one waynorthward. 1.  B and E 4.  B and D

2.  A and B

10. A. Nobody knows how many NGOs are there in India. B. It is said that there are at least a thousand of them with an annual income of Rs l crore and more. C. Estimates vary from a million to several times that number. D. By definition, Non-Governmental Organizations (NGOs) must have come into being along with governments. E. Though NGOs have, in this manner, a long history, it is only in the past 20 years that they have become ubiquitous.

3.  A and C

9. A. Business Process Outsourcing (BPO) is one of the hottest career destinations for young Indians. B. The number of Indians working in this sector was about 2,50,000 by March 2004 and is to grow to 12 million in three years.

ANSWER KEYS

C. In addition to infrastructure facilities, BPO units have been exempted from several labour laws and environmental regulations.

1.  B and E 4.  B and C

2.  A and B

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4

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3.

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2

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2

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1

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2

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4

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3.  D and E

HINTS AND EXPLANATIONS 1. A introducing the topic must begin the passage, but instead of B, D should follow A, AD being mandatory. C should be next with its data on retail trade. CB being mandatory, B giving data on ‘The retailer’s Association of India’, should follow C, thus B and D should be interchanged to make the sequence a coherent paragraph, E already concluding the passage appropriately with its ‘the Association is confident’ etc., ADCBE is the right sequence, (4) is the answer.

3. A initiating the argument is an appropriate opener of the passage. B picking up well the argument of ‘the aviation policy’ being ‘bundle of contradictions’ advances it with ‘whiff of fresh air’ etc., but B should be followed by D, its ‘open skies’ agreement argument picks up appropriately form B, instead, C wrongly follows it, so both C and D are misplaced. E with its ‘Much more is on the cards’ is an apt conclusion of the passage. ABDCE is the right sequence, (4) is the answer.

2. E introducing the topic, describing ‘Sadruddin stepped down after 12 years’ etc., is the best starter but here E is wrongly placed. B should be next, its ‘He’ referring to ‘Sadruddin’ of E which should have begun the passage, EB being mandatory. C is at the right place with its ‘stories circulated’ etc., similarly D is also at the right place, again CD being mandatory. Only A is an appropriate conclusion of the coherent passage but is misplaced. So only interchanging A and E would make the passage coherent. EBCDA is the right sequence, (1) is the answer.

4. B introducing the topic is the best starter for the paragraph. A should be next its ‘That is availability of service’ picks up the argument from B. Both A and B are misplaced. C, D and E are in right sequence. BA being mandatory A and B are to be interchanged to bring out a coherent passage. BACDE is the right sequence, (2) is the answer. 5. C initiating the argument is the best starter but is misplaced. B is rightly placed but C is misplaced. B is rightly placed as it picks up

English Usage  the argument from C and advances it appropriately. A with its ‘fiscal picture’ etc., should follow B but A is also misplaced. D and E are in order and rightly placed. CB and AD being the links, CBADE is the right sequence and (2) is the answer as A and C are to be interchanged to make a coherent passage. 6. E being the most general statement or introducing the topic is the best starter but it is misplaced. B with its ‘Three major companies’ etc., should follow E as it picks up E’s argument appropriately and advances the argument. C should be next its ‘This has thrown’ etc., refers to B’s describing ‘Three companies’ have ‘serious problems’. D must be next giving the reason behind the ‘serious problems’. A is an appropriate conclusion but it also is misplaced, interchanging A and E would set right the sequence i.e., EBCDA hence (2). 7. A being the most general statement or initiating the argument must begin the passage. B should be the next, as it sums up the argument appropriately and gives the details of ‘Problems relating to higher education’. C has the proper logical question, should follow B. Now comes the disruption, E should follow C with its ‘That is the question’ etc., the logical corollary to C’s question, but it is misplaced in the end as the conclusion, which it is not. What D says is the appropriate conclusion of the passage which is also misplaced. So, D and E should be interchanged to make the sequence coherent, i.e., ABCED. (1) is the answer.

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8. B being the most effective and optimistic starter is the suitable statement as it initiates the topic telling that there is ‘a shift in steel use’, there are ‘sunshine days again in the Indian steel industry.’ A sustains the spirit or the force by stating that. C is the logical corollary with its ‘A combination of factors’ etc., D is rightly placed. E is rightly placed at the end, as what it says concludes the paragraph appropriately with its contrasting picture. A and B are misplaced which can be set right on interchanging them. BACDE is the sequence, (2) is the answer. 9. A telling BPO ‘is one of the hottest career’ etc., is the suitable starter. B with its details and data on BPO sector should be the next. But E, its ‘This supersonic trajectory’ etc., is the logical corollary of AB, so it is misplaced. D with its ‘In addition’ etc., is rightly placed. C with its ‘In addition to infrastructure facilities’ etc., is the appropriate conclusion but it is also misplaced. So, C and E should be interchanged to make the right sequence i.e., ABEDC, hence (4). 10. A initiating the argument should obviously be the opening sentence. But then C with its ‘Estimates vary’ etc., should be next, so C is misplaced. B with its ‘there are at least thousand of them’ being the logical corollary, should follow, which again is misplaced. D with its ‘By definition’ etc., has rightly followed. E appropriately concluding the sequence with its ‘NGOs have, in this manner, a long history’ etc., is rightly placed in the end. So, B and C have to be interchanged to make the sequence coherent–ACBDE, hence (4).

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  CRITICAL REASONING In reasoning and argumentation, it is important to be focussed on the topic at issue. What it means for a student is—give reasons or evidence that bears on the topic, that is relevant to it. Although this sounds easy theoretically, but to a larger extent, ‘bad’ or invalid reasoning occurs because of lose of focus. Critical reasoning is one of the tools that CAT uses to evaluate this. Before we move ahead, let us make ourselves aware of some of the basic concepts:

Example  1

A critical reasoning paragraph which is usually an argument consists of the following:

There are two parts of this passage:

Hindus are protesting against breaking off the Ram-Setu, an ancient monument, because they believe that this monument is made by Lord Rama himself and breaking it will hurt their religious sentiments. According to a recent finding by a politician, “Rama did not have an Engineering degree, hence this monument should be broken.”

Explanation

1. Premise(s):  statement of fact which are given.

1st part–The monument was made by Lord Rama, and hence breaking it will hurt the sentiments of Hindus.

2. Assumption(s):  are gaps in the arguments and are unstated they are usually the basis of conclusion.

2nd part–Since Lord Rama did not have an Engineering degree, so he cannot construct a monument.

3. Inference:  is what we draw from the premises. It is specific and indirect. If the assumption is stated it becomes an inference. 4. Conclusion:  premise(s) + assuption = conclusion, it is holistc and direct in nature. 1.  Argument–An argument is a claim backed by reason/s. Go through this converstation to understand what is an argument: Son–I need a laptop(Right now its just a claim). Father–Why? (Father is asking for reason ) Son–Because i have taken a course Quantitative Analysis, and most of the course work happens on laptop. Father–Why laptop? Why not desktop? Son–I need mobility too. So son’s initial claim of “laptop” is supported by two reasons: i. A course in Quantitative Analysis ii. Mobility 2.  Inferences—Judgement based upon some evidence or assumptions or reasons or intuitive feelings. Now we will learn some of techniques to identify the relevance of the reasoning and the ways in which reasoning goes awry.

1.  Fallacy of irrelevant reason Bad reasoning is said to be fallacious. Please understand that it need not be necessarily wrong. It may be true, but not relevant in the case given, and hence fails to establish logical connection between the argument and conclusion. Understand that relevance is not same as being strong reason.

At the end, conclusion is derived—Since the monument was not made by Lord Rama, breaking it will not hurt the sentiments of Hindus. Now we will try to find flaws in this whole passage: 1st part introduces the statements, and hence we will not verify that “breaking off the monument hurts the religious sentiments of Hindus or not?” The statement given that “breaking it will hurt their religious sentiments” is true. 2nd part puts logic to establish the connection with 1st part using the statement that “Rama did not have an engineering degree, and hence he cannot construct a monument”. If this statement is true and universally acceptable, then it is proved that: Rama did not have an engineering degree ⇒ he cannot construct the monument ⇒ What Hindus believe is false ⇒ So breaking the monument off will not hurt the sentiments of Hindus. We can see that the statement of politician has the connotation that only engineers can construct any monument. Or in other words “any non-engineer cannot construct any monument” which is false. Hence politician’s logic fails to establish its veracity, hence belief of the Hindus that monument was made by Lord Rama is not disapproved, and hence the conclusion is wrong.

2.  Correlating the wrong ends This occurs when on the basis of a certain result, it is tried to establish a conclusion without examining the proper credentials.

Example  2 During a recent survey done by a newspaper, it has been found that 65 per cent of the people who responded in

English Usage 

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the survey have voted as good governance as their most important expectation from the government. So, a party that uses good governance as its main issue in the coming election will win the election and form the government.

b. During rainy season, dengue mosquitoes are more prevalent. Therefore, dengue mosquitoes must thrive in rainy season.

Explanation

Conclusion:  Rainy season causes dengue mosquitoes. In this case, one phenomenon leads to other phenomenon. Hence, the reasoning exhibited here is similar to the statement given in the question.

Let us find out flaws in the above logic: 1. Survey results are based on the “people who responded” and does not consider the whole population. Hence any conclusion derived out of this sample of the respondents may not depict the correct expectation of the whole population. 2. People who responded to the survey results may not vote in the election, and hence any conclusion about “who will win the elections” is not definitely true.

Example  3

Premise:  Dengue mosquitoes are correlated with rainy season.

c. ERP helps increase the work efficiency of employees. As a result, employees have more free time for their family. This statement demonstrates a different pattern of reasoning than the original statement given in the question: Premise:  ERP causes increase in efficiency. Assumption:  Increase in efficiency causes free time.

Beautiful monuments attract people, no doubt about it. Just look at this city’s beautiful monuments, which are among the most overcrowded monuments in the country. The original argument bases a conclusion that one phenomenon causes another on an observed correlation between the two phenomena. Whole argument can be seen as following:

Conclusion:  ERP causes free time.

Premise:  “Beautiful monument” correlated with “crowd of people”. Conclusion:  Beautiful monument causes “crowd of people”.

Example  4

We have to take this conclusion as ‘given’ and we will not verify this. Let us identify which of the following statements exhibit a pattern of reasoning most similar to the one exhibited in the argument above: a. Students who are scolded severely tend to misbehave more often than other students. Hence, if a student is not scolded severely that student is less likely to misbehave. Premise:  Scolding students is correlated with misbehaviour among students. Conclusion:  Not scolding will be correlated with ‘no misbehaviour’. Despite the conclusion, in isolation with the statement given in the question, may be true, but it does not exhibit the same argument as in case of the statement given in the question which talks about one phenomenon causing other, and this statement talks about absence of one phenomenon causing the absence of other phenomenon. Hence the reasoning is not similar to what is given in the original statement.

It can be seen above that 1st phenomenon causes the 2nd phenomenon and this 2nd phenomenon causes the 3rd phenomenon, hence 1st phenomenon caused the 3rd phenomenon. This reasoning is not similar to the original one in the question.

Beautiful monuments attract tourists, no doubt about it. Tourists bring revenue to the location. Just look at this city’s beautiful monuments, which are among the most revenue generating locations in the country. Understand the logic There are three phenomenon: 1st phenomenon–Beautiful monument attract tourists. 2nd phenomenon–Tourists bring revenue. Conclusion–Beautiful monuments are the most revenue generating locations. Let us identify which of the following statements exhibit a pattern of reasoning most similar to the one exhibited in the argument above: a. ERP helps increase the work efficiency of employees. As a result, employees have more free time for their family. This statement demonstrates the following pattern of reasoning: Premise:  ERP causes increase in efficiency. Assumption:  Increase in efficiency causes free time. Conclusion:  ERP causes free time.

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It can be seen above that 1st phenomenon causes the 2nd phenomenon and this 2nd phenomenon causes the 3rd phenomenon, hence, 1st phenomenon caused the 3rd phenomenon. This reasoning is exactly similar to the original one in the question.

5.  Strengthening/Weakening the argument There are several ways in which an argument can be strengthened or weakened. Let us understand that process:

b. Pesticides are known to cause health hazards for human beings. However, most health hazards occur in the regions where pesticides are not commonly used.

There are three parts of a critical reasoning question:

This statement demonstrates a different pattern of reasoning than the original argument. In fact, it contains two premises but no conclusion:

Connection between premise and conclusion

Premise

Conclusion

Premise:  Pesticides causes health hazards.  Pesticide-free regions are correlated with health hazards.

3.  Generalization of the situations It has been found that if any company goes for sales promotion route, for example giving free samples, or giving atleast 20 per cent discount on the MRP, of establishing a shampoo brand, the company is bound to be the market leader in 5 years. Company XYZ, which produces computer motherboard has used the same sales promotion route. Hence company XYZ is going to be the market leader in coming 5 years.

Explanation It is quite understandable that what is true for shampoo market may not be true for computer motherboard market because of (i) different target group, (ii) different expectations of the target group regarding the product features, (iii) involvement of the customers in buying the product. So we cannot have a ‘generalized’ method of being the market leader. The product category plays its own role in deciding the method to be used for establishing a brand and being a market leader. So the conclusion suffers from the problem of “generalization”.

4.  Equivocation Equivocation is the fallacy that can result when an ambiguous word or phrase is used in different senses within a single argument. It generally occurs because words have a contextual meaning, and seeing the words without the proper context will give only the ‘literal’ meaning of the word, without the proper assimilation of the metaphorical usage.

In normal situations, a premise is a ‘given’ statement, and hence cannot be used to weakening or strengthening the argument. However, this should not be taken as a rule. In maximum number of cases, strengthening or weakening happens at 2nd level—‘Connection between premise and conclusion’. This connection can happen using data or logical argument, and if a reliable data or logic can be given against the given in the question, then the argument has got weakened. On the other hand, if a reliable data or logic can be given in favour of the given in the question, then the argument has got strengthened. Another way of weakening can happen using “Fallacy of irrelevant reason” as discussed at the starting of this concept → Show that despite the logic given is correct, but is not relevant in this case. To understand this, let us take a very elementary example: Researches done at XYZ university last year says that drinking carbonated drinks more than 300 ml per day reduces the life expectancy by 12 hours, in case of a healthy human being.

Strengthen this argument 1. A similar research done at Kelloggs University also shows same result.

Weaken this argument 1. Out of total 72 researches done at XYZ University last year, inferences of 59 researches have been proved to be questionable owing to the methodology adopted.

How to approach CR 1. Firstly, pay attention to what is asked. 2. Read the given argument and mark important facts. 3. Employ the process of elimination of options to find the answer, avoiding too narrow choices or generalitions.

English Usage 

Exercise 1. The Prime Minister has announced our Governments intention of approaching the IAEA on India specific Nuclear safeguards. The Left parties, always opposing the nuclear deal, have threatened to topple the govt. The BJP is licking its lips in anticipation of a return to power. The population wonders whether another Rs 30,000 crore expense on elections will push up already galloping inflation. Q. Identify the assumption in the above passage. a. The IAEA will approve India’s safeguards and the BJP will win the election. b.  The BJP will win the election. c. The Left parties hope their threat will stop the Govt. from approaching IAEA and elections will cost Rs 30,000 crore. d. The population is indifferent to which party comes to power and only wonders about inflation woes. e.  None of the above.

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c. An attitude change is necessary in our people to convert their love of cricket from mere spectatorship to participation also. d. Absenteeism in offices will actually reduce if we decrease the amount of cricket shown on TV. e.  None of these 4. Americans are puzzled as to why the world, including most of their friends, view them with anger and disapproval. After all, they argue, it is their taxes which pay out billions of dollars for everything good in the world today from AIDS control to food for starving Sudan. It is their lives and funds which fight the terrorists and bad guys everywhere. It is their ingenuity which gives the world every technological marvel from the PC to the iphone at affordable prices. Is it mere sordid jealousy the world feels against them?

2. Weather Forecasting in India still uses antiquated methods, which are slow, inaccurate and cumbersome. Advanced countries have adopted satellite based, computer extrapolated, weather predictions which are flexible, quick and can change their own mathematical models as swiftly as the winds which they predict.

Q. Infer what the Americans want as per this passage: a.  Gratitude for all the good things they are doing. b.  The world should not be jealous of them. c. Americans fail to understand the worlds strange attitude towards them. d.  a, b and c above. e. Americans would like the world sympathetically understand and accept their contributions to the human race.

Q. Identify the premise or premises on which this passage is based. a.  Indian weather forecasting is slow and cumbersome. b. Forecasting in advanced countries is quick and flexible. c. Computer and Satellite forecasting is faster than our methods. d.  (a) and (b) above but not (c). e.  a, b, c, above.

5. For 95 per cent of the time, well known psychopaths have been known to be normal, even gentle, people. Jack the Ripper was a regular churchgoer. Blue Beard was a ladies man of incredible charm who befriended one and all at the Kings court. Timothy McVeigh, the infamous Oklahoma bomber, was quiet, law abiding, intellectual and neighbourly. The police have had to rely on painstaking forensic work, huge patience and plain dumb luck to catch these mass murderers.

3. There is a valid line of argument, which states that if Indians actually play a lot of cricket, this is good. It promotes good health, team camaraderie and positive mindedness. But what actually happens is that millions of people merely hear cricket on Radio or see it on TV and have never ever played it. On a typical India-Pakistan one day match, the country loses a few thousand crore rupees in poor productivity and absenteeism in offices. Is this what we want in the long term?

Q. Which of the following would strengthen the author’s argument?

Q. Which of these statements best summarizes the passage?

e.  ‘a’ and ‘d’ above.

a.  Indians are talkers not performers. b. Cricket should be promoted as a sport, not just as visual entertainment.

a. Mass murders do not sprout horns. You have to look for them among normal people. . b.  Psychopaths are basically normal people. c.  Normal people can be psychopaths. d. Catching a psychopath demands the same techniques from the police as is demanded by any other serious fellow. 6. There are questions being raised on the Beijing Olympics. For instance, more than 2 million families have been displaced to make room for stadia and games facilities. Workers have been labouring at slave rates and sub-human

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conditions to erect these facilities. There are major issues related to air pollution levels of Beijing hurting the athletes. Tibet has become a sensitive issue. For a secretive dictatorship like China Goverment it must be galling that the Games may well prove a Pandoras Box.

c. Naxalites and others are misusing the situation for their own selfish ends. d.  a, b, c above. e. State Governments must industrialize to improve economy.

Q. Which conclusion is best supported by this passage? a. China would have been less embarrassed if it hadn’t held the Olympics. b. The world is taking this opportunity to take pot shots at China. c. Tibetans who did not have a voice till now suddenly find themselves center stage. d. The Chinese Goverment is dismayed at its carefully hidden dirty linen coming out in public. e.  The Chinese Goverment is determined to host a magnificent Olympics at any human cost.

9. As per a UGC Study, the quality of engineers in Indian industry is actually diminishing in spite of outstanding training at the IIT’s and other premium technical institutions. This is because a fair percentage of engineers choose to become MBA’s where life in an air-conditioned office is more comfortable than a greasy, hot, sweaty shop floor. The few who do M. Techs mostly go abroad on better job prospects. Hence the engineers left in India for engineering functions are from the non-premier institutions. This is a worrying development for our industries, that have to be satisfied with the second best, in spite of training the best.

7. In spite of knowing the bad effects of cigarette smoking on our health, governments around the world are hesitant to shut down cigarette companies. The tax revenues, the huge employment generated, the benefits to the powerful tobacco farmers, are only some of the reasons holding back the governments. Q. Which of these statements would weaken the author’s arguments? a. Governments are being manipulated by rich and powerful tobacco lobbies. b. People enjoy smoking. They would not like it if the government did away with cigarettes. c. If the government banned cigarettes, a huge black market would develop, like in boot legging or drugs. d. The government would not mind a bit of danger to your health as long as the revenues come in. e. Many governments believe stronger legislation can and should curb smoking. 8. In West Bengal, Orissa, Chattisgarh, farmers and adivasis have refused to sell their land for industrialization. The State Governments are trying to explain that apart from compensation, the objective is to generate lucrative employment, not decimate their livelihood. A combination of middlemen, selfish politicians and rebels like Naxalites are trying to ensure there is no compromise possible. Q. What can we infer from the above passage? a. Farmers and adivasis of these states have refused to part with their land for industry. b. The state is unable to communicate its idealistic objectives to the affected people.

Q. Which of the following statements closest echoes the author’s argument? a. The best Indian engineers are no longer interested in engineering. b. Youngsters these days want to earn money comfortably, so they are opting out of dirty, greasy, factory shops. c. In spite of giving best possible training in premier engineering colleges, India has to do without the best in its industrial factory floors. d. All our efforts on world class engineering training has gone waste. e.  None of the above. 10. Considerable press space has been expended on the damages of Iran or North Korea having nuclear weapons; or the dangers of nuclear proliferation from Pakistan. The real danger zone, erstwhile USSR, has been largely ignored. Huge quantities of fissile material have been allegedly left unguarded here. With the disintegration of the USSR, checks and balances on nuclear weapons and materials have been largely missing. The potential terrorist has a treasure trove of highly dangerous material and trained technicians available here. Q. Which statement comes closest to the conclusion drawn by the author? a. A potential terrorist has a treasure trove of dangerous material available in erstwhile USSR; this fact has hardly been noticed by the world. b. Large quantities of nuclear fissile material are allegedly left unguarded at USSR. c. The press has been raising false alarms about Iran, N. Korea and Pakistan.

English Usage  d. The world has ignored the real danger zone from where fissile material can be stolen or proliferated. e. The USSR has been criminally careless about its nuclear stockpiles. 11. Studies by Interpol suggest that crime rates in border areas of any country are higher than those in the interior, all over the world. Reasons speculated include alienation of border population from the rest of the country, or conversely their identification with the neighbouring country to whom they are geographically closer. Also, the thought that law and order and political levers of government emanating from the center of the country, the capital, get weaker and slacker as they reach the fringes; or even an out of sight, out of mind attitude at the capital. Q. Which statement would strengthen the author’s argument? a. Criminals in the borders can commit crimes in their country and escape across the borders. b. Army and border patrols in border areas though present, look for external enemies rather than internal crimes. c. If you want a career in crime, stick to border areas. d. Imposition of Martial law in border areas makes good sense. e. Governments would be better off making extra efforts at tightening administration in border areas, by involving local people. 12. No Indian has ever been a Wimbledon Tennis Champion. Fitness and competition levels are increasing every year. Competitors use latest technologies to train and equip themselves for the tournament. Considering the caliber of the current crop of Indian players, Apollo Tyres ambitious Mission 2018, aiming to create a tennis champion in 10 years, seems a pipe dream. Q. Conclude the passage: a. So give up the idea and utilize the funds for some more worth while target, or sport. b. It needs more than 10 years and cash to create a Wimbledon Champion. c. But dreams come true. Look at Spain and Raphael Nadal, this years Champion. d. The only way for Apollo Tyres to reach this target is to send 14–15 years olds with potential to USA or Europe for rigorous modern training. e. There are Indian youngsters already training in USA and Europe. Induce them to play for India, and give them all facilities.

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13. Xenophobia against Asians in USA and UK has increased since 9/11, an elderly Sikh was murdered in USA, mistaken for an Arab. Intelligence Services tap twice as many as phones of Asians as they do of Nordics. Visa rules for Asians have been tightened unreasonably. Now Germany states they will not allow Iranian or Middle East students to study nuclear physics at their universities. Are these steps playing into the hands of terrorist recruiters? Q. What would you infer from this passage? a. Al Quaida recruiters are delighted with these developments. b. It is time for Asian countries to impose retaliatory tit-for-tat restrictions on UK and USA. c. Increasing Xenophobia is a dangerous trend—it can cause problems, not solve them. d. There is no sense showing anger against decent law abiding Asians. It would be better to utilize energy to catch terrorists. e.  All of the above. 14. Opinion based, not fact based, reporting, seems to be the fad for most TV Channels these days. In the Aarushi murder case, the channels have already named at least three suspects as guilty, whereas the CBI is still groping in the dark. Each channel has made its own calculations on future confidence vote of the government and is presenting it as fact. Political analysts gleefully state their own speculations as gospel truths. Truth is indeed a casualty these days. Q. Which of these sentences would best conclude the paragraph? a. The press—print and electronic would be well advised to exercise restraint and may be have self regulatory bodies to oversee broadcasts for veracity. b. It would not be a bad idea for the Government to impose some discipline in the press, through legislation. It has been done in other countries. c. Freedom of press does not mean freedom to distort facts, present opinion as fact. d. People must give a thumbs down to blatantly opinionated channels via poor viewership. e.  None of the above. 15. The connection between top industrialists and politicians in India is as old as it is murky. Politicians need funds, which industrialists give. The industrialists in turn, need government support in tax laws, favourable legislation etc., which the politician can give. It is a cozy symbiotic relationship. So why would anyone want to rock the boat?

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Q. Which of these statements is not a premise? a. Politicians need funds. Industrialist needs governmental support. b. Industrialists pay politicians, who return the favour via favourable legislation. c.  This connection is old and murky. d.  It is a cozy symbiotic relationship. e.  Why would anyone want to rock the boat? 16. With crude oil price touching 146 dollars/barrel it is time to think small cars and petrol savers. It is time to think electric autos and Hydrogen cell vehicles. It is time to think CNG vehicles and hybrid technologies. It is time to think ethanol locos and natural gas furnaces. It is even probable that in our anxiety to save petrol, we will actually lower pollution levels since all the alternative technologies are more environment friendly than current petrol guzzlers. Q. Which of the following would strengthen the author’s argument? a. Petroleum crude prices are expected to cross 200 dollars/barrel in the next year. May be clean air will be economically forced on us ultimately! b. Thank God for alternative technologies. We would be back in Stone Age without them. c. It is time to seriously look for more petroleum resources by drilling more, perhaps in the seas and the poles, where huge reserves of the hydrocarbon apparently exist. d. Human ingenuity has found ways out of every crisis in history. Mankind will find a solution to this problem too. e.  None of the above. 17. Why is it that humans have not yet come up with a food preparation which is truly delicious, even additive, but actually very good for health? Every one loves chocolate and ice cream, but dare not gorge on them due to fat problems, over eat, delicious kebabs and invite cholesterol. Burgers and Pizzas while yummy, simply have to be kept at bay or you face obesity worries. So tell me of a dish as tasty as any of these delicacies, which actually reduces cholesterol, keeps weight in check, improve haemoglobin count and which doctors prescribe you to go ahead and gorge on! Q. What best would describe the mood of this passage? a. Tremulous: The authors whine about how good food is always bad for health. b. Longing: The author craves for decent food you can eat without guilt. c. Disapproval: Humans have wasted time on a million inventions but not on a healthy, tasty food.

d. Tongue in check: The author is willing to chuckle at our self created predicament. e. Humorous: He is being pleasantly sarcastic on our priorities in inventions. 18. Religion has claimed more lives through history than all famines, earthquakes, wars and pestilences put together. Hundreds of thousands were martyred in the centuries long Christian-Muslim wars of the middle ages. The popes and the Church have, over the centuries, burnt countless so called heretics at the stake. Jews have kicked out huge numbers of Palestinians from their homes, while themselves losing 5 million of their own in the holocaust. Even today, Al Quaida and large numbers of Islamic militant organizations have declared Jehad against all other Kaffirs. Hindu extremists talk of imposing their own brand of Hinduism in India at the cost of secularism. Q. Select a suitable conclusion to the paragraph? a. Religion is a curse on humanity and we would be better off as agnostics—believe in God but not in religion. b. Religion should be confined to the boundaries of ones house—not bandied about in public. c. Every religion is out to prove—even with violence —that our God is greater than your God. d. There is a disconnect between the ideas and the practice of religions. The ideals preach peace but its followers use violence. e.  None of the above. 19. United Nations Food experts have recommended that India would be better served by eating more potatoes and less rice. Potatoes are easier to grow and harvest. They are more resistant to pests. They are easier to store. They deliver more calories and starch per kilo than rice. They are cheaper per kilo. Their yield per acre is higher. They need less kcals/kgm heat to cook. If somehow, attitude changes could be motivated in India’s population, and more people switched to potatoes as a staple food, even to poorest of Indians population would be better served. Q. What is not a premise in this passage? a.  Potatoes are easier to grow than rice. b.  Potatoes are easier to store than rice. c.  Potatoes need less heat to cook than rice. d. Potatoes deliver more calories and energy to our body. e. India would be better off eating more potatoes than rice.

English Usage  20. Teenagers are best reached via their favourite pastimes and hobbies—internet, music, movies, peer groups, sports etc., It is through these very formats they can be told of things that would be good for them in the long run—decency, patriotism, honesty, hard work, fair play, community feeling, harmony and tolerance. Being natural rebels, no teenager likes to be lectured. These values must be communicated to them in palatable ways of their own choice via their own favourite communication modes. Only then will the lessons stick. Q. Which of these would continue the mood of this passage? a.  Everything can’t be taught in schools & colleges. b. Subtlety and sensitivity would help in reaching out to teenagers. c. Being young, teenagers tend to have short attention spans. Long term issues must be communicated in special ways, which they are attracted to. d.  a, b, c above. e.  a, b above. 21. Mumbai’s Municipal Corporation has a budget of Rs 116,000 crores with savings deposit of Rs 8,000 crores. They do not depend on State Governmental doles and generate their own revenue through Octroi (46 percent) etc., Yet year after year when rains clog the city’s streets the most common excuse given is “lack of funds”. Similar excuses are given for lack of cleanliness, solid waste mismanagement and hideous pollution. It is speculated that the Corporation authorities would rather keep themselves busy building flyovers and super highways with its potential for illegal gratification rather than tedious jobs like sewer and road cleaning where such “perquisites” are hardly on offer. So it is high time decent bureaucrats came into the picture, who would utilize huge funds available and rid Mumbai’s citizenry of its perennial miseries. Q. Name the premise/s on which this para is not constructed: a. Mumbai’s Corporation has enormous funds. b. Mumbai’s Corporation would arguably rather build highways and roads than clean sewers and pipelines. c. The Corporation does not depend on State Government funding but generates its own huge revenue. d. Mumbai’s clogging during rains, solid waste disposal problems and pollution continue unabated. e. Decent, honest, bureaucrats should be brought into control the corrupt political masters of the Mumbai’s Corporation. 22. Lobbying is the attempt by a person or a group, to pass or defeat a law. People trying to influence lawmakers

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are called lobbyists. From the days that earliest governments made rules and regulations, people and groups have worked for and against the rules. At first an individual might petition the ruler or the law making body to get his special requests. As populations and cities grew, people with some of the same interests organized groups and associations. Members of these special interest groups became lobbyists to work for what they wanted in the state or national capitals. Q. Select the statement or statements, which could best continue the passage: a. As industry and business grew, lobbying became the tool whereby taxes and tariffs could be manipulated to huge profits for petitioning companies. b. Lobbying itself has now become a profession employing thousands of top grade professionals and enjoys huge turnovers. c. Since lawmakers are supposedly on the side of the citizenry, and lobbyists on the side of their paymasters, government view lobbyists with suspicion. d. Lobbyists these days are allegedly conduits for bribes and kickbacks to authorities and political parties. e.  To varying extents all, the above. 23. Logic is about the form, or structure of an argument — about thinking from reasons or evidence to conclusion. Logic is not about the contents of an argument. The following two arguments, for example, are exactly the same logically—and they are both logically correct: If all house cats are felines and if all felines are mammals, then all house cats are mammals. If all house cats are fish, and if all fish are insects, then all house cats are insects. But because logic does not deal with house cats, feline, mammals, fish or insects, a logician—one who studies logic—might write this argument: if all X is Y, and if all Y is Z, then all X is Z. He would show, therefore, that logic is not concerned with content of the argument. Q. After reading this passage, if I was a logician, I would say in summary: a.  I am not interested in contents of an argument. b. I look for lines of thought from reasons to conclusion. c.  Specifies do not concern me. d. I deal with universal generalities which would apply to all content. e.  None of these

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24. The growth of international commerce has been hampered by restrictive measures imposed by different nations. In order to gain revenue, nations impose duties or tariffs, on imports and exports. Tariffs are also used as a means of restricting imports. Tariffs may be used to protect a home industry, to reduce imports thus lessening the demand for a limited supply of foreign exchange, or to check declines in exchange rates. Such steps restrict trade.

government. Every citizen is expected to work for the government according to his ability and each is supposed to be rewarded according to his need. In recent years, the term “communist” mainly applies to China, Cuba, Vietnam and a few small pockets. Most East European countries even Russia who had adopted Communion have now rejected it because of its flawed tenets. Q. What premise or premises in the above para give you a hint of why communism has been largely rejected till today?

Q. Select a suitable title for this passage which would convery its essence:

a. Common ownership—Humans like owning things on their own, not give everything to the govt.

a.  Protecting national commercial interest. b. Methods used by nations to consume foreign exchange and increase revenue.

b. Property, industry & distribution is controlled by government. Where is the inducement to work hard and gain by it?

c.  Functions of Tariffs. d.  How nations check declines in exchange rates.

c. Each citizen works to the best of his talents but is paid only as per need. So a less talented working man is quite likely to be paid more simply because he needs it more.

e.  Barriers to commerce.

ANSWER KEYS

25. Communism is a form of government that advocates common ownership and use of all means of producing goods. Under a communist government, all property, industry and methods of distribution of wealth are owned and controlled by the

d. It is implied that every citizens life under communism is pretty much controlled by the government. e.  All the above.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

e

2.

e

3.

e

4.

e

5.

e

6.

e

7.

a

8.

c

9.

c

10.

a

11.

b

12.

b

13.

c

14.

c

15.

e

16.

e

17.

a

18.

b

19.

d

20.

b

21.

e

22.

b

23.

a

24.

e

25.

e

English Usage 

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  FACT—INFERENCE—JUDGEMENT Facts—which deal with pieces of information that one has heard, seen or read, and which are open to discovery or verification (the answer option indicates such a statement with a “F”).

So a fact can be A Universal truth (Sun rises in the east), Analyzed truth, something which has transpired in past. Even the statement “Sun rises in the west” will come in the category of “Fact” statement because it can be verified.

Inference Inferences—are conclusions drawn about the unknown, on the basis of the known (the answer option indicates such a statement with an “I”). They tell us something more about a fact or a judgement.

Judgement Judgments—are opinions that imply approval or disapproval of persons, objects, situations and occurrences in the past, the present or the future (the answer option indicates such a statement with a “J”). For example, a Futuristic prediction is judgement. So, when Ms Chhayawati says that Mr Arun will once again give provocative speech despite giving affidavit in the supreme court that he will not do so, she is passing a judgement about Mr Arun (or we can say that she is becoming judgemental about Mr Arun.) Let us understand this through an example: 1. 1. Given the poor quality of service in the public sector, the HIV/AIDS affected should be switching to private initiatives that supply anti-retroviral drugs (ARVs) at a low cost. 2. The government has been supplying free drugs since 2004, and 35000 have benefited up to now— though the size of the affected population is 150 times this number. 3. The recent initiatives of networks and companies like AIDS Care Network, Emcure, Reliance-CiplaCII, would lead to availability of much needed drugs to a larger number of affected people. 4. But how ironic it is that we should face a perennial shortage of drugs when India is one of the world’s largest suppliers of generic drugs to the developing world. 1.  JFIJ 2.  JIIJ 3.  IFIJ 4.  IFFJ 5.  JFII Here statement 2 is a fact, because it can be verified. so

option (2) is out. Now, statement 1 is a judgement because of the use of the words ‘should be’ in the first statement, so options (3) and (4) are out. Now the last statement is a judgement. But we can see that none of the option ends with an ‘F’. Thus, Ans. (1)

Practice Questions 1. 1. So much of our day-to-day focus seems to be on getting things done, trudging our way through the tasks of living—it can feel like a treadmill that gets you nowhere; where is the childlike joy? 2. We are not doing the things that make us happy; that which brings us joy; the things that we cannot wait to do because we enjoy them so much. 3. This is the stuff that joyful living is made of— identifying your calling and committing yourself wholeheartedly to it. 4. When this happens, each moment becomes a celebration of you; there is a rush of energy that comes with feeling completely immersed in doing what you love most. 1.  IIIJ 4.  JJJJ

2.  IFIJ 5.  JFII

3.  JFJJ

2. 1. According to all statistical indications, the Sarva Shiksha Abhiyan has managed to keep pace with its ambitious goals. 2. The Mid-day Meal Scheme has been a significant incentive for the poor to send their little ones to school, thus establishing the vital link between healthy bodies and healthy minds. 3. Only about 13 million children in the age group of 6 to 14 years are out of school. 4. The goal of universalisation of elementary education has to be a pre-requisite for the evolution and development of our country. 1.  IIFJ 4.  IJFI

2.  JIIJ 5.  JIFI

3.  IJFJ

3. 1. We should not be hopelessly addicted to an erroneous belief that corruption in India is caused by the crookedness of Indians. 2. The truth is that we have more red tape—we take eighty-nine days to start a small business, Australians take two. 3. Red tape leads to corruption and distorts a people’s character.

  Verbal and Logical Reasoning

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4. Every red tape procedure is a point of contact with an official, and such contacts have the potential to become opportunities for money to change hands. 1.  JFIF 4.  IFJF

2.  JFJJ 5.  JFJI

2

3

Here statement 1 is surely an inference as it is a conclusion based on known facts and 3 is a fact. This eliminates (2) and (5). Also statement 4 is a judgment as it is simply an opinion, ruling out (4). Also, statement (2), which can be taken to be an inference by a lot many, is, indeed a judgment as there is no reason presented here as to why this is happening. So in the absence of sufficient, this statement should be considered a ‘judgement’. Ans. (3)

3

5

Here 1 and 3 are judgements–hese are opinions on ‘not so firm evidence’–as given in the question and 2 is a fact. This eliminates (1) and (4). The last statement can either be an inference or a judgement, which eliminates option (3). Now, there is contention between the 2nd option and the 5th option. The 4th statement cannot be a judgement because it is not an approval or a disapproval of anything. It is just a opinion based on the something known (the second part of the sentence). Hence, Ans. (5)

4

2

The first statement uses words like, ‘certainly’ and ‘most sinister’. Such strong modifiers are clear indicators of a Judgment. Statement 2 is a little difficult to classify at first glance, but we can see a cause-effect relationship in the statement ‘Even without war’ can be written as ‘Even if there is no war’. Hence the statement means. ‘Even if there is no war, we know that……’. Hence, the second statement is an Inference. The third statement is a Judgment because of the use of the word ‘only’, a non-verifiable modifier in the context of the statement. The fourth statement is clearly a categorically stated Fact.

3.  JIJF

4. 1. Inequitable distribution of all kinds of resources is certainly one of the strongest and most sinister sources of conflict. 2. Even without war, we know that conflicts continue to trouble us—they only change in character. 3. Extensive disarmament is the only insurance for our future; imagine the amount of resources that can be released and redeployed. 4. The economies of the industrialized western world derive 20 per cent of their income from the sale of all kinds of arms. 1.  IJJI 4.  JIIF

2.  JIJF 5.  IJIF

3.  IIJF

Solution and Explanation Q. Correct Explanation No. Answer 1

4

This is a very tricky one but as we can see there is no statement that can be called a fact, so we eliminate (2), (3) and (5). Also we can see that (1), (2) and (3) are not conclusions based on any fact given as there are simply no facts presented. This eliminates (5). So it is a set of four judgments. Ans. (4)

English Usage 

  2.147

ENGLISH USAGE   PRACTICE EXERCISE  1 Direction for questions 1 to 5:  Sentences given in each question, when properly sequenced, form a coherent paragraph. The first and last sentences are 1 and 6, and the four in between are labelled A, B, C and D. Choose the most logical order of these four sentences from among the four given choices to construct a coherent paragraph from sentences 1 to 6. 1. 1. Security inks exploit the same principle that causes the vivid and constantly changing colours of a film of oil on water. A. When two rays of light meet each other after being reflected from these different surfaces, they have each travelled slightly different distances. B. The key is that the light is bouncing off two surfaces, that of the oil and that of the water layer below it. C. The distance the two rays travel determines which wavelengths, and hence colours interfere constructively and look bright. D. Because light is an electromagnetic wave, the peaks and troughs of each ray then interfere either constructively, to appear bright, or destructively, to appear dim. 6. Since the distance the rays travel changes with the angle as you look at the surface, different colours look bright from different viewing angles. 1.  ABCD 4.  DCAB

2.  BADC

3.  BDAC

2. 1. Commercially reared chicken can be unusually aggressive, and are often kept in darkened sheds to prevent them pecking at each other. A. The birds spent far more of their time-up to a third-pecking at the inanimate objects in the pens, in contrast to birds in other pens which spent a lot of time attacking others. B. In low light conditions, they behave less belligerently, but are more prone to ophthalmic disorders and respiratory problems.

C. In an experiment, aggressive head-pecking was all but eliminated among birds in the enriched environment. D. Altering the birds’ environment, by adding bales of wood-shavings to their pens, can work wonders. 6. Bales could diminish aggressiveness and reduce injuries; they might even improve productivity, since a happy chicken is a productive chicken. 1.  DCAB 4.  BDCA

2.  CDBA

3.  DBAC

3. 1. The concept of

a ‘nation-state’ assumes a complete correspondence between the boundaries of the nation and the boundaries of those who live in a specific state.

A. Then there are members of national collectivities who live in other countries, making a mockery of the concept. B. There are always people living in particular states who are not considered to be (and often do not consider themselves to be) members of the hegemonic nation. C. Even worse, there are nations which never had a state or which are divided across several states. D. This, of course, has been subject to severe criticism and is virtually everywhere a fiction. 6. However, the fiction has been, and continues to be, at the basis of nationalist ideologies. 1.  DBAC 4.  DACB

2.  ABCD

3.  BACD

4. 1. In the sciences, even questionable examples of research fraud are harshly punished. A. But no such mechanism exists in the humanities—much of what humanities researchers call research does not lead to results that are replicable by other scholars. B. Given the importance of interpretation in historical and literary scholarship, humanities researchers are in a position where they can explain away deliberate and even systematic distortion.

2.148 

  Verbal and Logical Reasoning

C. Mere suspicion is enough for funding to be cut off; publicity guarantees that careers can be effectively ended. D. Forgeries which take the form of pastiches in which the forger intersperses fake and real parts can be defended as mere mistakes or aberrant misreading. 6.  Scientists fudging data have no such defences. 1.  BDCA 4.  CDBA

2.  ABDC

3.  CABD

8. It will take some time for many South Koreans to __ _______ the conflicting images of North Korea, let alone to _________ what to make of their northern cousins. 1.  reconcile, decide 2.  understand, clarify 3.  make out, decide 4.  reconcile, understand

5. 1. Horses and communism were, on the whole, a poor match.

9. In these bleak and depressing times of _________ prices, non-performing governments and _________ crime rates, Sourav Ganguly has given us, Indians, a lot to cheer about.

A. Fine horses bespoke the nobility the party was supposed to despise.

1.  escalating, increasing 2.  spiralling, booming

B. Communist leaders, when they visited villages, preferred to see cows and pigs.

3.  spiralling, soaring

C. Although a working horse was just about tolerable, the communists were right to be wary. D. Peasants from Poland to the Hungarian Pustza preferred their horses to party dogma. 6. “A farmer’s pride is his horse; his cow may be thin but his horse must be fat,” went a Slovak saying. 1.  ACDB 4.  DCBA

2.  DBCA

3.  ABCD

Direction for questions 6 to 10:  In each of the following sentences, parts of the sentence are left blank. Beneath each sentence, four different ways of completing the sentence are indicated. Choose the best alternative from among the four. 6. Though one eye is kept firmly on the _________, the company now also promotes _________ contemporary art.

1.  present, experimental 2.  future, popular 3.  present, popular 4.  market, popular

7. The law prohibits a person from felling a sandalwood tree, even if it grows on one’s own land, without prior permission from the government. As poor people cannot deal with the government, this legal provision leads to a rip-roaring business for _________, who care neither for the _________, nor for the trees.

1.  middlemen, rich 2.  the government, poor 3.  touts, rich 4.  touts, poor

4.  ascending, debilitating 10. The manners and _________ of the nouveau riche is a recurrent _________ in the literature. 1.  style, motif 2.  morals, story 3.  wealth, theme 4.  morals, theme Direction for questions 11 to 15:  The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the four given choices to construct a coherent paragraph. 11. A. If caught in the act, they were punished, not for the crime, but for allowing themselves to be caught another lash of the whip. B. The bellicose Spartans sacrificed all the finer things in life for military expertise. C. Those fortunate enough to survive babyhood were taken away from their mothers at the age of seven to undergo rigorous military training. D. This consisted mainly of beatings and deprivations of all kinds like going around barefoot in winter, and worse, starvation so that they would be forced to steal food to survive. E. Male children were examined at birth by the city council and those deemed too weak to become soldiers were left to die of exposure. 1.  BECDA 4.  ECDAB

2.  ECADB

3.  BCDAE

  2.149

English Usage  12. A. This very insatiability of the photographing eye changes the terms of confinement in the cave, our world. B. Humankind lingers unregenerately in Plato’s cave, still revelling, its age-old habit, in mere images of truth. C. But being educated by photographs is not like being educated by older images drawn by hand; for one thing, there are a great many more images around, claiming our attention. D. The inventory started in 1839 and since then just about everything has been photographed, or so it seems. E. In teaching us a new visual code, photographs alter and enlarge our notions of what is worth looking at and what we have a right to observe. 1.  EABCD

2.  BDEAC

3.  BCDAE

4.  ECDAB

13. A. To be culturally literate is to possess the basic information needed to thrive in the modern world.

B. Nor is it confined to one social class; quite the contrary. C. It is by no means confined to “culture” narrowly understood as an acquaintance with the arts. D. Cultural literacy constitutes the only sure avenue of opportunity for disadvantaged children, the only reliable way of combating the social determinism that now condemns them. E. The breadth of that information is great, extending over the major domains of human activity from sports to science. 1.  AECBD 4.  DBCAE

2.  DECBA

E. A bank may purchase more and more complicated and sophisticated safes, forcing safecrackers to invest further in safecracking equipment. 1.  ABCDE 4.  CBEDA

2.  CABDE

15. A. The likelihood of an accident is determined by how carefully the motorist drives and how carefully the pedestrian crosses the street. B. An accident involving a motorist and a pedestrian is such a case. C. Each must decide how much care to exercise without knowing how careful the other is. D. The simplest strategic problem arises when two individuals interact with each other, and each must decide what to do without knowing what the other is doing. 1.  ABCD 4.  DBAC

2.  ADCB

16. Exceed Dictionary definition

To extend outside of or E The mercy of God exenlarge beyond—used ceeds our finite minds chiefly in strictly physical relations

B

To be greater than or superior to

F

C

Be beyond the comprehension of

G He exceeded his authority when he paid his brother’s gambling debts with money from the trust.

D

To go beyond a limit set by (as an authority or privilege)

H If this rain keeps up, the river will exceed its banks by morning.

to secure property rights.

D. These costs may escalate as a type of technological arms race unfolds.

Usage

A

14. A. Both parties use capital and labour in the struggle

C. A social cost of theft is that both the thief and the potential victim use resources to gain or maintain control over property.

3.  DBCA

Direction for questions 16 to 20:  For the word given at the top of each table match the dictionary definitions on the left (A,B,C,D) with their corresponding usage on the right (E,F,G,H). Out of the four possibilities given in the boxes below the table, select the one that has all the definitions and their usages correctly matched.

3.  ACBED

B. The thief spends time and money in his attempt to steal (he buys wire cutters) and the legitimate property owner expends resources to prevent the theft (he buys locks).

3.  ACBED

1 A B C D

Their accomplishments exceeded our expectation.

2 H F E G

A B C D

3 H E F G

A B C D

4 G F E H

A B C D

F G H E

2.150 

  Verbal and Logical Reasoning

17. Infer

19. Relief

Dictionary definition A

Usage

Dictionary definition

Usage

To derive by reasoning E We see smoke and infer or implication fire. To surmise F Given some utterance, a listener may infer from it all sorts of things which neither the utterance nor the utterer implied.

A Removal or lightening E A ceremony follows the of something distressrelief of a sentry after the ing morning shift. B Aid in the form of necessities for the indigent

F

C

To point out

C

G The only relief I get is by playing cards.

D

To hint

B

G I waited all day to meet him. From this you can infer my zeal to see him. H She did not take part in the debate except to ask a question inferring that she was not interested in the debate.

1 A B C D

2 G E H F

A B C D

3 F H E G

A B C D

D Release from the performance of duty 1 A B C D

4 H G F E

A B C D

E F G H

2 E H E G

A B C D

3 F H E G

A B C D

Dictionary definition

Dictionary definition A Adequately and properly aged so as to be free of harshness B Freed from the rashness of youth C Of soft and loamy consistency D Rich and full but free from stridency

E

Usage He has mellowed with age.

The tones of the old violin were mellow. G Some wines are mellow.

3 E F G H

A B C D

A B C D

A B C D

G E H F

E

The opposition was purged after the coup.

The committee heard his F attempt to purge himself of a charge of heresy.

C Get rid of

G

Drugs that purge the bowels are often bad for the brain.

H

It is recommended to purge water by distillation.

To cause evacuation of

A B C D

H G F E

Usage

Removal a stigma from the name of

1

4 G E H F

4 H G F E

Make clean by reB moving whatever is superfluous, foreign

D

H Mellow soil is found in the Gangetic plains.

2 A B C D

A

F

ANSWER KEYS

1 E G F H

H Disaster relief was offered to the victims.

20. Purge

18. Mellow

A B C D

Diversion

It was a relief to take off the tight shoes.

2 E G F H

A B C D

3 F E H G

A B C D

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

4

3.

3

4.

1

5.

3

6.

2

7.

4

8.

1

9.

3

10.

4

11.

1

12.

3

13.

1

14.

2

15.

4

16.

1

17.

4

18.

3

19.

2

20.

4

4 H F G E

A B C D

F H E G

English Usage 

  2.151

  PRACTICE EXERCISE  2 Direction for questions 1 to 5:  In each of the following sentences, a part of the sentence is underlined. Beneath each sentence, four different ways of phrasing the underlined part are indicated. Choose the best alternative from among the four. 1. It was us who had left before he arrived. 1.  we who had left before time he had arrived. 2.  us who had went before he arrived. 3.  us who had went before had arrived. 4.  we who had left before he arrived. 2. The MP rose up to say that, in her opinion, she thought the Women’s Reservation Bill should be passed on unanimously. 1. rose to say that she thought the Women’s Reservation Bill should be passed. 2. rose up to say that, the Women’s Reservation Bill should be passed on. 3. rose to say that, in her opinion, she thought that the Women’s Reservation Bill should be passed. 4. rose to say that, in her opinion, the Women’s Reservation Bill should be passed on. 3. Mr Pillai, the president of the union and who is also a member of the community group, will be in charge of the negotiations. 1.  since he is a member of the community group. 2.  also being a member of the community group. 3.  a member of the community group. 4. in addition, who is a member of the community group. 4. Since the advent of cable television, at the beginning of this decade, the entertainment industry took a giant stride forward in our country. 1.  this decade saw the entertainment industry taking. 2.  this decade, the entertainment industry has taken. 3.  this decade, the entertainment industry had taken. 4.  this decade, the entertainment industry took. 5. His mother made great sacrifices to educate him, moving house on three occasions, and severing the thread on her loom’s shuttle whenever Mencius neglected his lessons to make him understand the need to persevere.

1. severing the thread on her loom’s shuttle whenever Mencius neglected his lessons to make him understand the need to persevere. 2. severed the thread on her loom’s shuttle whenever Mencius neglected his lessons to make him understand the need to persevere. 3. severed the thread on her loom’s shuttle whenever Mencius neglected his lessons to make him understand the need for persevering. 4. severing the thread on her loom’s shuttle whenever Mencius neglected his lessons, to make them understand the need to persevere. Direction for questions 6 to 10:  The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 6. A. Although there are large regional variations, it is not infrequent to find a large number of people sitting here and there and doing nothing. B. Once in office, they receive friends and relatives who feel free to call any time without prior appointment. C. While working, one is struck by the slow and clumsy actions and reactions, indifferent attitudes, procedure rather than outcome orientation, and the lack of consideration for others. D. Even those who are employed often come late to the office and leave early unless they are forced to be punctual. E. Work is not intrinsically valued in India. F. Quite often people visit ailing friends and relatives or go out of their way to help them in their personal matters even during office hours. 1.  ECADBF 4.  ABFCBE

2.  EADCFB

3.  EADBFC

7. A. But in the industrial era destroying the enemy’s productive capacity means bombing the factories which are located in the cities. B. So in the agrarian era, if you need to destroy the enemy’s productive capacity, what you want to do is burn his fields, or if you’re really vicious, salt them. C. Now in the information era, destroying the enemy’s productive capacity means destroying the information infrastructure.

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  Verbal and Logical Reasoning

D.  How do you do battle with your enemy? E. The idea is to destroy the enemy’s productive capacity, and depending upon the economic foundation, that productive capacity is different in each case. F. With regard to defense, the purpose of the military is to defend the nation and be prepared to do battle with its enemy. 1.  FDEBAC 4.  DFEBAC

2.  FCABED

3.  DEBACF

8. A. Michael Hofman, a poet and translator, accepts this sorry fact without approval or complaint. B. But thanklessness and impossibility do not daunt him. C. He acknowledges too—in fact he returns to the point often—that best translators of poetry always fail at some level.

D. However, binding the obligation to kill, members of feuding families engaged in mutual massacre will be genuinely appalled if by some mischance a bystander or outsider is killed. 1.  DABC 4.  DBAC

2.  ACDB

Direction for question 11 to 15:  In each of the following sentences, parts of the sentence are left blank. Beneath each sentence, four different ways of completing the sentence are indicated. Choose the best alternative from among the four. 11. But ________ are now regularly written not just for tools, but well- established practices, organizations and institutions, not all of which seem to be ________ away. 1.  reports, withering

D. Hofman feels passionately about his work, and this is clear from his writings.

2.  stories, trading

E. In terms of the gap between worth and rewards, translators come somewhere near nurses and street-cleaners.

4.  obituaries, fading

1.  EACDB 4.  DCEAB

2.  ADEBC

3.  EACBD

B. In areas where there are no lords or laws, or in frontier zones where all men go armed, the attitude of the peasantry many well be different. C. So indeed it may be on the fringe of the unsubmissive. D. However, for most of the soil-bound peasants the problem is not whether to be normally passive or active, but when to pass from one state to another. E. This depends on an assessment of the political situation. 2.  CDABE

3.  books, dying 12. The Darwin who __________ is most remarkable for the way in which he __________ the attributes of the world class thinker and head of the household. 1.  comes, figures

9. A.  Passivity is not, of course, universal.

1.  BEDAC 4.  ABCDE

3.  CBAD

3.  EDBAC

10. A. The situations in which violence occurs and the nature of that violence tends to be clearly defined at least in theory, as in the proverbial Irishman’s question: ‘Is this a private fight or can anyone join in?” B. So the actual risk to outsiders, though no doubt higher than our societies, is calculable. C. Probably the only uncontrolled applications of force are those of social superiors to social inferiors and even here there are probably some rules.

2.  arises, adds 3.  emerges, combines 4.  appeared, combines 13. Since her face was free of __________ there was no way to __________ If she appreciated what had happened. 1.  make-up, realize 2.  expression, ascertain 3.  emotion, diagnose 4.  scars, understand 14. In this context, the __________ of the British labour movement is particularly__________ 1.  affair, weird 2.  activity, moving 3.  experience, significant 4.  atmosphere, gloomy 15. Indian intellectuals may boast, if they are so inclined, of being __________ to the most elitist among the intellectual __________ of the world.

English Usage  1.  subordinated, traditions

1.  Prevent 4.  Bolster

2.  heirs, cliques 4.  heir, traditions

1.  Prevalent 2.  Discarded 4.  Unfashionable

Direction for questions 16 to 20:  For each of the words below, a contextual usage is provided. Pick the word from the alternatives given that is most inappropriate in the given context.

2.  Fallacious

3.  Obliterated

19. Parsimonious: The evidence was constructed from very parsimonious scraps of information. 1.  Frugal 4.  Altruistic

16. Specious: A specious argument is not simply a false one but one that has the ring of truth.

2.  Penurious

3.  Thrifty

20. Facetious: When I suggested that war is a method of controlling population, may father remarked that I was being facetious.

3.  Credible

1.  Jovian 4.  Joking

17. Obviate: The new mass transit system may obviate the need for the use of personal cars.

ANSWER KEYS

3.  Preclude

18. Disuse: Some words fall into disuse as technology makes objects obsolete.

3.  ancestors, societies

1.  Deceitful 4.  Deceptive

2.  Forestall

  2.153

2.  Jovial

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

1

3.

3

4.

2

5.

1

6.

3

7.

1

8.

3

9.

4

10.

1

11.

4

12.

3

13.

2

14.

3

15.

4

16.

3

17.

4

18.

1

19.

4

20.

1

3.  Jocular

  PRACTICE EXERCISE  3 Direction for questions 1 to 5:  In each of the question below, you are expected to choose the word having opposite meaning to the word given in the question. 1. Kudos: 1.  congratulations 2.  moron 4.  dishonour 5.  apprentice

3.  inveterate

2. Invincible: 1.  strong 4.  voluble

2.  dull 5.  defenseless

3.  cowardly

3. Loquacious: 1.  talkative 4.  civilized

2.  eloquent 5.  laconic

3.  tyrannical

4. Parochial: 1.  rebellious 4.  peevish 5. Ephemeral:

2.  fanatical 3.  discursive 5.  cosmopolitan

1.  dying 4.  ethereal

2.  lasting 5.  spiritual

3.  mortal

Direction for questions 6 to 10:  A number of sentences are given below which, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the five given choices to construct a coherent paragraph. 6. 1. Compared to that, the $3 billion needed to build the facilities and relocate tens of thousands of residents to the outskirts is a trifle. 2. Hanover, site of the last such event in 2000, suffered a disappointing turnout. 3. But Shanghai sees it as comparable to Beijing’s hosting of the Olympic Games in 2008: an event that will fix the world’s attention on the city’s, and the country’s, achievements. 4. Shanghai’s planners regard the World Expo as the city’s greatest opportunity to show off its resurgent glory.

2.154 

  Verbal and Logical Reasoning

5. Skepticism may abound about the ability of World Expos to generate profits. 1.  DEBCA 4.  ECDBA

2.  EDBCA 5.  DEBAC

3.  DCABE

7. 1. Now the second, constitutional monarchy, is under threat from a growing republican movement. 2. There have been hundreds of arrests, but the rioters’ wrath shows no signs of abating.

5. This erased the barriers between brokers, merchant banks and market makers, allowing them to merge and grow in new ways. 1.  BACED 4.  DABCE

2.  BEACD 5.  DCEAB

3.  DCEBA

10. 1. After six months, true acupuncture was about 33 precent more effective than the sham treatment. 2.  Maybe they should try acupuncture.

3. The two pillars of the modern Nepali state are in big trouble.

3. Millions of arthritis sufferers are still searching for pain relief.

4. Parliamentary democracy, the first, is in limbo after King Gyanendra dismissed the most recent elected government 15 months ago.

4. Those who had real acupuncture had a 40 pre cent decrease in pain and nearly 40 pre cent improvement in functioning; the pain-education group had only slight improvement.

5. For weeks now, students chanting anti-king slogans have clashed daily with the security forces in the streets of the capital, Kathmandu. 1.  CDEBA 4.  EABCD

2.  CBDEA 5.  CDABE

3.  CDAEB

8. 1. These institutions face fierce competition in coming years, as a falling birth rate produces too few applicants for too many places. 2. Universities in Japan are used to being ranked by their academic prowess. 3. Now their finances are being ranked as well. 4. This month SLP, an international ratings agency, published its first ratings of the creditworthiness of universities. 5. Good ratings should help to reassure applicants that the university they choose will be able to survive. 1.  EBACD 4.  BCDAE

2.  BECAD 5.  CBDAE

3.  DCEAB

9. 1. While this shift should have paved the way for global banks based in Britain, the homegrown firms weren’t able to navigate the new landscape. 2. British banks like Barings, Kleinvort, Morgan Grenfell, Warburgs, and NatWest became involved n various pairings, and generally moved towards an American-style model in which ongoing, personal relationships with clients were less important than bidding aggressively on each new piece of business. 3. The change goes back to Prime Minister Margaret Thatcher’s deregulation of British financial markets in 1983, known as “the Big Bang”. 4. Despite the City of London’s position as the centre of the European financial universe, nearly every independent bank in Britain is in foreign hands.

5. In a multi-centre trial, doctors found 570 people with knee osteoarthritis and gave them acupuncture, fake acupuncture or had them attend sessions where they learned to cope with pain. 1.  EADCB 4.  CEABD

2.  EDCBA 5.  CBEAD

3.  CBEDA

Direction for questions 11 to 15:  Each sentence below contains either one or two blanks. A blank indicates that a word or brief phrase has been omitted. Select among the five choices the word or phrase for each blank that best fits the meaning of the sentence as a whole. 11. There is a general ________ in India that our ethics are declining and that out moral standards are _______ 1.  feeling - normalizing 2.  idea–futile 3.  optimism–improving 4.  complaint–deteriorating 5.  outlook–escalating 12. Homo sapiens, the proud splitter of the atom, inventor of the electronic computer, ____ of the genetic code may be humbled by a lowly ____ of the sewers and soils—the microbe. 1.  designer–inhabitant 2.  discoverer–rodent 3.  writer–organism 4.  decipherer–denizen 5.  author–purifier 13. After centuries of obscurity, this philosopher’s thesis is enjoying a surprising ____.

English Usage  1.  dismissal 2.  remission 3.  decimation 4.  longevity 5.  renaissance 14. The threat of war, far from ____ , lay heavily in the air, and the villagers, while ____ going about their normal activities, were unable to shake off the feeling of impending catastrophe. 1.  receding—ostensibly 2.  diminishing—contentedly 3.  increasing—apparently 4.  escalating—joyfully 5.  subsiding—felicitously 15. People from all over the world are sent by their doctors to breathe the pure, ____ air in this mountain region. A.  invigorating B.  soporific C.  debilitating D.  insalubrious E.  aromatic Direction for questions 16 and 17:  Four alternative summaries are given below each text. Choose the option that best captures the essence of the text. 16. You seemed at first to take no notice of your school fellow, or rather to set yourself against them because they were strangers to you. They knew as little of you as you did of them; this would have been the reason for their keeping aloof from you as well, which you would have felt as a hardship. Learn never to conceive a prejudice against others because you know nothing of them. It is bad reasoning, and makes enemies of half of them. It is bad reasoning, and makes enemies of the half of world. Do not think ill of them till they behave ill to you; and then strive to avoid the faults which you see in them. This will disarm their hostility sooner than pique or resentment or complaint. 1. The discomfort you felt with you school fellows was because both sides knew little of each other. You should not complain unless you find others prejudiced against you and have attempted to carefully analyse the faults you have observed in them. 2. The discomfort you felt with you school fellows was because both sides knew little of each other. Avoid prejudice and negative thoughts till you encounter

  2.155

bad behaviour from others, and then win them over by shunning the faults you have observed. 3. You encountered hardship amongst your school fellows because you did not know them of well. You should learn to not make enemies because of your prejudices irrespective of their behaviour towards you. 4. You encountered hardship amongst your school fellows because you did not know them well. You should learn to not make enemies because of your prejudices unless behave badly with you. 5. One’s behaviour is not the true reflection of one’s personality. Same is true with your school fellows. 17. The human race is spread all over the world, from the polar regions to the tropics. The people of whom it is made up eat different kinds of food, partly according to the climate in which they live, and partly according to the kind of food which their country produces. In hot climates, meat and fat are not much needed; but in the Arctic regions they seem to be very necessary for keeping up the heat of the body. Thus, in India, people live chiefly on different kinds of grains, eggs, milk, or sometimes fish and meat. In Europe, people eat more meat and less grain. In the Arctic regions, where no grains and fruits are produced, the Eskimo and other races live almost entirely on meat and fish. 1. Food eaten by people in different regions of the world depends on the climate and produce of the region, and varies from meat and fish in the Arctic to predominantly grains in the tropics. 2. Hot climate require people to eat grains while cold regions require people to eat meat and fish. 3. In hot climates require people eat mainly grains while in the Arctic, they eat meat and fish because they cannot grow grains. 4. While people in Arctic regions like meat and fish and those in hot regions like India prefer mainly grains, they have to change what they eat depending on the local climate and the local produce. 5.  What people eat depends upon the many factors. Direction for questions 18 to 20:  Arrange the sentences A, B,C and D to form a logical sequence between sentences 1 and 6. 18. 1. That was the day that Walter Alva made the boldest decision of his career. A. He had believed that somehow the situation would resolve itself. B. First, he apologized to his teammates for put ting them in danger.

2.156 

  Verbal and Logical Reasoning

C. He now encouraged anyone who wished to leave to do so without delay. D. Until recently, he explained, his fascination with the tomb had blinded him to the peril of their position. 6. None did. 1.  BACD 2.  DBAC 3.  BDAC 4.  DCBA 5.  ABCD

of completing the sentence are indicated. Choose the best alternative among the four.

19. 1. During this summer, I spent blissfully long days with my friend. A. In the afternoons, we would retire to the cottage, and she would talk about her husband what a fine man he’d been. B. I discovered she made the finest shortbread (a kind of biscuit) in the universe. C. Once or twice she seemed about to cry and left the room quickly to make more tea. D. We could explore Bear Wood, munching happily and discussing the books she had lent me. 6.  But she always came back smiling. 1.  BCAD 2.  ADCB 3.  ACBD 4.  BDAC 5.  ABCD

4.  The more pronounced the transformation

21. _______________, the more they remain the same. 1.  The more the merrier 2.  The less the dynamism 3.  The more things change 22. The stock market is probably ____________ and the way the market has been plunging says a lot about investor’s confidence. 1. the best barometer to assess the sentiment of the public. 2. an ideal indication of the health of public sentiment. 3. the least imperfect mechanism for judging the quantity of the sentiment of the public. 4.  the best indicator of public sentiment. 23. ________ that in this apparent mess, two things need not be interfered with 1.  It is important 2.  It is of cardinal importance 3.  It should be urgently understood 4.  It cannot be emphasized

20. 1. The chainsaw howled as I finished cutting through the branch. A.  The branch crashed to the ground, taking my spectacles with it. B. I almost dropped the saw as I shielded my face from the twigs that brushed by.

24. The highest reward for a man’s toil is not what he gets for it, but what _________ 1.  he makes out of it. 2.  he gets for others. 3.  he has overcome through it. 4.  he becomes by it.

C.  Howard retrieved my glasses and handed them up to me. D. I pulled the saw away, and my husband tugged against the other end of the rope that I had tied just above the cut.

25. Wines that yield a good commercial profit__________ in the same limited areas of France as now. 1.  seem to have been produced

6.  Are you okay? He asked. 1.  BCAD 4.  BDAC

2.  DBAC 5.  ABCD

3.  DCAB

2.  appear to have a remarkable semblance

ANSWER KEYS

Direction for questions 21 to 25:  In each of the  following sentences a part of the sentence is left unfinished. Beneath each sentence, four different ways

3.  bear a significant similarity in terms of produce 4.  appear to have been similarly produced

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

5

3.

5

4.

5

5.

2

6.

1

7.

3

8.

4

9.

3

10.

5

11.

4

12.

4

13.

5

14.

1

15.

1

16.

2

17.

1

18.

3

19.

4

20.

2

21.

3

22.

4

23.

1

24.

4

25.

1

English Usage 

  2.157

HINTS AND EXPLANATIONS 1. Kudos means honour, so dishonor is the right word.

declining (deteriorating). Almost any word except ‘optimism’ would have fit the first blank.

2. Invincible means one who can’t be defeated, so defenseless. 3. Loquacious means talkative, so laconic.



4. Parochial means narrow-minded, so cosmopolitan, a broadminded person.

12. The first blank requires something that conveys what man has done to the genetic code–the only two suitable words are ‘discoverer’ or ‘decipherer’. But since a microbe is not a rodent, we can eliminate that pair.

5. Ephemeral means short lived, so lasting. 6. B tells us the reason why “scepticism may abound”. Hence EB is a sequence. However, CA again vindicates the need to spend on the World Expo. 7. Which are “the two pillars of the modern Nepali state” referred to in C? The first is “parliamentary democracy” mentioned in D and the second is “constitutional monarchy” mentioned in A. Thus we get CDA as a sequence. The last two sentences EB elaborate the “growing republican movement” further. 8. Note the phrase “are ... being ranked” in B and C. Obviously, BC is a sequence. And then DAE talks about their rating on the basis of creditworthiness—an obvious reference to “finances” in C. 9. Note the phrase “the change in C”. Now this is a reference either to B or to D. So we should get BC or DC. Thus 1 and 2 are ruled out. A similar phrase is “this shift” in A. So we should get BA or DA. That still leaves us with 3 and 4. Now, if you read the sentences in both the orders, you find 3 is better than 4 because B is an explanation of E— “to merge and grow in new ways.” 10. Two sequences are clearly established: CB and EAD. Now, which of these should we place first? CB, because the sentence B introduces us to “acupuncture”, the details of which are talked about in EAD. Hence we get CBEAD. 11. ‘and’ usually joins things of similar meaning or weight. This suggests that since ethics are declining, moral standards are also



(futile = useless, ineffective; escalating = increasing)

(rodent = animal like a rat or mouse; decipherer = someone who decodes; denizen = inhabitant)

13. The sentence tells us that the thesis has been in obscurity (forgotten or neglected) but now it is being revived. We can say it is undergoing a renaissance (revival).

(remission = temporary cessation of a disease; decimation = destruction; longevity = length of life)

14. ‘Far from’ indicates that an opposite point is being made. So, since there is a feeling of impending catastrophe the threat of war is far from getting less. This indicates that ‘receding’, diminishing’, or ‘subsiding’ might be suitable. We can eliminate these last two since their partner words ‘contentedly’ and ‘felicitously’ are inappropriate for a feeling of danger. So the villagers are only apparently (ostensibly) behaving normally.

(escalating = increasing ; felicitously = happily, suitably)

15. Since the air is described as ‘pure’ we need a positive word. Also, since doctors recommend it, the air must be good for health. Therefore, we choose invigorating which means energizing.

(soporific = sleep-inducing; debilitating = weakening; insalubrious = unhealthy; aromatic = pleasant-smelling)

c h a p t e r

 3

Logical Reasoning

 LEARNING OBJECTIVES After completion of this chapter, you should have a thorough understanding of the following:   Different type of LR questions   Skill-set required to excel in LR   Approach to solve the questions

L

ogical reasoning plays an important role in CAT as well as other B-School exam papers. In recent years, specially CAT 05 onwards, importance of LR has increased. In this chapter, we will learn the methods to solve different types of LR questions.



 SEQUENCING AND ARRANGEMENT PROBLEMS

Sequencing is the act of putting things in a specific sequence, or ordered list. In our day-to-day life too, we go through many examples of sequencing or arranging the things or events such as:  While writing appointments on a calendar or on a mobile, or,  While placing orders in a restaurant—Talumein soup, then kebabs, then chicken combo food, then ice cream and finally mocha.  While taking a test and deciding that which section is to be attempted first, then second and so on.

The only difference between the sequencing in our practical life and the LR set will be the fact that the LR set given in the questions will have a prior order of variables. As a student, your job will be to find out that order of sequence.

 TYPES OF SEQUENCING AND ARRANGEMENT While a good number of times, the statements/conditions given in the LR set will specify the exact positioning of the entities given, many a times only the relative positioning of the variables will be there. Let us see some examples of such statements:

Logical Reasoning 

Context

Statement goes like…

Which variables are exactly M is fourth. placed in the sequence? Which variables are forbidden M is not fifth. from specific position in the sequence? Which variables are next M and N are consecutive to, before, or immediately A is next to B. preceding or following one No variable comes between another? A and B. A and B are consecutively in the sequence. Which variables cannot be next to, before, or immediately preceding or following one another?

A does not immediately precede or follow B. A is not immediately before or after B. M and N are not consecutive in the sequence.

How far apart in the sequence Exactly two people come are two particular variables? between A and B. What is the relative position A comes before B in the of A and B in the sequence? queue. M comes after N in the queue.

In the above given examples, we observe two types of sequencing:

1.  Strict Sequencing and Arrangement In these kinds of sequencing, relative positioning of the variables will be almost fixed. These are the rules which give us the exact position of the variables.

  2.159

2.  Loose Sequencing and Arrangement In this kind of sequencing, data given will give us the relative positioning of one variable with respect to the other variable, without giving the exact position. To see the examples of strict sequencing and loose sequencing, consider the following statement: There are seven movies to be shown in a day at the Goa film festival 09—one movie from each of the following countries—India, Japan, US, UK, Israel, Pakistan, South Korea, Iran and Ireland. Movies have a particular pattern of showing which is given as follows:  Movie from India is shown third.  Movie from Japan is shown before the movie from Ireland.  Movie from Israel cannot be shown after the movie from Pakistan. And so on, many more such conditions are given to identify the sequence of showing the movies. Now let us identify which of these are strict sequencing statements and which of these are loose sequencing statements. Movie from India is shown third–It gives a fixed location for the movie from India–so it’s a strict sequencing statement. Movie from Japan is shown before the movie from Ireland—With this statement, we do not get the exact positioning of any of the movies, however, we get the relative positioning of movie from Japan with respect to the movie from Ireland—so it’s a loose sequencing statement. Movie from Israel cannot be shown after the movie from Pakistan—With this statement, we do not get the exact positioning of any of the movies, however, we get the relative positioning of Movie from Pakistan with respect to the movie from Israel—so it’s a loose sequencing statement.

  EXERCISE 1 Direction for questions 1 to 6: Read the passage given below and solve the questions based on it. Bus route no. 761 has exactly six stops on its route. Any bus plying on this route starts from the initial position, then stops first at stop one and then at stops two, three, four, five, and six respectively. After the bus reaches stop six, the bus turns and returns to its initial position and repeats the cycle. Buses are not allowed to carry people on its return journey. The following are the six stops—L, M, N, O, P, and Q- in no particular order. Further, the following

observations have been made regarding the stops on this route:  Observation 1:  P is the third stop.  Observation 2:  M is the sixth stop.  Observation 3:  The stop Q is the stop immediately after O.  Observation 4:  N is the stop immediately before L. 1. If N is the fourth stop on this route, which among the following must be the stop immediately before stop P?

2.160 

  Verbal and Logical Reasoning

1.  N 4.  M

2.  Q 5.  L

3.  O

5. If we relax the observation 3, then in how many different ways can the stops be fixed on this route?

2. If L is the second stop on this route, which among the following must be the stop immediately before M?

1.  1 4.  4

1.  N 4.  P

6. How many of the stops have a fixed position?

2.  Q 5.  L

3.  O

3. A passenger boards a bus on this route at O, rides past one of the stops, and alights at P. Which of the following must be true? 1.  O is stop one 3.  N is stop five. 5.  None of these

2.  P is stop four. 4.  L is stop six.

4. In how many different ways can the stops be fixed on this route? 1.  1 4.  4

Patel roadways Rajan roadways

2.  2 5.  None of these CHD  (dep) 09:30 14:30

AB   (arr) 10:40 15:40

3.  3

AB  (dep) 10:42 15:42

KU  (arr) 11:30 16:20

2.  2 5.  None of these

1.  1 4.  4

2.  2 5.  None of these

3.  3

3.  3

Direction for questions 7 to 12:  Go through the data set given below and solve the questions based on it. There are two bus services available to travel from Chandigarh (CHD) to Delhi - one of Patel Roadways and the other of Rajan Roadways. The distance between the two places is 250 km. Each of these buses stop at four locations on the way from Chandigarh (CHD) to Delhi. These locations are codenamed as (AB), (KU), (SH) and (PAN). The arrival and departure times of the two buses are given below in the table: KU (dep) 11:35 16:23

SH (arr) 12:10 17:00

SH (dep) 12:12 17:15

PAN  (arr) 13:40 18:15

PAN (dep) 13:42 18:18

Delhi (arr) 14:30 19:00

NOTE: Arr stands for arrival and Dep stands for departure.

7. What is the difference between the speeds of faster and slower bus (including stoppages)? 1.  3.33 km/h

2.  5.55 km/h

4.  7.77 km/h

5.  8.88 km/h

3.  6.66 km/h

the percentage difference in time taken by the Patel Roadways bus, if its speed is decreased by 20%? 1.  20%

2.  25%

4.  42.5%

5.  50%

3.  33.33%

8. Between which stretches is the ratio of the speeds of the two bus services 1:1?

12. For how many stretches, is it possible to identify the speed of the bus of both the roadways?

1.  AB to KU

2.  CHD to AB 3.  SH to PAN

1.  0

2.  1

4.  PAN to Delhi

5.  cannot be determined

4.  3

5.  All the stretches

9. What is the percentage difference between the maximum speed of Rajan roadways bus and the minimum speed of Patel roadways bus? 1.  12%

2.  19%

3.  26%

4.  33%

5.  Cannot be determined

10. In which stretches of the journey is the speed of Patel roadways bus minimum (Assume distance between the stops to be equal)? 1.  CHD to AB

2.  AB to KU

3.  KU to SH

4.  SH to PAN

5.  cannot be determined

11. If the average speed is calculated keeping in mind only the running time of the bus, what would be

3.  2

Direction for questions 13 to 16: Read the passage given below and solve the questions based on it. Six games—Hockey, Football, Basketball, Volleyball, Handball and Kabaddi are to be arranged from Thursday, 5 August 2109 to 11 August 2109, in accordance with the following conditions: (i) Football should not be either on the first or the second day and Hockey should be held three days before Football. (ii) There should be one rest day when no game will be held. (iii) Volley ball should be immediately before Hockey and immediately after Kabaddi. (iv) Handball should be followed by rest day and Handball cannot be held on 5 August 2109.

Logical Reasoning 

  2.161

13. Which day will be the rest day for the game?

20. Which of the following is the last lecture in the series?

1.  Tuesday 2.  Thursday 3.  Friday 4.  Cannot be determined 5.  None of these

2.  Agri Input Marketing 1.  Budget 3.  Carbon market 4.  Cannot be determined 5.  None of these

14. On Wednesday, which of the following games will be played? 1.  Handball 2.  Hockey 3.  Volleyball 4.  Cannot be determined 5.  None of these 15. On which day will Handball be played? 1.  Friday 2.  Saturday 3.  Monday 4.  Cannot be determined 5.  None of these 16. For how many of the games can we have a certain day of happening of that game? 1.  0 4.  3

2.  1 3.  2 5.  None of these

Direction for questions 17 to 21: Read the passage given below and solve the questions based on it. Six lectures on different topics—environment, Budget, Carbon market, Agri Input Marketing, Education, and law—are to be organized in a span of seven days—from Tuesday to Monday, only one lecture on each day in accordance with the following: (i) The lecture on Budget should not be organized on Saturday. (ii) The lecture on Agri Input Marketing should be organized immediately after lecture on environment. (iii) There should be a gap of two days between the lectures on Law and Education, Education occuring before Law. (iv) One day there will be no lecture (Sunday is not that day). Just before that day the lecture on Education will be organized. (v) Lecture on Carbon Market should be organized on Thursday and should not be followed by lecture on Education. 17. How many lectures are organized between Agri Input Marketing and Law? 1.  None 4.  Three

2.  One 3.  Two 5.  None of these

18. On which day there is no lecture? 2.  Sunday 3.  Wednesday 1.  Tuesday 4.  Cannot be determined 5.  None of these 19. On which day will the lecture on Environment be organized? 1.  Sunday 4.  Saturday

2.  Monday 5.  None of these

3.  Tuesday

21. Which of the information’s is not required in finding the complete sequence of organization of lectures? 1.  (ii) only 4.  (ii) only

2.  (i) and (ii) only 5.  All are required

3.  (i) only

Direction for questions 22 to 25: Read the passage given below and solve the questions based on it. The tourism department has organized four hours sightseeing tours in Delhi. For this, the department operates seven buses. The schedule and the frequency of the buses are given below: The buses are marked alphabetically as A, B, C, D, E, F and G. From Monday to Friday, the first bus leaves at 8 AM sharp. Subsequent buses leave at intervals of 45 mins and 30 mins alternately. On Saturdays and Sundays, the first bus will leave at 7:30 AM and others follow regularly after a gap of one hour each. Bus E leaves immediately after bus A and bus E is immediately followed by bus G. Bus C is not followed by any other bus. Bus F leaves immediately before bus A but not immediately after bus D. None of the buses precedes bus B. 22. On Sunday, when bus D completes its tour, which of the following buses will begin its tour? 1.  B 4.  F

2.  C 5.  None of these

3.  E

23. If the gap after bus A leaves on Saturday-Sunday is increased by 30 mins, at what time will the tour of bus G be completed? 1.  2 PM 4.  4:30 PM

2.  4 PM 5.  None of these

3.  5 PM

24. On Saturday, at what time does the bus A starts its tour? 1.  9 AM 4.  10:30 AM

2.  9:30 AM 5.  None of these

3.  10 AM

25. If the time gap between two buses is uniformly kept at 45 mins from Monday to Friday, then the beginning of tour of bus C will mark completion of tour of which of the following buses? 1.  B 4.  F

2.  C 5.  None of these

3.  A

  Verbal and Logical Reasoning

Q. 1. 6. 11. 16. 21.

ANSWER KEYS

2.162 

Ans. 2 2 4 1 5

Q. 2. 7. 12. 17. 22.

Ans. 2 4 2 2 5

Q. 3. 8. 13. 18. 23.

Ans. 1 4 4 3 4

Q. 4. 9. 14. 19. 24.

Ans. 2 4 4 4 2

Q. 5. 10. 15. 20. 25.

Ans. 4 5 4 1 5

HINTS AND EXPLANATIONS Solutions 1 to 12:

Solutions 13 to 16:

Following is the structure of the stops on this route:

N Stop 1

L

P

O

Stop 2 Stop 3 Stop 4

Q

M

Stop 5 Stop 6

OR O Stop 1

Q

P

N

Stop 2 Stop 3 Stop 4

L

M

Stop 5 Stop 6

Now all the questions can be answered. 7. Average speed of Patel roadways bus => 250 / 5 = 50 km/hr Average speed of Rajan roadways bus => 250 / 4.5 = 55.55 km/hr. Hence difference is 5.55 km/hr. Hence, option (2) is correct. 8. From the table it is clear that option (2) is correct. 9. Cannot be determined because we do not know the distance between the four stops. Hence, option (4) is correct. 10. Time taken to travel from SH to PAN is 1hour 28 min, which is the highest. Hence, Speed is lowest in this stretch. Hence, option (4) is correct.  1  = 1.25  . 11. If speed decreases by 20% => time increases by 25%  = 0.8   Hence, option (2) is correct.

Days

Date

Either

Or

Thursday

  5  August

Basketball

Kabaddi

Friday

  6  August

Kabaddi

Volleyball

Saturday

  7  August

Volleyball

Hockey

Sunday

  8  August

Hockey

Handball

Monday

  9  August

Handball

Rest day

Tuesday

10  August

Rest day

Football

Wednesday

11  August

Football

Basketball

13. 14. 15. 16.

(4)  Either on Monday or Tuesday (4)  Football or Basketball (4)  Sunday or Monday (1) It can be seen that each of the games can be played on two different days.

Solutions 17 to 21:  Tues

Wed

Thurs

Fri

Sat

Sun

Mon

Education

Rest

Carbon

Law

Env.

AIM

Budged

Solutions 22 to 25: Following is the arrangement: BFAEGDC.

12. It is not possible for any of the stretches, as we don’t have the distance given between any two stretches. Hence option (1) is the answer.

  LOGICAL LINKS Statements like “I will go to watch a movie” or “She will go to picnic” are known as simple statements. Now we can join these two simple statements in a number of ways:

 If I do not go to watch a movie, only then she will not go to picnic.

 If I go to watch a movie, only then she will go to picnic.

 If I go to watch a movie, only then she will not go to picnic. After we have joined the simple statements, we call these statements as Compound Statements. And the words which we used to join two simple statements are known as Logical Links.

Or, if we allow a bit of change in the nature of statements then statements could be seen as follows too:

Some Standard Logical Links And Their Usages

 If I go to watch a movie, then she will not go to picnic.

If – then

 Either I will go to watch a movie or she will go to picnic.  If I go to watch a movie, then she will go to picnic.

 If I do not go to watch a movie, then she will go to picnic.  If I do not go to watch a movie, then she will not go to picnic.

1. If A happens then B happens. Given – A has happened.

Logical Reasoning 

Conclusion – B will happen.

7. If A happens only then B happens.

This is a valid conclusion.

Given – A has happened.

2. If A happens then B happens.

Conclusion – B will also happen.

Given – A has not happened.

This is an invalid conclusion.

Conclusion – B will not happen.

Either–or

This is an invalid conclusion.

  2.163

1. Either A will happen or B will happen.

3. If A happens then B happens.

Given – A will happen.

Given – B has happened.

Conclusion – B will not happen

Conclusion – A would also have happened.

This is a valid conclusion.

This is an invalid conclusion.

2. Either A will happen or B will happen.

4. If A happens then B happens.

Given – A will not happen.

Given – B has not happened.

Conclusion – B will happen

Conclusion – A would also not have happened.

This is a valid conclusion.

This is a valid conclusion.

3. Either A will happen or B will happen.

5. If A happens only then B happens.

Given – B will happen.

Given – B has happened.

Conclusion – A will not happen

Conclusion – A would also have happened.

This is a valid conclusion.

This is a valid conclusion.

4. Either A will happen or B will happen.

6. If A happens only then B happens.

Given – B will not happen.

Given – A has not happened.

Conclusion – A will happen

Conclusion – B would also not happen.

This is a valid conclusion.

This is a valid conclusion.

  EXERCISE 2

1. When Devdas comes, Umrao Jaan sings. A.  Umrao Jaan is singing. B.  Devdas has come. C.  Devdas hasn’t come. D.  Umrao Jaan is not singing.

1.  AB 4.  CD

2.  BA 5.  None of these

2. Amit Kumar is either an engineer or a doctor. A.  Amit Kumar is an engineer. B.  Amit Kumar is not a doctor C.  Amit Kumar is not an engineer. D.  Amit Kumar is a doctor.

1.  AB 4.  BC

3.  BC

2.  AD 5.  None of these

3. Either Raghav is sick or he is stoned. A.  Raghav is sick. B.  Raghav is not sick. C.  Raghav is stoned. D.  Raghav is not stoned. 1.  AB 2.  DA 4.  CD 5.  None of these

3.  DA

3.  AC

4. Unless you catch the criminals, the crimes will not stop. A.  The criminals have been caught. B.  The crimes have stopped. C.  The criminals have not been caught.

2.164 

  Verbal and Logical Reasoning

D.  The crimes have not stopped. 1.  DC 4.  DA

2.  CD 5.  None of these

3.  BC

i.  BA

ii.  AD

iii. CB

1.  ii only 4.  ii and iii

2.  i and iii 5.  None of these

3.  i and iii

5. If you fall down from the roof, then your legs will get fractured.

8. Either Hari will do the project or dada will free ride.

A.  You have fallen down the roof.

B.  Hari is not doing the project.

B.  Your legs have got fractured.

C.  Dada is free riding.

C.  You have not fallen down the roof.

D.  Dada is not free riding.

D.  Your legs have not fractured.

i.  BA

i.  BA

ii.  AB

1.  i and ii

2.  ii and iii

4.  i, ii and iii

5.  None of these

A.  Hari is doing the project.

iii.  DC

ii.  AC

1.  ii only 4.  iv only

3.  ii only

iv.  AD

2.  i and iii 5.  None of these

3.  i and iii

9. Only in Bengal, you can see the Bengal Tiger. A.  You went to Bengal.

6. Only if you fall down from the roof, then your legs will get fractured.

B.  You didn’t go to Bengal. C.  You saw the Bengal Tiger.

A.  You have fallen down the roof.

D.  You didn’t see the Bengal Tiger.

B.  Your legs have got fractured.

1.  AC 4.  BD

C.  You have not fallen down the roof. D.  Your legs have not fractured. i.  BA

ii.  AB

1.  i and ii 4.  i, ii and iii

2.  ii and iii 5  None of these

2.  DB 5.  None of these

3.  AD

10. If Nishit works, then Hari free rides and if Hari free rides, then dada works. If dada works, then Nishit free rides.

iii.  DC 3.  i and iii

A.  Nishit worked. B.  Nishit did free ride.

7. If Prashant gets good marks in mid-term exam, he will not study for end term exams.

C.  Hari worked.

A.  Prashant has got good marks in mid-term exams.

E.  Dada worked.

D.  Hari did free ride.

B.  Prashant has not got good marks in mid-terms exams.

F.  Dada did free ride.

C.  Prashant is studying for end terms exams.

1.  AE 4.  CE

D.  Prashant is not studying for end terms exams.

ANSWER KEYS

iii.  BD

2.  EA 5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

2

2.

1

3.

2

4.

2

5.

2

6.

4

7.

4

8.

4

9.

4

10.

1

3.  AF

Logical Reasoning 

  2.165

  CUBES A cube is a three-dimensional structure with the following features: It has six faces, eight corners and twelve edges. Cube is composed of six square faces that meet each other at right angles. Let us see how the six different faces of a cube can be represented:

Cutting the Cubes Before moving on to solve questions, we should be clear with the basics that what happens when we cut a cube: i. One cut divides the cube into two parts. ii. Second cut will divide the cube in either a total of 3 parts or 4 parts, depending upon the axis of cut. iii. Third cut will divide the cube in either a maximum of 8 parts or a minimum of 4 parts.

Painting the cubes and then Cutting the Cubes If we paint a cube of the dimension n × n × n by any one colour, and then we cut it to have n 3 symmetric cubelets, then following is the number of cubelets with colour on different faces of it:

And finally the cube appears like:

i. Cubelets with only one face painted = (n–2)2 × 6 ii. Cubelets with two faces painted = (n–2) × 12 iii. Cubelets with three faces painted = 8 iv. Cubelets with no sides painted = (n–2)3

  EXERCISE 3 Direction for questions 1 to 4: Read the passage given below and solve the questions based on it.

1.  20 4.  26

(1) There is a rectangular wooden block of length 5 cm, height 4 cm and breadth 3 cm.

4. How many cubes will have only one surface coloured?

(2) The two opposite surfaces of 4 cm × 3 cm are painted from outside by green colour. (3) The other two sides of 5 cm × 4 cm are coloured by blue. (4) The remaining sides are painted with black. (5) Now the block is cut in such a way that cubes of 1 cm × 1cm × 1 cm are created. 1. How many cubes will have 3 colours? 1.  4 4.  8

2. 6 5.  None of these

3.  2

2.  2 5.  None of these

3. How many cubes will have only two colours?

2.  22 5.  None of these

3.  24

3.  24

Direction for questions 5 to 8: Read the passage given below and solve the questions based on it. A large cube is dipped into a tub filled with colour. Now the cube is taken out and it was observed that all its sides are painted. This large cube is now cut into 125 small but identical cubes. 5. How many of the smaller cubes have no face painted at all? 1.  27 4.  25

2.  64 5.  None of these

3.  8

6. How many of the smaller cubes have exactly one face painted?

2. How many cubes will have no colour? 1.  6 4.  4

1.  20 4.  26

2.  22 5.  None of these

3.  3

1.  49 4.  45

2.  54 5.  None of these

3.  64

7. How many of the smaller cubes have exactly two faces painted?

2.166 

  Verbal and Logical Reasoning

1.  25 2.  16 3.  36 4.  48 5.  None of these 8. How many of the smaller cubes have exactly three faces painted? 1.  4 2.  8 3.  9 4.  12 5.  None of these

9. What is the least number of the smaller cubes that will have exactly three faces coloured? 1.  0 4.  12

10. How many smaller cubes have exactly two faces coloured?

Direction for questions 9 to 10: Read the passage given below and solve the questions based on it. Three different faces of a cube are coloured in three different colours—black, green and blue. This cube is now cut into 216 smaller but identical cubes.

ANSWER KEYS

2.  6 3.  2 5.  Cannot be determined

1.  32 4.  18

2.  45 3.  56 5.  Cannot be determined

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

1

3.

3

4.

2

5.

1

6.

2

7.

3

8.

2

9.

1

10.

5

HINTS AND EXPLANATIONS 2. (1) No surfaces coloured = (L – 2) (B – 2) (H – 2)

In above solutions, L = Length, B = Breadth, H = Height



The final cube can be seen as 5 × 5 × 5.

=3×2×1=6

3. (3) Two surfaces coloured = 4 (L -2) + 4 (B – 2) + 4 (H – 2)

5. (1)  No face painted = (5 – 2) (5 – 2) (5 – 2) = 27



=4×3+4×2+4×1

8. (2)  All the faces painted will remain 8.



= 12 + 8 + 4 = 24

9. (1) Since only three faces are coloured, the minimum number of smaller cubes that will have all the three colours = 0 [This is possible if all three colours have not been put on the adjacent sides of the cube]

4. (2) One surface coloured = 2 (L – 2) (B – 2) + 2 (L – 2) (H – 2) + 2 (B – 2) (H – 2)

=2×3×2+2×3 ×1+2×2×1



= 12 + 6 + 4 = 22

  SYLLOGISM

10. (5) Since which three faces are painted is not given, we cannot answer “exactly” how many smaller cubes will have two sides coloured.

Universally Negative Statement

In Syllogism, we study the ways to provide the evidences derived from the given statements to the conclusion in the clearest of term.

Example–No A are B.

Types of Statements

Particular Affirmative Statement

Universally Affirmative Statement

Example–Some A are B.

Example–All A are B. Subject-Predicate form:  These types of statements are known as ‘A- type’ statements.

Subject–Predicate form:  These types of statements are known as ‘E- type’ statements.

Subject–Predicate form:  These types of statements are known as ‘I- type’ statements.

Logical Reasoning 

Particular Negative Statement Example –Some A are not B. Subject–Predicate form:  These types of statements are known as ‘O- type’ statements. Standard deductions in a table format: Given statement

Deduction

All A are B

Some A are B Some B are A

Truthmetre

Summary

Definitely ‘All’ can give only True ‘Some’ as Definitely definitely true True statement.

Some B are not A

Probably True

Some A are not B

Definitely False

Definitely ‘Some’ can give only True ‘some’ as Probably definitely true Some B are not A statement. True

Some A are B Some B are A

Some A are not B Some A are not B

No ‘Definitely True’ deduction possible Some B are not A

No A are B

Probably True

Probably True

Definitely ‘No’ can give No B are A only ‘No’ True or ‘Some Definitely + Not’ as Some A are not B True definitely true statement. Definitely Some B are not A True

  2.167

First Not Second Possible statement possible statement ‘definitely true’ type type conclusions ALL

Some

Some

No/Some not

All

All

All/Some

No/Some not

All

No

Some not/No

Some/All

All

Some not

No such conclusion possible

Some

All

Some

Some

Some

No such conclusion possible.

Some

No

Some not

Some

Some not

No such conclusion possible

No

All

No/Some not

All/Some

No

Some

Some not

All/No/ Some

No

No

No/Some not

All/Some

No

Some not

No such conclusion possible

SOME All/Some not/No All/No/ Some

NO

SOME NOT Some not

All

No such conclusion possible

Some Some not No

  REMEMBER THAT 1. No positive statement can give rise to any negative definitely true conclusion. (excluding may be) 2. No negative statement can give rise to any positive definitely true conclusion. (excluding may be situations)

Example Statements:

i.  Some panthers are cats. ii.  No panther is river. iii.  All rivers are roads.

Conclusions:

I.  No cat is river. II.  Some roads are rivers.

2.168 

  Verbal and Logical Reasoning

III.  Some cats are not river.

panther and river simultaneously.

IV.  Some rivers are not cat.

Now use both the statements: Statement (i) tells that atleast one panther is cat or vice versa, and statement (ii) tells that if anything is a panther, then that cannot be a river and vice versa. Hence, we can conclude that at least one cat is there which is not river. So, it can be validly concluded that ‘Some cats are not river.’

Which of the above given conclusions is/are definitely true? Solution:  We will evaluate each conclusion one by one: Conclusion I—The relationship between ‘cat’ and ‘river’ can be established only through statement (i) and statement (ii) Looking upon the nature of statements I and II, we can say that the conclusion can only be in “Some + Not”, and not in “No”. Hence it is an invalid conclusion. Conclusion II—The relationship between ‘roads’ and ‘rivers’ can be established through statement (iii.) Since ‘all rivers are roads’, so it can be concluded that ‘some roads are rivers’.

Conclusion IV—Prima facie, it appears that conclusion IV is true. And if we see this conclusion in the absence of conclusion III, it appears definitely true, however it is only probably true. To evaluate this conclusion, we will take the recourse of venn-diagram:

Conclusion III—The relationship between ‘river’ and ‘cats’ can be established using statement (i) and statement (ii) The conclusion has to be of the type “Some + Not”. Let us understand the statements: Statement (i) Some panthers are cats—At least one panther has to be there which is cat. We cannot comment about remaining panthers if they are cats or not. Statement (ii) No panther is river—Anything cannot be a

Obviously, all the rivers are cat in the above given diagram. So, conclusion IV cannot be definitely true. Hence, only conclusion II and conclusion III are definitely true.

  EXERCISE 4 1. Statements:

(a)  All homes are mountains.

1.  Either II or I follows



(b)  All glasses are mountains.

2.  Both I and II follow



(c)  Some mountains are windows.

3.  Either II or III follows

Conclusions: 1.  Only I follows

I.  Some windows are glasses. II.  Some homes are windows III.  Some mountains are glasses.

4.  Only I follows

2.  Only II follows 3.  Only III follows

5.  None of these 3. Statements:

(a)  All coats are shirts.



(b)  some shirts are caps.



(c)  No caps are trousers

Conclusions:

4.  Only I and II 5.  None of these 2. Statements:   (a)  No planes are ships

I.  Some coats are caps. II. Some trousers are not shirts. III. No coats are trousers. IV. Some caps are shirts

  (b)  Some cars are not ships

1.  Only IV follows

  (c)  All cars are planes

2.  Only I and IV follow

Conclusion:

I.  Some ships are not cars II.  Some planes are not cars

3.  Only I, II and IV follow

III.  Some cars are ships

5.  None of these

4.  III and IV follow

Logical Reasoning 

4. Statements:

(a)  Some drums are vehicles. (b)  Some vehicles are machines

(c)  Some pants are levis Conclusions:

I.  Some jeans are levis II.  Some levis are jeans III.  Some levis are pants IV.  Some purses are pants

(c)  Some machines are mechanics. Conclusions:

I.  Some mechanics are machines. II.  Some vehicles are drums. III.  Some machines are drums. IV.  Some mechanics are vehicles.

1.  Only I and II follow 2.  only III and IV follow 3.  Only I and IV follow 4.  Only I follow 5. Statements:

(c)  No girl is a father. I.  Some girls are not boys II.  No boy is a girl. III.  Some girls are not fathers IV.  All girls are brothers

1.  I and II follow 2.  Either I or II and IV follow 3.  Only III follows 4.  Only II and IV follow 5.  None of these 6. Statements:

3.  Both I and III follow 4.  None follows 5.  Only III follows

(d)  Some democrats are bureaucrats. I.  Some bureaucrats are kleptocrats II.  Some democrats are politicians III.  No kleptocrats are autocrats IV.  Some democrats are kleptocrats

1.  I, III and IV follow

(c)  All flops are drops Conclusion:

I.  Some drops are flops II.  No flop is crop III.  Some drops are not flops IV.  All flops are not drops.

1.  Either I or IV and II follow 2.  I and II follow 3.  I and III follow 4.  Only II and IV follow 5.  None of these 9. Statements:

(a)  Some locks are docks (b)  Some docks are clocks (c)  Some locks are clocks (d)  No flocks are clocks

Conclusion:

I.  Some flocks are docks II.  Some docks are not flocks III.  No docks are locks IV.  Some flocks are not docks

1.  I and III follow 2.  Either I or IV follows 3.  II and I or IV follow 4.  Only III follows

2.  Only I follows

5.  None of these

3.  II and IV follow

10. Statements:

4.  None follows 5.  None of these 7. Statements:

(a)  No drop is crop (b)  Some crops are not flop

(a)  Some bureaucrats are politicians. (b)  All politicians are kleptocrats. (c)  No autocrats are democrats

Conclusion:

2.  Either II or III and IV follow

(a)  All boys are girls. (b)  All brothers are boys.

Conclusions:

1.  Only I and III follow

8. Statements:

5.  None of these

  2.169

(a)  Some jeans are pants (b)  Some purses are jeans

Conclusions:

(a)  All docks are dogs. (b)  All bads are dogs. (c)  Some docks are not bads. I.  Some bads are docks. II.  Some dogs are not docks.

2.170 

  Verbal and Logical Reasoning

III.  Some bads are not dogs. 1.  None follows 2.  Only I and II follow 3.  Only II and III follow 4.  Either I or II and III follow 5.  All follow 11. Statements:

(a)  All executives are officers. (b)  Some officers are not clerks. (c)  No clerk is an executive.

Conclusions:

I.  Some clerks are officers. II.  Some officers are not executives. III.  No officers are executives.

1.  Only II follows 2.  Either I or IV follows 3.  None follows 4.  Either II or III and I follow 5.  None of these 12. Statements:



Conclusions:

(a) Some homes are tables. (b)  Some tables are gardens. (c)  All lantern are gardens I.  Some lanterns are tables. II.  Some gardens are homes. III.  Some lanterns are homes.

1.  I and II

Conclusions:

I.  Some winds are kinds. II.  Some cools are not winds. III.  No kinds are winds.

1.  Only I follows 2.  Both I and II follow 3.  Either II or III follows 4.  None follows 5.  None of these 15. Statements: (a)  All trays are pens. (b)  Some pens are pencils. (c)  All pencils are bags. Conclusions:

I.  Some trays are bags. II.  No bags are pens. III.  Some pencils are trays. IV.  All pens are bags.

1.  None follows 2.  Only II and III follow 3.  Either IV or III and I follow 4.  Either II or I follows 5.  Only I follows 16. Statements:

Conclusions:

2.  Only I follows 3.  Only II follows 4.  Only III follows (a)  Some fans are computers. (b)  All CPUs are computers. (c)  No disks are CPUs. Conclusions:

I.  Some computers are disks. II.  Some computers are not disks . III.  No CPUs are fans.

2.  Either I or IV and III follow 3.  Only II and III follow 4.  Either III or IV follows 5.  None of these 17. Statements:

2.  Either I or II follows 3.  Only II follows

(c)  Some tats are rats. (d)  No cat is fat. Conclusions:

I.  Some fat are not tats. II.  Some cats are not hats.

4.  Either I or III follows

III.  Some rats are hats.

5.  None of these (a) All winds are kinds. (b)  Some cools are kinds. (c)  Some cools are not winds.

(a)  All cats are not hats. (b)  All rats are fat.

1.  Both I and II follows

14. Statements:

I.  Some schools are not shirts. II.  All helmets are shirts. III.  All helmets are schools. IV.  Some shirts are schools.

1.  Only IV follows

5.  None of these 13. Statements:

(a)  Some shirts are helmets. (b)  Some schools are helmets. (c)  All schools are shirts.

IV.  No hat is cat. 1.  Only II follows 2.  I, II and III follow

Logical Reasoning 

3.  I, III and IV follow

IV.  Some Santros are Esteems. 1.  Either I or IV follows 2.  Only III follows 3.  Either I or III and IV follow 4.  Only II and I follow 5.  None of these

4.  III and IV follow 5.  None of these 18. Statements:

(a)  All Reeboks are Phoenix. (b)  Some Nikes are Adidas. (c)  No Adidas are Reeboks.

Conclusion:

20. Statement:

I.  Some Phoenixes are Adidas.  II.  Some Adidas are Not Reeboks.  III.  All Phoenixes are Nike.   IV.  No Reeboks are Nike.

1.  Only IV follows 2.  Only I and IV follow 3.  Only I, II and IV follow 4.  II and either I or IV

I.  Some Santros are not Esteems. II.  Some Marutis are Santros. III.  All Omnis are Esteems.

ANSWER KEYS

I.  Some phone are recorders. II.  Some phones are not radio. III.  All phones are radios. IV. Some radios are not televisions.

(a)  Some Marutis are Omnis. (b)  All Esteems are Marutis. (c)  No Omnis are Santros.

Conclusion:

(a)  Some phones are radios. (b)  Some radios are recorders (c) Some recorders are not televisions.

Conclusions:

1.  Only IV follows 2.  Either II or III and IV follow 3.  Only III follows 4.  Either I or IV and II follow 5.  None of these 19. Statements:

  2.171

5.  None of these

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

3

2.

4

3.

1

4.

1

5.

3

6.

2

7.

5

8.

2

9.

5

10.

1

11.

3

12.

5

13.

3

14.

2

15.

1

16.

1

17.

1

18.

5

19.

1

20.

5

HINTS AND EXPLANATIONS 4. (1) Some drums are vehicles      S ome machines are mechanics. machines.

Some vehicles are drums. Some mechanics are

5. (3)  III follows from third statement. 6. (2)  I follows by combining the first two statements.

10. (1) We cannot derive anything from (c), so conclusion I does not follow. From (a), we obtain: Some dogs are docks. So II may follow but not definitely. Statement (b) gives ‘some bads are dogs’, so, again, III is doubtful. 11. (3) I does not follow from (b). II may be true from (a), but not definitely so. From (a), we get, some officers are executives, so III does not follow.

7. (5) Some + some does not give any conclusion. So I and II do not follow. III follows from (c). Again, doing (b) + (a) = I + I = No conclusion. So IV does not follow.

13. (3) (c) + (b) gives some computers are not disks. So II follows. (b) + converted (a) gives no conclusion. So III does not follow.

8. (2) From the third statement, I follows while IV does not. Nor can we say about III. Again, II is derived.

14. (2) I follows from (a). (a) + converted (b) gives no conclusion. So II does not follow. III does not follow from (a).

2.172 

  Verbal and Logical Reasoning

15. (1) (b) + (c) = I + A = I = Some pens are bags. Thus IV and II do not follow. Now, (a) + some pens are bags = A + I = No conclusion. So I does not follow. (a) + (b) = A + I = No conclusion. So III does not follow. 16. (1) IV follows from (c). III does not follow from (b). II does not follow from (a). 17. (1) Some tats are rats + All rats are fat = Some tats are fat  some fats are tats. So I does not follow. II follows from the 1st statement. III and IV do not follow from any statement.

18. (5) Statements (c) + (a) = Some Phoenixes are not Adidas. So I does not follow. II follows from (c). III can’t be derived in the same way as conclusion I. Now, from (c) + (b) = No Reeboks are Adidas + Some Adidas are Nike = E + I = Some Nikes are not Reeboks. So IV does not follow. 19. (1) (a) + (c) gives some Marutis are not Santros. So II does not follow. (b) + (a) gives no conclusion. So III does not follow. I and IV make a complementary pair (I – O pair).

PRACTICE EXERCISE  1 Direction for questions 1 to 8:  Read the passage given below and solve the questions based on it. During a leadership meet on ‘Political crisis in India’, there are eight speakers A, B, C, D, E, F, G, H who are to be seated at the table with the moderator I placed exactly in the middle of the eight. The speakers will present paper on various aspects of the given topic. Each speaker will deliver one paper each as given below: Papers 1 2 3 4 5 6 7 8

Aspect Reform in election system Amendment in Constitution Need of people awareness Role of Political parties Role of press and electronic media Coalition government President from of government Bi-Party system

The order of the papers is not necessarily in the same order as the order of the speakers’ names given above. The seating arrangement of the different speakers is given below:

3. What does A speak about? 1.  Role of Political parties 2.  Amendment in Constitution 3.  Role of press and electronic media 4.  Reform in election system. 4. Which of the following cannot be determined on the basis of the information given? I.  The author of Coalition government II. The author of Amendment in Constitution III.  On what D delivered his lecture? 1.  II only 3.  I only

2.  I and III only 4.  II and III only

5. The person who delivers lecture no. 4 [if it is known that he is symmetrically seated with respect to the moderator from F] is.... 1.  E 3.  D

2.  G 4.  B

6. Who is the person seated three places to the right of the moderator?

1) The person delivering paper 2 is seated exactly in between A and F.

1.  B 3.  E

2) The speakers delivering the papers numbered 5 and 1 respectively sit together.

7. If the lecture number of the person seated to the immediate left of I is double the lecture number of the person seated the extreme left of I, then what does the former lecture upon?

3) E is seated to the immediate left of the moderator. 4) F is seated at one end. 5) G is seated beside the person delivering paper 3 and two places to the left of E. 6) H, who presents paper 5 and E, have only I in between them. 7) A is at the same distance from the moderator as the person who delivers paper 3. 8) D is seated 5 places from A, excluding I, while B and G are separated by 5 persons (including I). 1. Who speaks on Need of people awareness? 1.  F 3.  A

2.  G 4.  C

2. The speakers to the left of the moderator are 1.  D,G,A,B 3.  D,G,C,E

2.  H, A F, D 4.  E,G,A,B

2.  G 4.  A

1.  Bi. Party system 2.  Role of Political parties 3.  Role of press and electronic media 4.  cannot be determined Direction for questions 8 to 11:  Read the passage given below and solve the questions based on it. A big exhibition has been arranged in Pragati Maidan. There is a stream of visitors visiting it from 9 am to 8 pm. Following practice is observed while selling the tickets: i) Exhibition is arranged in 10 sections, named P, Q, R, S, T, U, V, W, X, Y. ii) To avoid crowding of people in a particular section visitors are expected to follow a particular sequence of sections. iii) The sequence of visit of sections is printed on the ticket. iv)  Every batch consists of 25 visitors

2.174 

  Verbal and Logical Reasoning

v) After every batch the sequence is changed. vi) The sequence of sections given on the tickets of 1st 3 batches is as follows: First batch: R S Q P U V X W Y T Second Batch: V R S Q P U T X W Y Third Batch: U R V S Q P Y T X W In fact, the sequence of actions follow a fixed logic and next bathes get the sequence of sections on the basis of this logic. 8. If every section takes 10 minutes, then batch seventh, which entered at 10 am, will be through last section at what time? 1.  11.20 3.  12.00

2.  11.40 4.  12.20

9. Which batch will have the sequence QPUVRSXWYT on their tickets? 1.  4th 3.  7th

2.  5th 4.  8th

10. Which batch will begin with section V and will visit section X at the end? 1.  5th 3.  7th

2.  6th 4.  8th

11. If a batch is to visit section S first and section Y at the end, which batch it would be? 1.  6th 3.  8th

2.  7th 4.  9th

1.  CGF 3.  DCG

2.  CEB 4.  None of those

16. Who reaches the office first? 1.  A 3.  C

2.  B 4.  D

Direction for questions 17 to 21: Read the passage given below and solve the questions based on it. A fortune teller has a unique way of predicting his customer prognosis. He has three parrots kept in 3 different cages. Each cage also has three cards with a single-digit, nonzero number inscribed on every card. No two cards have the same number and no cage contains two cards with numbers adding equal to ten. Further, the total of three cards in the first cage is greater by two than the second and by four than the third. When a customer orders for his prognosis, the fortune teller lets out the three parrots which randomly pick one card out of the respective cages. Before the prognosis is made, the fortune teller totals the digits on the three cards picked out and charges the customer, the same number of rupees as the total of the cards. On the first day of January a customer paid seven rupees for his prognosis. 17. What is the lowest payment possible? 1.  Rs 5 3.  Rs 6

2.  Rs 7 4.  Rs 8

18. What is the maximum possible that anyone can pay? 1.  Rs 22 3.  Rs 24

2.  Rs 23 4.  Rs 45

Direction for questions 12 to 16:  Read the passage given below and solve the questions based on it.

19. Which is the combination of 3 cards randomly chosen for a prognosis that is impossible?

Seven officers A, B, C, D, E, F and G reach office in a particular sequence, F reaches immediately before A and follows D, though not immediately. ‘C’ is the last one to reach office. ‘E’ comes immediately after ‘A’ and is subsequently followed by G.

1.  1, 2, 3 3.  7, 2, 3

12. Among the officers, who reaches the office third?

1.  Rs 19 3.  Rs 16

1.  Data inadequate 2.  A 3.  F 4.  B 13. Who reaches the office between C and E? 1.  E 3.  G

2.  F 4.  D

14. Who ranks fifth in the sequence of reaching the office? 1.  G 3.  F

20. Which of the following payments can never be made by the customer? 2.  Rs 17 4.  Rs 23

21. Which of the following payments is possible? 1.  Rs 8 3.  Rs 9

2.  Rs 13 4.  Rs 23

Direction for questions 22 to 24:  Read the passage given below and solve the questions based on it. Vaishali

2.  E 4.  Data inadequate

15. If after some scheduled time the management decides the officers will not be allowed to sign the attendance and A is not allowed to do so, then who are the other persons who will face the same treatment?

2.  5, 8, 9 4.  5, 7, 6

Avanti

 

Vidisha

Jyotishmati

Panchal

Practice Exercise 1  1.  300  3.  100

22. What is the free capacity in the Avanti–Vidisha pipeline:

1.  200 3.  700

ANSWER KEYS

The figure shows an oil Pipeline network among 5 cities. Each pipeline has the load carrying capacity of 1000 and each destination has a specific requirement that has to be met. The city of Vaishali and Jyotishmati have a requirement of 400 each. The requirement at Panchal is 700 where as that at Vidisha is 200. The load can be carried in the indicated directions only. It is further given that the load carried from Vaishali to Jyotishmati is 300.

  2.175

2.  200 4.  0

23. What is the free capacity in the Avanti – Vaishali pipeline: 1.  0 3.  200

2.  100 4.  300

24. What is the quantity moved from Avanti to Vidisha: 2.  800 4.  1000

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

3

3.

4

4.

2

5.

3

6. 11.

1 1

7. 12.

1 3

8. 13.

2 3

9. 14.

2 2

10. 15.

4 4

16. 21.

4 2

17. 22.

3 4

18. 23.

3 4

19. 24.

4 4

20.

4

HINTS AND EXPLANATIONS Solutions 1 to 7:

6th Batch: SQPUVR

TXWY

Following is the arrangement:

7th Batch: RSQPUV

YTXW

8th batch: VRSQPU

WYTX

Name

D

G

C

E

Moderator (I) H

A

B

F

Paper

 

 

3

 

 

1

2

 

5

Assume Moderator is facing Northward (North as in a map).

8. Time taken for 10 sections = 10×10 min = 100 min = 1 hr 40 min. So, if entrance time = 10 am, exit time

1. 5; Obviously, C speaks on topic 3.

= 10 + 1 hr 40 min = 11.40 am

2. 3;

9. 2;

3. 5;

10. 4;

4. 2;

11. 1;

5. 3;

Solutions 12 to 16:

6. 1;

FA …. (i)

7. 1;

D? F where ? = at least one person .… (ii) C is the last … (iii)

Solutions 8 to 11: 1st batch : RSQPUV

XWYT

2nd batch: VRSQPU

TXWY

3rd batch: UVRSQP

YTXW

Clearly, there are two groups: RSQPUV and XWYT. In each step each of these groups follows a cyclical order. The last letter becomes the first in the subsequent step while the remaining letters shift right ward. Thus RSQPUV in 1st batch becomes VRSQPU in the second and UVRSQP in the third. Similarly, XWYT in the first batch becomes TXWY in the 2nd and YTXW in the 3rd. Following this logic, the subsequent batches are:

AEG …. (iv) C  ombining (i) and (iv), we get FAEG. Because of (iii), in (ii) the (?) can be replaced only by B. So DBF. Together with FAEG, it becomes DBFAEG and C must come at the end. Hence the sequence is DBFAEGC. 12. 3; 13. 3; 14. 2; 15. 5; E, G and C Solutions 17 to 21:

4th Batch: PUVRSQ

WYTX

Following are cards in different cages:

5th Batch: QPUVRS

XWYT

(2, 9, 6),  (4, 8, 3),  (1, 5, 7)

2.176 

  Verbal and Logical Reasoning

Solutions 22 to 24:

flow from Vidisha. Again the demand at Panchal is 700, and it is also to be met by flow from Jyotishmati which can get it from Vidisha.

22. Total free capacity at Avanti-Vaishali pipeline is 300. Capacity of each pipeline is 1000 and demand at Vidisha is 400 and 300 flows to Jyotishamti. So, free capacity = {1000 – (400 + 300)}= 300

So, the quantity flowed from Avanti to vidisha = 200 + 100 + 700 = 1000

23. It can be very easily seen now that free capacity in Avanti-Vidisha is zero.

Exercise 1

24. It can be observed that flow from Vaishali to Jyotishmati is 300 where as demand is 400 so the deficient 100 would be met by

Attempts

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Wrong Marks

% Accuracy

PRACTICE EXERCISE  2 Direction for questions 1 to 6:  Go through the passage given below and solve the questions based on it.

1.  R 3.  Q

During a period of seven consecutive days, numbered from 1 to 7, seven movies—Lahoo ke do rang (L), Mard (M), Nagina (N), Omkara (O), Parineeta (P), Qurbaani (Q) and Rang de basanti (R) will be showed at the film festival. Exactly one movie will be showed on each day. The movies must be showed in accordance with the following conditions:

Direction for questions 7 to 9:  Read the passage given below and solve the questions based on it.

M is showed on either day 2 or day 4. P is not showed on day 3 or on day 5. If N is showed on day 1, then Q is showed on day 2. If R is showed on day3, then P is showed on day 4. L is showed the day after Q is showed. 1. Which of the following could be the order, in which the films are showed from day 1 through day 7? 1.  N, Q, R, P, M, L, O 2.  N, Q, L, M, P, O, R 3.  Q, L, M, P, O, N, R 4.  P, Q, L, M, N, O, R 2. If N is showed on day 1, which one of the following movies could be showed on day 5? 1.  L 3.  P

2.  M 4.  R

3. If R is showed on day 4, and N is showed some time after Q is showed, which of the following must be true? 1.  Q is showed on day 1. 2.  Q is showed on day 6. 3.  L is showed on day 7. 4.  O is showed on day 3. 4. If Q is showed on day 1, which of the following is a complete list of movies, any one of which could be viewed on day 3? 1.  N 3.  N, O

2.  O 4.  R

5. If Q is showed on the day after R is showed, and if M is showed on the day after P is showed, then R could be showed on 1.  day 1 3.  day 3

2.  day 2 4.  day 5

6. If L and P are showed before the day on which M is showed, then which movie is showed on day 2?

2.  N 4.  O

Ten coins are distributed among four people P, Q, R and S such that one of them gets one coin, another gets two coins, the third gets three coins and the fourth gets four coins. It is known that Q gets more coins than P, and S gets fewer coins than R. 7. If the number of coins distributed to Q is twice the number distributed to P, then which one of the following is necessarily true? 1.  R gets an even number of coins 2.  R gets an odd number of coins. 3.  S gets an even number of coins. 4.  S gets an odd number of coins. 8. If R gets at least two more coins than S, then which one of the following is necessarily true? 1.  Q gets at least two more coins. 2.  Q gets more coins than S. 3.  P gets more coins than S 4.  P & Q together get at least five coins. 9. If Q gets fewer coins than R, Then which one of the following not necessarily true? 1.  P & Q Together get at least four coins 2.  Q and S together get at least four coins. 3.  R and S together get at least five coins. 4.  P and R together get at least five coins. Direction for questions 10 to 13:  Read the passage given below and solve the questions based on it. There are three projects—P1, P2 and P3. A student can select either one project or two projects or all the three projects subject to the conditions given below: Condition 1: Both P1 and P2 have to be selected. Condition 2: Either P1 or P3, but not both, has to be selected. Condition 3: P2 can be selected only if P3 has been selected. Condition 4: P1 is selected only if P3 is selected. 10. How many selections can be made meeting both the conditions 1 and 2 as given above? 1.  0 3.  2

2.  1 4.  0 or 1

2.178 

  Verbal and Logical Reasoning

11. How many selections can be made meeting both the conditions 2 and 3 as given above? 1.  0 3.  2

2.  1 4.  None of these

12. How many selections can be made meeting the conditions 1, 2 and 3 as given above? 1.  0

2.  1

3.  2

4.  3

13. How many selection can be made if no condition is imposed? 1.  6 3.  8

2.  7 4.  10

Direction for questions 14 to 19:  Go through the data set given below and solve the questions based on it. Seven film buffs G, I, L, M, R, V, and Y-attend a showing of classic films. Three films are shown: one each directed by Guru Dutt, Satyajit Ray, and Ritwik Ghatak. Each of the film buffs sees exactly one of the three films. The films are shown only once, one film at a time. The following restrictions apply: Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film. G and R do not see the same film as each other. I and M do not see the same film as each other. V and Y see the same film as each other. L sees the Satyajit Ray film. G sees either the Guru Dutt film or the Ritwik Ghatak film. 14. If exactly one film buff sees the Ritwik Ghatak film, then which one of the following must be true?

1.  G: the Satyajit Ray film; I: the Ritwik Ghatak film; M: the Satyajit Ray film 2.  G: the Ritwik Ghatak film;I: the Guru Dutt film; V: the Guru Dutt film 3.  I: the Satyajit Ray film; R: the Ritwik Ghatak film; V: the Guru Dutt film 4.  M: the Satyajit Ray film; R: the Satyajit Ray film; Y: the Satyajit Ray film 18. If V and G see the same film, then which one of the following could be true? 1.  G sees the Guru Dutt film. 2.  I sees the Satyajit Ray film. 3.  R sees the Ritwik Ghatak film. 4.  V sees the Satyajit Ray film. 19. Each of the following could be a complete and accurate list of the film buffs who see the Guru Dutt film EXCEPT 1.  G, I 3.  I, R

2.  G, M 4.  V, Y

Direction for questions 20 to 21:  Read the passage below and solve the questions based on it. In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

1.  V sees the Satyajit Ray film. 2.  G sees the Guru Dutt film. 3.  M sees the Guru Dutt film. 4.  I sees the Guru Dutt film.

20. If group B contains 23 questions, then how many questions are there in group C?

15. Each of the following must be false EXCEPT

21. If group C contains 8 questions and group B carries at least 20% of the total marks, which of the following best describes the number of questions in group B?

1.  R is the only film buff to see the Guru Dutt film. 2.  R is the only film buff to see the Satyajit Ray film 3.  Y is the only film buff to see the Ritwik Ghatak film. 4.  Exactly two film buffs see the Ritwik Ghatak film. 16. Which one of the following could be a complete and accurate list of the film buffs who do not see the Satyajit Ray film? 1.  G, M 3.  G, I, R

2.  G, R 4.  G, M, Y

17. Which one of the following could be an accurate matching of film buffs to films?

1.  1 3.  3

1.  11 or 12 3.  13 or 14

2.  2 4.  Cannot be determined

2.  12 or 13 4.  14 or 15

22. Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is 1.  4 3.  2

2.  5 4.  3

ANSWER KEYS

Practice Exercise 2  Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

Q.

Ans.

1.

4

2.

4

3.

4

4.

3

5.

4

6. 11.

3 4

7. 12.

4 1

8. 13.

2 2

9. 14.

1 1

10. 15.

2 1

16. 21.

3 3

17. 22.

4 4

18.

2

19.

4

20.

1

  2.179

HINTS AND EXPLANATIONS 7. It is given that Q > P and R > S.

V and Y along with L must see the Satyajit Ray film. Hence option (4) is eliminated.

Q P R S 4 2 3 1 2 1 43 The distribution of coins can be of two types in both the cases, S gets an odd number. Hence option 4 is the answer. 8. Option 2 is the answer as it is one of the conditions mentioned in the question itself. 9. R   S   Q  

P

4  

2  

3  

1

4  

1  

3  

2

4  

3  

2  

1

Looking at the possible distribution of coins, we find that option1 is not always true. 12. Conditions are contradictory, hence no selection is possible. 13. Any project can meet two outcomes:- Selection or rejection. Hence total possible outcomes = 2 × 2 × 2 = 8 However he doesn’t have the option of choosing no projects. Hence total feasible number of projects = 8–1 = 7

17. G sees either the Guru Dutt film or the Ritwik Ghatak film. Hence option (1) is eliminated. If V sees the Guru Dutt film, Y also must see the Guru Dutt film. So along with I, three film buffs see the Guru Dutt film which is not possible. Hence option (2) is eliminated. If R sees the Ritwik Ghatak film, G must see the Guru Dutt film. So again G, V and Y see the Guru Dutt film. Hence option (3) is eliminated. Three film buffs can’t see the Ritwik Ghatak film. So, option (4) is the answer. 18. If V and G see the same film, they must see the Ritwik Ghatak film. Hence options (1) and (4) are eliminated. V and Y see the same film. G and R do not see the same film. Hence option (3) is eliminated. Hence option (2) is the answer. 19. lf V and Y see the Guru Dutt film, then exactly four film buffs see the Satyajit Ray film. Now G does not see the Satyajit Ray film. It means remaining four must see the Satyajit Ray film. But I and M do not see the same film. Hence Y and V can’t see the Guru Dutt film. Exercise 2

Attempts

Right

Wrong Marks

% Accuracy

Alternatively, we can do manual counting of the projects. Single projects – P1, P2, P3 Dual Projects – P1+P2, P2+P3, P1+P3 Triple projects – P1+P2+P3

Solutions 20 to 22: 20.

Hence total feasible number of projects = 7 14. If exactly one film buff sees the Ritwik Ghatak film, then four film buffs see the Satyajit Ray film and two film buffs see the Guru Dutt film. Now G can’t see the Satyajit Ray film and out of I and M only one can see the Satyajit Ray film. So V and Y must see the Satyajit Ray film.

A

B

C

Marks/Qn.

1

2

3

Option 1

76

23

1

Total

76

46

3

Total marks = 125.

15. Exactly twice as many of the film buffs see the Satyajit Ray film as see the Guru Dutt film. Hence options (2), (4) and (5) are eliminated. V and Y see the same film as each other. Hence option (3) is eliminated.

It can be seen that marks from A type Qns. is 60%.

16. Exactly four film buffs see the Satyajit Ray film and three don’t see the Satyajit Ray film. Hence options (1) and (2) are eliminated. Now,

Only for option (3), group B carries 20% of total marks and group A carries 60% of total marks.

It is not possible for other options. 21. Use options.

section test

1

Verbal and Logical Reasoning Direction for questions 1 to 3:  Read the information given below and solve the questions based on it. FnP is selling bouquets of roses of six different colours orange, pink, red, violet, white, and black. Bouquets are sold one at a time as per the following conditions: • The pink bouquet is the first, third, or fifth bouquet sold. • At least two bouquets are sold after the white bouquet is sold but before the violet bouquet is sold. • Exactly one bouquet is sold after the orange bouquet is sold but before the black bouquet is sold. 1. Which of following could be a correct order of bouquets sold (first to last)? 1.  orange, white, black, violet, pink, red 2.  pink, white, red, violet, orange, black 3.  black, white, orange, pink, red, violet 4.  red, white, pink, orange, violet, black 2. FnP sells the red bouquet fifth. Which one of the following must be true? 1.  The violet bouquet is sold sixth. 2.  The pink bouquet is sold third. 3.  The black bouquet is sold second. 4.  The orange bouquet is sold first.

3. If the black bouquet is sold immediately after the white bouquet, which one of the following could be the second bouquet sold? 1.  red

2.  pink

3.  orange

4.  violet

Direction for questions 4 to 8: Read the statements given below and solve the questions. 4. Certain messenger molecules fight damages to the lungs from noxious air by telling the muscle cells encircling the lungs airways to contract. This partially seals off the lungs. An asthma attack occurs when the messenger molecules are activated unnecessarily, in response to harmless things like pollen or household dust. Which of the following, if true, points to the most serious flaw in the plan to develop a medication that would prevent asthma attack by blocking receipt of any messages sent by the messenger molecules referred to above? 1.  Researchers do not yet know how the body produces the messenger molecules that trigger asthma attacks. 2.  Researchers do not yet know what makes one person’s messenger molecules more easily activated than another’s.

Section Test 1  3.  Such a medication would not become available for several years, because of long lead times in both development and manufacture. 4.  Such a medication would be unable to distinguish between messages triggered by pollen and household dust and messages triggered by noxious air. 5. In an attempt to promote the widespread use of paper rather than plastic and thus reduce non-biodegradable waste, the council of a small town plans to ban the sale of disposable plastic goods for which substitutes made of paper exist. The council argues that since most paper is entirely biodegradable, paper goods are environmentally preferable. Which of the following, if true, indicates that the plan to ban the sale of disposable plastic goods is ill suited to the town council’s environmental goals? 1.  Although biodegradable plastic goods are now available, members of the town council believe biodegradable paper goods to be safer for the environment. 2.  The paper factory at which most of the towns people are employed plans to increase production of biodegradable paper goods. 3.  After other towns enacted similar bans on the sale of plastic goods, the environmental benefits were not discernible for several years. 4.  Since most townspeople prefer plastic goods to paper goods in many instances, they are likely to purchase them in neighboring towns where plastic goods are available for sale.

  2.181

7. United States hospitals have traditionally relied primarily on revenues from paying patients to offset losses from unreimbursed care. Almost all paying patients now rely on governmental or private health insurance to pay hospital bills. Recently, insurers have been strictly limiting what they pay hospitals for the care of insured patients to amounts at or below actual costs. Which of the following conclusions is best supported by the information above? 1.  Although the advance of technology has made expensive medical procedures available to the wealthy, such procedures are out of the reach of low-income patients. 2.  If hospitals do not find ways of raising additional income for unreimbursed care, they must either deny some of that care or suffer losses if they give it. 3.  Some patients have incomes too high for eligibility for governmental health insurance but are unable to afford private insurance for hospital care. 4.  If the hospitals reduce their costs in providing care, insurance companies will maintain the current level of reimbursement, thereby providing more funds for unreimbursed care. 8. Match the several meanings of the word COMPLEX with their appropriate usages. Meaning

Usage

6. Crops can be traded on the futures market before they are harvested. If a poor corn harvest is predicted, prices of corn futures rise; if a bountiful corn harvest is predicted, prices of corn futures fall. This morning meteorologists are predicting much-needed rain for the corn-growing region starting tomorrow. Therefore, since adequate moisture is essential for the current crop’s survival, prices of corn futures will fall sharply today.

5. A new sports complex is coming up for the Common Wealth Games. 2.  abnormal state of mind 6. Culture is a complex whole of many things. 3.  group of structures 7. She has a complex about being overweight. 4.  mixture 8. His motives in carrying out the crime were complex.

Which of the following, if true, most weakness the argument above?

1.  1-6, 2-8, 3-7, 4-5 2.  1-8, 2-7, 3-5, 4-6 3.  1-5, 2-7, 3-6, 4-8 4.  1-8, 2-5, 3-6, 4-7

1.  Corn that does not receive adequate moisture during its critical pollination stage will not produce a bountiful harvest. 2.  Futures prices for corn have been fluctuating more dramatically this season than last season. 3.  The rain that meteorologists predicted for tomorrow is expected to extend well beyond the corngrowing region. 4.  Agriculture experts announced today that a disease that has devastated some of the corn crop will spread widely before the end of the growing season.

1.  complicated

Direction for questions 9 to 10:  Choose the option that fills the maximum number of blanks. The word may need some change of form. 9. A.  A _______of experts is going to study the case. B.  The torch failed to work as it ran out of _____ C.  They refused to eat eggs laid by _______hens D.  The shore _______opened fire. 1.  battery 2.  group 4.  artillery 3.  power

2.182 

  Verbal and Logical Reasoning

10. A.  We sailed into a beautiful and secluded _____ B.  A frightened animal at _____can turn violent. C.  Exercise can help keep fat at_______ D. Mom added some___leaves to the Rasam to improve its flavor. 2.  bay 1.  rest 4.  shore 3.  edge Direction for questions 11 to 13:  Read the information given below and answer the questions that follow: During the last film festival exactly six movies are to be shown. Following are the six movies – Last Lear, Mohini, NewYork, Omkara, Parineeta, and Qaidi – in no particular order. Further, following observations have been made regarding the films to be screened: Remark 1 – Parineeta is the third movie is to be shown. Remark 2 – Mohini is the sixth movie to be shown. Remark 3 – Movie Qaidi is the movie shown immediately after Omkara. Remark 4 – NewYork is the movie shown immediately before Last Lear. 11. If New York is the fourth movie to be shown, which among the following must be the movie to be shown immediately before the movie Parineeta? 1.  NEW YORK 3.  Omkara

2.  Qaidi 4.  Mohini

12. If Last Lear is the second movie to be shown, which among the following must be the movie shown immediately before Mohini? 1.  NEW YORK 3.  Omkara

2.  Qaidi 4.  Parineeta

13. A visitor watches Omkara, then skips the immediate next movie shown, and watches next movie shown Parineeta. Which of the following must be true? 1.  Omkara is1st movie shown 2.  Parineeta is 4th movie shown. 3.  NewYork is 5th movie shown. 4.  Last Lear is 6th movie shown. Direction for questions 14 to 17:  Read the following passage and answer within its context. Nearly two thousand years have passed since a census decreed by Caesar Augustus became part of the greatest story ever told. Many things have changed in the intervening years. The hotel industry worries more about overbuilding than overcrowding, and if they had to meet an unexpected influx, few inns would have managed to accommodate the weary guests. Now it is the census taker that does the travelling in the fond hope that a highly mobile population

will stay put long enough to get a good sampling. Methods of gathering, recording and evaluating information have presumably been improved a great deal. And where then it was the modest purpose of Rome to obtain a simple head count as an adequate basis for levying taxes, now batteries of complicated statistical series furnished by governmental agencies and private organizations are eagerly scanned and interpreted by sages and seers to get a clue for future events. The Bible does not tell us how the Roman census takers made out, and as regards our more immediate concern, the reliability of present-day economic forecasting, there are considerable differences of opinion. They were aired at the celebration of the 125th anniversary of the American Statistical Association. There was the thought that business forecasting might well be on its way from an art to a science, and some speakers talked about newfangled computers and high-faulting mathematical systems in terms of excitement and endearment, which we, at least in our younger years when these things mattered, would have associated more readily with the description of a fair maiden. But others pointed to a deplorable record of highly esteemed forecasts and forecasters with a batting average below that of the Mets and the President-elect of the Association cautioned that―high-powered statistical methods are usually in order where the facts are crude and inadequate, statisticians assume. We left his birthday party somewhere between hope and despair and with the conviction, not really newly acquired, that proper statistical methods applied to ascertainable facts have their merits in economic forecasting as long as neither forecaster nor public is deluded into mistaking the delineation of probabilities and trends for a prediction of certainties of mathematical exactitude. 14. According to the passage, taxation in Roman times were based on 1.  mobility 3.  population

2.  wealth 4.  census takers

15. The author refers to the Mets primarily in order to 1.  show that sports do not depend on statistics 2.  contrast verifiable and unverifiable methods of record keeping 3.  indicate the changes in attitudes from Roman days to the present 4.  illustrate the failure of statistical predictions. 16. The author’s tone can best be described as 1.  jocular 3.  pessimistic

2.  scornful 4.  humanistic

17. Disinterested is closest in meaning to 1.  bored 3.  not interested

2.  unbiased 4.  indifferent

Section Test 1 

  2.183

Direction for questions 18 to 20:  Go through the passages given and solve the questions based on it.

4.  It is mandatory to test the drug on guinea pigs before launching in the market.

After becoming the global IT and ITES hub, India is poised to be the global Petri dish. Major Pharma companies are outsourcing clinical trials to the country in a big way. With pharma majors facing increased pressure on profit margins, spiraling R&D costs and increasing overheads, outsourcing of clinical research processes to third parties in developing countries seems a viable option. Pharma companies are now looking to test drugs in a wider population to see if side-effects accrue as a result of difference in genetic or race profiles. With drug regulatory authorities amending rules on clinical research in India, MNC pharma companies are making a beeline for India. However, there are enough studies and reports to prove that Indians are being used as guinea pigs. The monthly index of medical specialties (MIMS) notes in an editorial how developing countries with poor and illiterate patients, lax laws, obliging bureaucrats and fund-starved hospitals have become hunting grounds for foreign pharma majors to test new drugs. Legally speaking, all clinical studies require the drugs controller-general of India’s (DCGI) permission and also approval of the hospital’s ethics committee before they can be administered to volunteers. The patient should also be explained the whole process and an informed consent should be taken in writing. The Indian council of medical research has also laid down ethical guidelines for clinical trials. But therein lies the problem. In case the trial goes wrong, the patient is not left with a legal remedy. They law is also silent on compensation to be provided to the victim in case the trial goes awry. Interestingly, in the developed world, strong consumerism and insurance hassles are preventing patients from signing up for clinical trials.

20. Why is conducting clinical trials in developed world difficult?

18. Why is India a viable option for outsourcing clinical research processes? 1.  India is a developing country. 2.  The population of India is increasing manifold. 3.  India’s success as major IT and ITes hub increasing its chances of growth in this sector too. 4.  Clinical research processes involves high costs and outsourcing to India proves cheaper to the pharma companies. 19. What allows Indians to be used as guinea pigs? 1.  It is a matter of pride to be useful in research process. 2.  Lack of stringent laws makes it easy to use patients as objects of assessment. 3.  Clinical research being an upcoming market in India has increased the need for guinea pigs.

1.  As the population in developed world is less, it is difficult to find patient for clinical trials. 2.  Lax consumerism policies make it difficult to conduct clinical trials in developed countries. 3.  Clinical trials are increasingly conducted in developing countries and hence decreasing in developed world. 4.  Patients are more vigilant in developed countries and therefore reluctant to undergo clinical trials. Direction for questions 21 to 22:  Go through the passages given and solve the questions based on it. There are two major systems of criminal procedure in the modern world-the adversarial and the inquisitorial. The former is associated with common law tradition and the latter with civil law tradition. Both systems were historically preceded by the system of private vengeance in which the victim of a crime fashioned his own remedy and administered it privately, either personally or through an agent. The vengeance system was a system of self-help, the essence of which was captured in the slogan “an eye for an eye, a tooth for a tooth.” The modern adversarial system is only one historical step removed from the private vengeance system and still retains some of its characteristic features. Thus, for example, even though the right to institute criminal action has now been extended to all members of society and even though the police department has taken over the pre-trail investigative functions on be\half of the prosecution, the adversarial system still leaves the defendant to conduct his own pre-trail investigation. The trial is still viewed as a duel between two adversaries, refereed by a judge who, at the beginning of the trial has no knowledge of the investigative background of the case. In the final analysis the adversarial system of criminal procedure symbolizes and regularizes the punitive combat. By contrast, the inquisitorial system begins historically where the adversarial system stopped its development. It is two historical steps removed from the system of private vengeance. Therefore, from the standpoint of legal anthropology, it is historically superior to the adversarial system. Under the inquisitorial system the public investigator has the duty to investigate not just on behalf of the prosecutor but also on behalf of the defendant. Additionally, the public prosecutor has the duty to present to the court not only evidence that may lead to the conviction of the defendant but also evidence that may lead to his exoneration. This system mandates that both parties permit full pre-trial discovery of the evidence in their possession. Finally, in an effort to make the trial less like a duel between two adversaries, the

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inquisitorial system mandates that the judge take an active part in the conduct of the trial, with a role that is both directive and protective. Fact-finding is at the heart of the inquisitorial system. This system operates on the philosophical premise that in a criminal case the crucial factor is not the legal rule but the facts of the case and that the goal of the entire procedure is to experimentally recreate for the court the commission of the alleged crime. 21. The primary purpose of the passage is to 1.  Explain why the inquisitorial system is the best system of criminal justice. 2.  Explain how the adversarial and the inquisitorial systems of criminal justice both evolved from the system of private vengeance. 3.  Show how the adversarial and inquisitorial systems of criminal justice can both complement and hinder each other’s development. 4.  Analyse two systems of criminal justice and deduce which one is better. 22. According to the passage, the inquisitorial system differs from the adversarial system in that 1.  It does not make the defendant solely responsible for gathering evidence for his case. 2.  It does not require the police department to work on behalf of the prosecution. 3.  It does not allow the victim the satisfaction of private vengeance. 4.  It requires the prosecution to drop a weak case. Direction for questions 23 to 26:  Sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the given OPTIONS to construct a coherent paragraph. 23. P. Besides, on slimming alone, an annual expenditure of $10 to 15 billion a year has been estimated Q. All are potential buyers of designer hand bonds, nylon running shoes, polypropylene underwear pedometer for logging the mileage, special wrist bands to hold house keys, digital stop-watches for monitoring heart rate, reflecting gear for nightjogging etc. R. England or other European countries are no exception to their trend. S. It has been estimated that the turnover of the sporting industry here is about $20 billion a year. 1.  SRPQ 3.  SPQR

2.  QSPR 4.  SPRQ

24. P. Most notably excluded from any such consideration is the labour of the housewife. Q. Unfortunately, this recognition has not spread to all fields of labour. R. The question, therefore, of a weekly off for her has not crossed many minds. S. Why, the work the housewife does within the confines of her home rearing children, cooking , washing, cleaning and doing other daily chores is not even thought of as work. 1.  PQRS 3.  QPRS

2.  QPSR 4.  PSQR

25. P. He said “Most of my friends who have spoken on this amendment have quite forgotten that upto 1935 the North-West Frontier Province (NWFP) was not subject to the Shariat law. Q. Characteristically, Ambedkar went to the heart of the matter and made important observations. R. He pointed out that the Muslim Personal law was not immutable and uniform throughout India, contrary to what had been claimed in the amendment move by Muslim members. S. This is not all and until 1937 in the rest of India, in various part, such as the United Provinces, the Central Provinces and Bombay, the Muslims to a large extent were governed by the Hindu law in the matter of succession. 1.  PQSR 3.  QRSP

2.  QRPS 4.  PSRQ

26. P. But an unprecedented high rent may not be the meeting point of the prevailing demand and supply, says Pawan Sinha, a real estate watcher. Q. A new house-hunter’s illusions were dispelled on going to the “posh” localities, where her seemingly “sufficient” income could not get her more than a ramshackle “ barsati” for Rs 4500 a month. R. Some property consultants are of the view the rents howsoever high, have a rational basis – the ratio between demand and supply of property. S. Others do not share it, saying it is due to the unrealistically inflated and sometimes “unreachable” rentlevels by haughty landlords. 1.  PQSR 3.  QRPS

2.  QRSP 4.  QPRS

Direction for questions 27 to 30: Mark (1): If the question can be answered by using one of the statements alone, but cannot be answered by using other statement alone.

Section Test 1  Mark (2): If the question can be answered by using either statement alone.

charges less for purchasing a set of 8 chairs than for purchasing 8 chairs individually. How much does the Shop charge for purchasing a set of 8 chairs?

Mark (3): If the question can be answered by using both statements together, but cannot be answered by using either statement alone.

Statement A: Buying a set of 8 is 10% less than buying 8 individually Statement B : Buying a set of 8 is Rs 200 more than buying 7 individually

Mark (4): If the question cannot be answered even by using both the statements together.

29. If ax + b = 0, is x > 0?

27. There are 20 members in a club. Each member who speaks Hindi also speaks English, and 7 of members only speak Urdu. If no member speaks all 3 languages, how many of the members speak two of the three languages mentioned.

Statement A : a + b > 0 Statement B: a – b > 0 30. How long did it take to travel from Dehradun to Delhi – a distance of 400km by a car?

Statement A: 6 members speak only English

Statement A : The car travelled the first 200km in 2.5hrs Statement B: If the car’s average speed had been 20 km/h faster, it would have travelled the 400 km in 1 hour less time.

Statement B: 2 members do not speak any of the three languages 28. Furniturewallah.com, a premium online furniture shop, sells chairs individually or in sets of 8. The Shop

ANSWER KEYS

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HINTS AND EXPLANATIONS 4. The medication to be developed is intended to prevent asthma attacks by suppressing the natural action of certain molecules in the lungs. Option (d) asserts that this suppression would occur not only when the molecules action is superfluous, but also when it is necessary. This would be a serious flaw in the medication, so (d) is the best answer. Options (a) and (b) refer to a lack of knowledge about how the messenger molecules are produced or activated built not about how they act in the lungs. Option (c) describes how long the development might take, but does not rule out the possibility of success.

6. The argument predicting a drop in the price of corn futures relies on news suggesting a good-sized corn crop. This prediction is undermined if there is, at the same time, news suggesting a small crop. Option (d) presents such news and is therefore the best answer. Option background information describing a stage at which rains are essential and option (c) makes rain over the entire corn-growing area seem more certain. Both are fully compatible with the argument and do nothing to weaken it. Past price changes (option b) cannot affect the eventual size of this year’s corn crop, so it is not relevant to the argument.

5. Option (d) is true. Townspeople are likely to circumvent the local ban by purchasing disposable plastic goods in neighboring towns. The ban is thus likely to be largely ineffective. Option (d) is therefore the best answer. None of options (a), (b) or (c) indicates that the ban is ill chosen as a means of reaching the town council’s environmental goals.

7. The passage explains that the primary way hospitals have covered the cost of unreimbursed care in the past is no longer available to them. It follows that they have three options: finding a new way to cover that cost, reducing it by giving less unreimbursed care, or suffering a loss. This is essentially what option (B) concludes, so (B) is the best answer. The passage does not touch on kinds of medical

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procedures administered in hospitals (option A). The passage gives no hint of who the paying patients are who do not rely on insurance, so option (C) is unsupported. Concerning option (D), the passage actually suggests that it is false. 9. 1 ‘Battery’ fills the blanks in A, B and C (maximum number). In options (2), (3), (4), ‘group’ and ‘power’ fill no blanks , ‘artillery’ fills the blanks only in D all the three options are wrong. 10. 2 ‘Bay’ fills the blanks in A, C and D (maximum number). In options (1), (3), (4), ‘rest’ fills the blank in only B, ‘edge’ and ‘shore’ fill no blank thus they are wrong. 14. Ans.(b) The actual reason for the desperate need is that ‘hits’ help them overcome the uncertainties associated with how consumers will react to the movies. Thus, option (b) gives the reason. 15. Ans. (c). The statement aims at establishing that we are involved in a process of bookkeeping. Option (3) speaks of this. Hence only option (c) forms a sound basis. 16. Ans. (a). Contextually, option (a) is the appropriate answer.

17. Ans. (d). Option (d) is the appropriate answer, which is elaborated upon in the last paragraph. 18. The complete focus of the passage is on showing, through examples, that sports and intellectual activity are inextricably linked. Hence the viewpoint of the author can be deduced to be option (c). Other options are contradicted in various parts of the passage. 19. Option (b) is the obvious answer. The author is trying to show that mental activity is enhanced if people engage in simple physical activity. Option (a) is nowhere mentioned in the paragraph and option (d) is incorrect. 27. Answre 3. 28. Answer 3. 29. Answer 4. 30. Statement B alone is sufficient but statement A alone is not sufficient. Hence option (A) is the answer.

section test

2

Verbal and Logical Reasoning Direction for questions 1 to 4:  The underlined part of the statements could be corrected or expressed more appropriately using one of the four options that follow. 1. In the Netherlands, a larger percentage of the gross national product is spent on defence of their coasts from rising seas than is spent on military defence in the United States. 1.  In the Netherlands, a larger percentage of the gross national product is spent on defence of their coasts form rising seas than is spent on military defence in the United States. 2.  In the Netherlands they spend a larger percentage of their gross national product on defending their coasts from rising seas than the United States does on military defence 3.  The Netherlands spends a larger percentage of its gross national product defending its coasts from rising seas than the military defence spending of the United States 4.  The Netherlands spends a larger percentage of its gross national product on defending its coasts form rising seas than the United States does on military defence. 2. While some propose to combat widespread illegal copying of computer programs by attempting to change people’s attitudes toward pirating, others by suggesting

reducing software prices to decrease the incentive for pirating, and still others by calling for the prosecution of those who copy software illegally. 1.  by suggesting reducing software prices to decrease the incentive for pirating, and still others by calling 2.  suggest reducing software prices to decrease the incentive for pirating, and still others are calling 3.  by suggesting the reduction of software prices to decrease the incentive for pirating and still others call 4.  suggest the reduction of software prices for decreasing the incentive for pirating, and still others call 3. Proponents of artificial intelligence say they will be able to make computers that can understand English and other human languages recognize objects, and reason as an expert does-computers that will be used to diagnose equipment breakdowns, deciding whether to authorize a loan, or other purposes such as these. 1. as an expert does, which may be used for purposes such as diagnosing equipment breakdowns or deciding whether to authorize a loan 2. like an expert-computers that will be used for such purposes as diagnosing equipment breakdowns or deciding whether to authorize a loan 3. like an expert, the use of which would be for purposes like the diagnosis of equipment breakdowns,

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or the decision whether or not a loan should be authorized 4.  like an expert, to be used to diagnose equipment breakdowns, deciding whether to authorize a loan or not, or the like Direction for questions 4 and 5:  Which among the following set of words appropriately fits in the blank spaces in the sentence? 4. “India is an immensely ……………………….. country with many …………………….. pursuits, vastly conviction, widely …………………………….. customs and a ……………………….. feast of viewpoints”. 1. Diverse, distinct, disparate, divergent, veritable 2. divergent, disparate, distinct, veritable, diverse 3. distinct, disparate, diverse, divergent, veritable 4.  diverse, divergent, distinct, disparate, veritable 5. “Indian texts include ………………………religious expositions and ……………………… defence. They also contain lengthy and ………………………….. between defenders of religiosity on one side and advocates of general  ………………………….. on the other”. 1. elaborate, protracted, sustained, controversies, skepticism 2. protracted, sustained, controversies, skepticism, elaborate 3. elaborate, protracted, controversies, skepticism, sustained 4.  elaborate, sustained, protracted, skepticism, controversies Direction for questions 6 to 9: Go through the information given below and solve the questions based on it. In a club, combinations of five out of the eight songs P, Q, R, S, T, U, V and Ware to be played by a DJ on a daily basis. On anyone day, except for the first day of a month, only three of the songs must be the ones that were played on the previous day. The song combinations must also satisfy the following conditions: (i) If song “P” is to be played on a day, song “V” cannot be played. (ii) If song “Q” is to be played on a day, “T” must be one of the songs to be played after “Q”. (iii) If “R” is to be played on a day, “V” must be one of the songs to be played after “R”. (iv) The last song to be played on any day must be either “S” or “U”.

6. Which of the following could be the combination of songs to be played on the first day of a month? 1. P, R, V, S, U 3.  T, U, R, V, S

2.  Q, S, R, V, U 4.  U, Q, S, T, *

7. If the songs “R” and “*” are to be played on the first day, which of the following could be the other songs to be played on that day? 1. P, T, U 3. T, S, V

2. Q, S, V 4.  Q, T, V

8. Which of the following is TRUE of any day’s valid combination of songs? 1. “P” cannot be played at third place 2. “Q” cannot be played at third place 3. “T” cannot be played at third place 4.  None of these 9. If song “R” is played at third place in a sequence, which of the following cannot be the second song to be played in that sequence? 1. Q 3.  T

2. S 4.  U

Direction for questions 10 to 13:  Go through the information given below and solve the questions based on it. In a business school, four students Dinakaran, Sumit, Tarun and Amul exhibit a very strange mix of hobbies and subject interests. One of them studies Commerce and plays Golf and Lawn Tennis. Dinakaran and Sumit study Psychology. Dinakaran plays Billiards. Both the Psychology students play Chess. Tarun is a student of Physics. The Physics student plays Chess and Badminton. All the friends play two games each and study one subject each. One of the students also does Weight Training. 10. Who does not play Chess? 1. Dinakaran 3.  Tarun

2. Sumit 4.  Amul

11. Who studies Psychology and plays Billiards? 1. Dinakaran 3.  Tarun

2. Sumit 4.  Amul

12. How many games are played and subjects studied by all the four students? 1. 2, 1 3.  6, 3

2. 3, 2 4.  5, 4

13. Sanjay says, “I have as many sisters as brothers.” Sarita says, “Each of us sisters has only half as many sisters as brothers.” Assuming that Sanjay and Sarita are brother

Section Test 2  and sister, how many brothers and sisters are there in the family? 1. 6 brothers and 4 sisters 2.  4 brothers and 6 sisters 3.  3 brothers and 4 sisters 4.  4 brothers and 3 sisters Direction for questions 14 to 17:  Read the passage given below and solve the questions based on it. Another style which is only partially dependent on situational factors for its effectiveness is the PioneeringInnovative management. Like Likert, Khandwalla preferred to use the expression ‘management’ rather than ‘leadership’, though his theory could easily be taken for a theory of leadership styles of top executive. He accepted that the operative mode of the top management sets the tone for the lower levels. He therefore administered a questionnaire to the top level executives of 75 varied organizations. In addition to other variables, the responses disclosed a mode of functioning which he labeled as ‘PI Management’. PI Management is characterized by a strong emphasis on attributes such as (1) Adapting freely to changing circumstances without concern for past management practices or traditions; (2) Marketing new and novel products or services; (3) Acquiring the latest most sophisticated plant, machinery and equipment; (4) High return on investments even if they involve high risk; (5) High quality and high price orientation in marketing company’s established products or services; (6) Innovation and experimentation in every area of management; (7) Ability to come up with original solutions and novel ideas; (8) Being a pioneer within the industry in marketing technologically sophisticated products and services. Managements that score high on PI claim to pursue a business strategy of pioneering, novel, technologically sophisticated, high quality products and plants. They seem willing to take necessary risks attendant on this strategy. Since they seek to be pioneers, they cannot afford not to adapt or innovate. Indeed, they try to be aggressively adaptive and innovative, not merely technologically but also in various areas of management. Interestingly enough. The current levels of PI in organizations are more strongly influenced by strategic decisions taken in the past than the other way around. That is, the past PI has an insignificant effect on present norms, decisions and managerial functions. For example, the past policy of recruiting creative managers at junior levels deliberate efforts to inject pioneering and innovative practices regarding business strategies (with reference to diversification, integration, marketing), operating modes (e.g. autonomy, accountability, cooperation),m and personnel (e.g. reward and punishment, communication) were found to have significant effects on the current levels of PI; but past PI did not influence any of it. Similarly,

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past norms regarding excellence, expertise, dedication and the lower levels of dependency facilitated current PI levels, but not the other way around. In sum, PI management is an outcome rather than a cause of managerial policies and practices. Furthermore, PI management is more effective in an environment which offers opportunities than one which is highly controlled. Once PI management becomes operative, it improves overall performance, the organization’s growth, public image as well as adaptability to circumstances improve. It heightens the achievement and result orientation of top management and lowers authoritarian norms at middle management levels. In order to realize the organisation’s goals, the PI executives seek out a complex, turbulent but favorable environment. It is worth noting that past PI is negatively related to the maintenance of friendly relations with colleagues. PI ‘perhaps temporarily lowers friendship ties at senor management levels.’ Relationship orientation, particularly primary relationship, is probably not part of the PI package. Relationship is an offshoot of the ‘afflictive orientation which is a business typical of the traditional style of management. According to Khandwalla “a traditional top management wedded to the status quo, may breed a blabby kind of affinitive, even somewhat task-oriented, work ethic at the next level of management, but a politicized’, cliquish, conflict ridden, low work ethic, passivity prone culture at middle-junior management levels. Also, the tenure of senior managers tends to be long in conservative set-ups. This may breed a fairly strong, affinitive orientation among the old timers.” Khandwalla devised an essentially PI-like strategy for the turnaround management of sick enterprises. A few years later, Khandwalla added that it is the ‘humane’ rather than the ‘surgical turnaround strategy turnaround and PI styles should be considered as a whole and integrated model in which the relative relevance of each depends on the health of the organization. The sick ones need turnaround to be followed by PI management in order to make the organization even more vibrant and healthy. The underlying basic assumption in both of them is the centrality of the task system which must be built, restructured and managed rationally and scientifically. 14. According to the passage, managers who adopt PI management style 1. Avoid risks 2. Adopt sophisticated technology 3.  Do not adapt or innovate 4.  None of the above 15. Which of the following is NOT a correct statement? 1. Organization’s growth is regulated by PI Management Style 2. Organization’s image improves with PI Management Style

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3.  PI Management improves organisation’s adaptability 4.  PI Management improves the result orientation of organization 16. According to the passage 1. Effectiveness of ‘Pioneering – Innovative Management’ style is not dependent on situational factors 2. Situational factors have no influence on ‘Pioneering – Innovative Management’ style 3.  Effectiveness of ‘Pioneering – Innovative Management style is partially influenced by situational factors 4.  Situational factors totally control ‘Pioneering – Innovative Management style 17. Which of the following is a correct statement? 1. the present norms and managerial functions are influenced by ‘Pioneering – Innovativeness 2. ‘Pioneering – Innovativeness of the past has no significant influence on present norms and managerial functions 3.  The ‘Pioneering – Innovativeness of the past has very little impact on present norms and managerial functions 4.  None of the above Direction for questions 18 to 21:  Each question consists of a number of sentence which, when properly sequenced, form a coherent paragraph. Each sentence is labeled with a letter. Choose the most logical order of sentences from among the four choices options. 18. A.  The men jumped up and rushed to the river B.  They poured it on the glowing bed of charcoal C. The water gurgled out and the dying embers hissed and sent up little curls of vapour D. They quickly came back with pitchers laden with water. 1. DABC 3.  CBAD

2.  ADBC 4.  BADC

2 0. A. I also believe in the possibility as well as the desirability of applying science to problems arising in social science B. Believing as I do in social science, I can only look with apprehension upon social pseudo science C. I am a rationalist, which means that I believe in discussion and argument D. I may say why I have chosen this particular subject 1. CDAB 3.  BCAD

2.  DCAB 4.  DBAC

21. A. The investigation was confined to manufacturing firms in the area B. Those concerned with mining and quarrying, construction, transport, and trade and commerce, were excluded C. The number of workers employed by the firms in the area ranged from a dozen to approximately 35,000 D. A long search produced a com comprehensive list of 203 manufacturing firms. 1. ABDC 3.  DCBA

2.  BCDA 4.  CBDA

Direction for questions 22 to 25:  Each question consists of sentences each of which contains one or two idioms. Four possible meanings labeled options (1) through (4) are provided below each sentence. Choose the one which best expresses the meaning of the idiom. 22. I would like to see Ramu do his own work for a change instead of always back-seat driving. 1. driving a car form the back 2. being critical of work being done by others 3.  offering advice 4.  annoying

19. A. Failure to put the right person at the right place could prove expensive for the organization B.  All managers are decision makers C. The rightness of a decision largely depends upon whether or not the manager has utilized the right persons in right ways. D. the effectiveness of managers is largely reflected in their track record in taking the right decisions

1. he was crying 2.  discouraged the rest from having fun 3.  he wet the blanket 4.  he had covered himself with a wet blanket

1. DCBA 3.  ABCD

1. had a variety of jobs and experiences 2.  a career which helped him make lots of money

2.  BDCA 4.  BACD

23. He proved to be quite a wet blanket at the party for he spoke to no one and morosely sat by himself.

24. Debu had a chequered career since I first knew him as a clerk in the local bank.

Section Test 2 

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3.  a career where he signed a lot of cheques 4.  did odd jobs

All the following statements, if true, provide support to the claim made above, except.

25. Women should be paid the same as men when they do the same job, for surely, what is sauce for gander is sauce for the goose.

1.  Employee participation in the management boosts the confidence of the workers. 2.  Employee union ownership drives up the salaries & wages. 3.  Employee union ownership enables the workers to have a share in the profits. 4.  Employee ownership generally improves the performance of workers.

1. both goose and gander should be equally treated 2. what is thought suitable for a man should also be for a woman 3. goose and gander eat the same sauce 4.  the principle of equal treatment should be implemented

Direction for questions 28 to 30:  Go through the information given below and solve the questions based on it.

Direction for questions 26 to 27:  Read the statements given below and solve the questions.

Six products—Ariel, Vivel, Rin, Nirma, Gillette Gel and Pepsodent—are to be placed in six display windows’ of a shop numbered 1-6 from left to right of a shopper standing outside the shop. As per the company requirements, Rin and Ariel should be displayed next to each other, but Ariel should be at least three windows away from Nirma. Pepsodent is preferred to be kept between Gillette Gel and Rin but away from Vivel at least by two windows. Vivel cannot be displayed next to Rin for the reasons of mixed-product identity. Also Vivel cannot be displayed in window 1.

26. When fossil fuels like coal, oil and other substances are burnt, they produce carbon dioxide which is already present in the atmosphere. However, as the carbon dioxide level rises, it leads to the greenhouse effect. Already there is a lot of carbon dioxide which has caused an increase in the temperature, in order to stem this trend, growth in industrial production must be slowed down or methods of production without carbon dioxide emission must be found. Which of the following, if true, would tend to weaken the impact of the above conclusion?

28. Which of the following products is displayed immediate left of Ariel?

1. Most of the carbon dioxide responsible for the greenhouse effect comes from automobiles. 2. Many cold countries would benefit from a rise in temperature. 3. Carbon monoxide is more harmful than carbon dioxide. 4.  Industry is soon shifting to synthetic fuel extracted from waste.

1. Vivel 3. Rin

29. If the positions of Rin and Ariel are interchanged, which item will be displayed in window 5? 1. Ariel 3. Rin

2.  Nirma 4.  Vivel

30. Which of the following products except Rin will be displayed left of Ariel but right of Gillette Gel?

27. The latest step in the progression from management ownership to employee ownership is the movement to ownership by unions. Employee ownership can save depressed and sick units.

ANSWER KEYS

2.  Nirma 4.  Pepsodent

1. Vivel 3. Pepsodent

2.  Rin 4.  None of these

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PART

3

CAT PAPERS

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CAT 2002 Total Marks = 150 Section I – 50 Ques. Section II – 50 Ques. Section III – 50 Ques.

Time Given = 120 minutes CAT 2002 has a total of 150 questions distributed in three sections. Each section has 50 questions. There is negative marking.

  SECTION  I

1

Direction for questions 1 to 5:  For the word given at the top of each table match the dictionary definitions on the left (A, B, C, D) with their corresponding usage on the right (E, F, G, H). Out of the four possibilities given in the boxes below the table, select the one that has all the definitions and their usages correctly matched.

1.  Measure

Size or quantity found by measuring.

Usage E

A measure was instituted to prevent outsiders from entering the campus.

B

Vessel of standard capacity.

F

Sheila was asked to measure each item that was delivered.

C

Suitable action.

G

The measure of the cricket pitch was 22 yards.

D Ascertain extent or

quantity

H F E G

A B C D

3

G E F H

H

Ramesh used a measure to take out one litre of oil.

A B C D

4

G H E F

A B C D

F H E G

2.  Bound Dictionary definition

Usage

A Obliged,

E

B Limiting value

F

C Move in a speci-

G

D Destined or cer-

H

constrained

Dictionary definition A

A B C D

2

fied direction. tain to be

1

A B C D

Dinesh felt bound to walk out when the discussion turned to kickbacks. Buffeted by contradictory forces he was bound to lose his mind. Vidya’s story strains the bounds of credulity. Bound for a career in law, Jyoti was reluctant to study Milton.

2

F H G E

A B C D

3

E G H F

A B C D

4

E H F G

A B C D

F G E H

  CAT Papers

3.4 

3.  Catch

D Opportunity

Dictionary definition

Usage

A Capture

E

All her friends agreed that Prasad was a good catch.

B Grasp with senses

F

The proposal sounds very good but where is the catch.

C Deception

G

Hussain tries to catch the spirit of India in this painting.

D Thing or person

H

Sorry, I couldn’t catch you.

or mind

worth trapping

1

A B C D

2

H F E G

A B C D

3

F G E H

A B C D

4

G F E H

A B C D

G H F E

4.  Deal Dictionary definition

Usage E Dinesh insisted on dealing the

B Stock, sell

F This contract deals with hand-

C Give out to

G My brother deals in cards.

D Be concerned

H I decided not to deal with

cards.

made cards.

a number of people with

1

A B C D

A B C D

3

H G E F

A B C D

A B C D

3

G F E H

A B C D

4

G E F H

A B C D

G F H E

Direction for questions 6 to 10: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labell with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 6. A. Branded disposable diapers are available at many supermarkets and drug stores. B. If one supermarket sets a higher price for a diaper, customers may buy that brand elsewhere.

D. So, the demand for branded diapers at any particular store may be quite price sensitive. E. For instance, only SavOn Drugs stores sell SavOn Drugs diapers.

A B C D

2.  ABCEDF 4.  AEDBCF

7. A.  Having a strategy is a matter of discipline. H E G F

B. It involves the configuration of a tailored value chain that enables a company to offer unique value. C. It requires a strong focus on profitability and a willingness to make tough trade-offs in choosing what not to do. D.  Strategy goes far beyond the pursuit of best practices.

5.  Turn Dictionary definition

Usage

A Give new direc-

E

It was now his turn to be angry.

B Send

F

Leena never turned away a beggar.

C Change in form

G

Ashish asked Laxman to turn his face to the left.

tion to

H E F G

1.  ABCDEF 3.  ADBCEF 4

F H G E

A B C D

2

F. Then, stores should set a higher incremental margin percentage for private-label diapers.

handmade cards.

2

F E G H

1

been turned into a museum.

C. By contrast, the demand for private-label products may be less price sensitive since it is available only at a corresponding supermarket chain.

A Manage, attend

to

H The old school building has

coming successively for each person.

E. A company must stay the course even during times of upheaval, while constantly improving and extending its distinctive positioning. F. When a company’s activities fit together as a selfreinforcing system, any competitor wishing to imitate a strategy must replicate the whole system. 1.  ACEDBF 3.  DCBEFA

2.  ACBDEF 4.  ABCEDF

CAT 2002  8. A. As officials, their vision of a country shouldn’t run too far beyond that of the local people with whom they have to deal. B.  Ambassadors have to choose their words. C. To say what they feel they have to say, they appear to be denying or ignoring part of what they know. D. So, with ambassadors as with other expatriates in black Africa, there appears at a first meeting a kind of ambivalence. E. They do a specialized job and it is necessary for them to live ceremonial lives. 1.  BCEDA 3.  BEADC

2.  BEDAC 4.  BCDEA

9. A. “This face off will continue for several months given the strong convictions on either side,” says a senior functionary of the high-powered task force on drought. B. During the past week-and-half, the Central Government has sought to deny some of the earlier apprehensions over the impact of drought. C. The recent revival of the rains had led to the emergence of a line of divide between the two. D. The state governments, on the other hand, allege that the Centre is downplaying the crisis only to evade its full responsibility of financial assistance that is required to alleviate the damage. E. Shrill alarm about the economic impact of an inadequate monsoon had been sounded by the Centre as well as most of the states, in late July and early August. 1.  EBCDA 3.  BDCAE

2.  DBACE 4.  ECBDA

10. A. This fact was established in the 1970s by French survey expeditions to Equator near the Equator and Lapland in the Arctic, which found that around the middle of the earth the arc was about a kilometer shorter. B. One of the unsettled scientific questions in the late 18th century was the exact nature of the shape of the earth. C. The length of one-degree arc would be less near the equatorial latitudes than at the poles. D. One way of doing that is to determine the length of the arc along a chosen longitude or meridian at one-degree latitude separation. E. While it was generally known that the earth was not a sphere but an ‘oblate spheroid’, more curved at

  3.5

the equator and flatter at the poles, the question of ‘how much more’ was yet to be established. 1.  BECAD 3.  EDACB

2.  BEDCA 4.  EBDCA

Direction for questions 11 to 15: Fill the gaps in the passages below with the most appropriate word from the options given for each gap. The right words are the ones used by the author. Be guided by the author’s overall style and meaning when you choose the answers. Von Neumann and Morgenstern assume a decision framework in which all options are thoroughly considered, each option being independent of the others, with a numerical value derived for the utility of each possible outcome (these outcomes reflecting, in turn, all possible combinations of choices). The decision is then made to maximize the expected utility. (11)______, such a model reflects major simplifications of the way decisions are made in the real world. Humans are not able to process information as quickly and effectively as the model assumes; they tend not to think (12)________ as easily as the model calls for; they often deal with a particular option without really assessing its (13)________, and when they do assess alternatives, they may be extremely nebulous about their criteria of evaluation. 11. 1.  regrettably 3.  obviously

2.  firstly 4.  apparently

12. 1.  quantitatively 3.  scientifically

2.  systematically 4.  analytically

13. 1.  implications 3.  utility

2.  disadvantages 4.  alternatives

In a large company, (14)________ people is about as common as using a gun or a switch-blade to (15)________ an argument. As a result, most managers have little or no experience of firing people, and they find it emotionally traumatic; as a result, they often delay the act interminably, much as an unhappy spouse will prolong a bad marriage. And when the firing is done, it’s often done clumsily, with far worse side effects than are necessary. Do the world-class software organizations have a different way of firing people? No, but they do the deed swiftly, humanely, and professionally. The key point here is to view the fired employee as a “failed product” and to ask how the process (16) ________ such a phenomenon in the first place. 14. 1.  dismissing 3.  firing

2.  punishing 4.  admonishing

15. 1.  resolve 2.  thwart

3.  defeat

16. 1.  derived 2.  engineered 3.  produced 4.  allowed

4.  close

3.6 

  CAT Papers

Direction for questions 17 to 20: In each of the questions below, four different ways of writing a sentence are indicated. Choose the best way of writing the sentence. 17. A. The main problem with the notion of price discrimination is that it is not always a bad thing, but that it is the monopolist who has the power to decide who is charged what price. B. The main problem with the notion of price discrimination is not that it is always a bad thing, it is the monopolist who has the power to decide who is charged what price. C. The main problem with the notion of price discrimination is not that it is always a bad thing, but that it is the monopolist who has the power to decide who is charged what price. D. The main problem with the notion of price discrimination is not it is always a bad thing, but that it is the monopolist who has the power to decide who is charged what price. 1.  A 3.  C

2.  B 4.  D

18. A. A symbiotic relationship develops among the contractors, bureaucracy and the politicians, and by a large number of devices costs are artificially escalated and black money is generated by underhand deals. B. A symbiotic relationship develops among contractors, bureaucracy and politicians, and costs are artificially escalated with a large number of devices and black money is generated through underhand deals. C. A symbiotic relationship develops among contractors, bureaucracy and the politicians, and by a large number of devices costs are artificially escalated and black money is generated on underhand deals. D. A symbiotic relationship develops among the contractors, bureaucracy and politicians, and by large number of devices costs are artificially escalated and black money is generated by underhand deals. 1.  A 3.  C

2.  B 4.  D

19. A. The distinctive feature of tariffs and export subsidies is that they create difference of prices at which goods are traded on the world market and their price within a local market. B. The distinctive feature of tariffs and export subsidies is that they create a difference of prices at

which goods are traded with the world market and their prices in the local market. C. The distinctive feature of tariffs and export subsidies is that they create a difference between prices at which goods are traded on the world market and their prices within a local market. D. The distinctive feature of tariffs and export subsidies is that they create a difference across prices at which goods are traded with the world market and their prices within a local market. 1.  A 3.  C

2.  B 4.  D

20. A. Any action of government to reduce the systemic risk inherent in financial markets will also reduce the risks that private operators perceive and thereby encourage excessive hedging. B. Any action by government to reduce the systemic risk inherent in financial markets will also reduce the risks that private operators perceive and thereby encourage excessive gambling. C. Any action by government to reduce the systemic risk inherent due to financial markets will also reduce the risk that private operators perceive and thereby encourages excessive hedging. D. Any action of government to reduce the systemic risk inherent in financial markets will also reduce the risks that private operators perceive and thereby encourages excessive gambling. 1.  A 3.  C

2.  B 4.  D

Direction for questions 21 to 25: For each of the words below, a context is provided. From the alternatives given pick the word or phrase that is closest in meaning in the given context. 21. Opprobrium: The police officer appears oblivious to the opprobrium generated by his blatantly partisan conduct. 1.  Harsh criticism 2.  Acute distrust 3.  Bitter enmity

4.  Stark oppressiveness

22. Portend: It appears to many that the US “war on terrorism” portends trouble in the Gulf. 1.  Introduces 3.  Spells

2.  Evokes 4.  Bodes

23. Prevaricate: When a videotape of her meeting was played back to her and she was asked to explain her presence there, she started prevaricating.

CAT 2002 

1.  Speaking evasively 2.  Speaking violently 3.  Lying furiously 4.  Throwing a tantrum

24. Restive: The crowd became restive when the minister failed to appear even by 10 pm. 1.  Violent 3.  Restless

2.  Angry 4.  Distressed

25. Ostensible: Manohar’s ostensible job was to guard the building at night. 1.  Apparent 3.  Ostentatious

2.  Blatant 4.  Insidious

Direction for questions 26 to 50:  Each of the six passages given below is followed by questions. Choose the best answer for each question.

PASSAGE  1 The production of histories of India has become very frequent in recent years and may well call for some explanation. Why so many and why this one in particular? The reason is a twofold one: changes in the Indian scene requiring a re-interpretation of the facts and changes in attitudes of historians about the essential elements of Indian history. These two considerations are in addition to the normal fact of fresh information, whether in the form of archeological discoveries throwing fresh light on an obscure period or culture, or the revelations caused by the opening of archives or the release of private papers. The changes in the Indian scene are too obvious to need emphasis. Only two generations ago British rule seemed to most Indian as well as British observers likely to extend into an indefinite future; now there is a teenage generation which knows nothing of it. Changes in the attitudes of historians have occurred everywhere, changes in attitudes to the content of the subject as well as to particular countries, but in India there have been some special features. Prior to the British, Indian historiographers were mostly Muslims, who relied, as in the case of Sayyid Ghulam Hussain, on their own recollection of events and on information from friends and men of affairs. Only a few like Abu’l Fazl had access to official papers. These were personal narratives of events, varying in value with the nature of the writer. The early British writers were officials. In the eighteenth century they were concerned with some aspect of Company policy, or, like Robert Orme in his Military Transactions, gave a straight narrative in what was essentially a continuation of the Muslim tradition. In the early nineteenth century the writers were still, with two notable exceptions, officials, but they were now engaged in chronicling, in varying moods of zest, pride, and awe, the rise of the British power in India to supremacy. The two

  3.7

exceptions were James Mill, with his critical attitude to the Company and John Marchman, the Baptist missionary. But they, like the officials, were anglo-centric in their attitude, so that the history of modern India in their hands came to be the history of the rise of the British in India. The official school dominated the writing of Indian history until we get the first professional historian’s approach, Ramsay Muir and P.E. Roberts in England and H. H. Dodwell in India. Then Indian historians trained in the English school joined in, of whom the most distinguished was Sir Jadunath Sarkar and the other notable writers: Surendranath Sen, Dr Radhakumud Mukerji, and Professor Nilakanta Sastri. They, it may be said, restored India to Indian history, but their bias was mainly political. Finally have come the nationalists who range from those who can find nothing good or true in the British to sophisticated historical philosophers like K.M. Panikker. Along with types of historians with their varying bias have gone changes in the attitude to the content of Indian history. Here Indian historians have been influenced both by their local situation and by changes of thought elsewhere. It is in this field that this work can claim some attention since it seeks to break new ground, or perhaps to deepen a freshly turned furrow in the field of Indian history. The early official historians were content with the glamour and drama of political history from Plassey to the Mutiny, from Duplex to the Sikhs. But when the raj was settled down, glamour departed from politics, and they turned to the less glorious but more solid ground of administration. Not how India was conquered but how it was governed was the theme of this school of historians. It found its archpriest in H.H. Dodwell, its priestess in Dame Lilian Penson, and its chief shrine in the Volume VI of the Cambridge History of India. Meanwhile in Britain other currents were moving, which led historical study into the economic and social fields. R.C. Dutt entered the first of these currents with his Economic History of India to be followed more recently by the whole group of Indian economic historians. W.E. Moreland extended these studies to the Mughal Period. Social history is now being increasingly studied and there is also of course a school of nationalist historians who see moderm Indian history in terms of the rise and the fulfillment of the national movement. All these approaches have value, but all share in the quality of being compartmental. It is not enough to remove political history from its pedestal of being the only kind of history worth having if it is merely to put other types of history in its place. Too exclusive an attention to economic, social, or administrative history can be as sterile and misleading as too much concentration on politics. A whole subject needs a whole treatment for understanding. A historian must dissect his subject into its elements and then fuse them together again into an integrated whole. The true history of a country must contain all the features just cited but must present them as parts of a single consistent theme.

  CAT Papers

3.8 

26. Which of the following may be the closest in meaning to the statement “restored India to Indian history”?

1.  Indian historians began writing Indian history. 2.  Trained historians began writing Indian history. 3.  Writing India-centric Indian history began. 4.  Indian history began to be written in India.

27. Which of the following is the closest implication of the statement “to break new ground, or perhaps to deepen a freshly turned furrow”? 1.  Dig afresh or dig deeper. 2. Start a new stream of thought or help establish a recently emerged perspective. 3. Begin or conduct further work on existing archeological sites to unearth new evidence. 4.  Begin writing a history free of any biases. 28. Historians moved from writing political history to writing administrative history because:

1.  Attitudes of the historians changed. 2.  The raj was settled down. 3.  Politics did not retain its past glamour. 4.  Administrative history was based on solid ground.

29. According to the author, which of the following is not among the attitudes of Indian historians of Indian origin?

1.  Writing history as personal narratives. 2.  Writing history with political bias. 3.  Writing non-political history due to lack of glamour. 4.  Writing history by dissecting elements and integrating them again.

30. In the table given below, match the historians to the approaches taken by them: A

Administrative

E Robert Orme

B

Political

F

C

Narrative

G Radha Kumud Mukherji

D

Economic

H R. C. Dutt

1

H. H. Dodwell

2

3

4

A B C

F G E

A B C

G F E

A B C

E F G

A B C

F H E

D

H

D

H

D

H

D

G

PASSAGE  2 There are a seemingly endless variety of laws, restrictions, customs and traditions that affect the practice of abortion around the world. Globally, abortion is probably the single most controversial issue in the whole area of women’s rights

and family matters. It is an issue that inflames women’s right groups, religious institutions, and the self-proclaimed “guardians” of public morality. The growing worldwide belief is that the right to control one’s fertility is a basic human right. This has resulted in a worldwide trend towards liberalization of abortion laws. Forty per cent of the world’s population lives in countries where induced abortion is permitted on request. An additional 25 per cent live in countries where it is allowed if the women’ s life would be endangered if she went to full term with her pregnancy. The estimate is that between 26 and 31 million legal abortions were performed in 1987. However, there were also between 10 and 22 million illegal abortions performed in that year. Feminists have viewed the patriarchal control of women’s bodies as one of the prime issues facing the contemporary women’s movement. They observe that the definition and control of women’s reproductive freedom has always been the province of men. Patriarchal religion, as manifest in Islamic fundamentalism “traditionalist Hindu practice, orthodox Judaism, and Roman Catholicism, has been an important historical contributory factor for this and continues to be an important presence in contemporary societies. In recent times, governments, usually controlled by men, have “given” women the right to contraceptive use and abortion access when their countries were perceived to have an overpopulation problem. When these countries are perceived to be under populated, that right has been absent. Until the nineteenth century, a woman’s rights to an abortion followed English common law; it could only be legally challenged if there was a “quickening”, when the first movements of the foetus could be felt. In 1800, drugs to induce abortions were widely advertised in local newspapers. By 1900, abortion was banned in every state except to save the life of the mother. The change was strongly influenced by the medical profession, which focused its campaign ostensibly on health and safety issues for pregnant women and the sanctity of life. Its position was also a means of control of nonlicensed medical practitioners such as midwives and women healers who practiced abortion. The anti-abortion campaign was also influenced by political considerations. The large influx of eastern and southern European immigrants with their large families was seen as a threat to the population balance of the future United States. Middle and Upper class Protestants were advocates of abortion as a form of birth control. By supporting abortion prohibitions the hope was that these Americans would have more children and thus prevent the tide of immigrant babies from overwhelming the demographic characteristics of Protestant America. The anti-abortion legislative position remained in effect in the United States through the first sixty-five years of the twentieth century. In the early 1960s, even when it was widely known that the drug thalidomide taken during

CAT 2002  pregnancy to alleviate anxiety was shown to contribute to the formation of deformed “flipper-like” hands or legs of children, abortion was illegal in the United States. A second health tragedy was the severe outbreak of rubella during the same time period, which also resulted in major birth defects. These tragedies combined with a change of attitude towards a woman’s right to privacy lead a number of states to pass abortion-permitting legislation. On one side of the controversy are those who call themselves “pro-life”. They view the foetus as a human life rather than as an unformed complex of cells; therefore, they hold to the belief that abortion is essentially murder of an unborn child. These groups cite both legal and religious reasons for their opposition to abortion. Pro-lifers point to the rise in legalized abortion figures and see this as morally intolerable. On the other side of the issue are those who call themselves “pro-choice”. They believe that women, not legislators or judges, should have the right to decide whether and under what circumstances they will bear children. Pro-choicers are of the opinion that laws will not prevent women from having abortions and cite the horror stories of the past when many women died at the hands of “backroom” abortionists and in desperate attempts to selfabort. They also observe that legalized abortion is especially important for rape victims and incest victims who became pregnant. They stress physical and mental health reasons why women should not have unwanted children. To get a better understanding of the current abortion controversy, let us examine a very important work by Kristin Luker titled Abortion and the Politics of Motherhood. Luker argues that female pro-choice and pro-life activists hold different world views regarding gender, sex, and the meaning of parenthood. Moral positions on abortions are seen to be tied intimately to views on sexual behaviour, the care of children, family life, technology, and the importance of the individual. Luker identifies “pro-choice” women as educated, affluent, and liberal. Their contrasting counterparts, “pro-life” women, support traditional concepts of women as wives and mothers. It would be instructive to sketch out the differences in the world views of these two sets of women. Luker examines California, with its liberalized abortion law, as a case history. Public documents and newspaper accounts over a twenty-year period were analyzed and over 200 interviews were held with both pro-life and pro-choice activists. Luker found that pro-life and pro-choice activists have intrinsically different views with respect to gender. Prolife women have a notion of public and private life. The proper place for men is in the public sphere of work; for women, it is the private sphere of the home. Men benefit through the nurturance of women; women benefit through the protection of men. Children are seen to be the ultimate beneficiaries of this arrangement by having the mother as a full-time loving parent and by having clear role models.

  3.9

Pro-choice advocates reject the view of separate spheres. They object to the notion of the home being the “women’s sphere”. Women’s reproductive and family roles are seen as potential barriers to full equality. Motherhood is seen as a voluntary, not a mandatory or “natural” role. In summarizing her findings, Luker believes that women become activists in either of the two movements as the end result of lives that center around different conceptualizations of motherhood. Their beliefs and values are rooted to the concrete circumstances of their lives, their educations, incomes, occupations, and the different marital and family choices that they have made. They represent two different world views of women’s roles in contemporary society and as such the abortion issues represent the battleground for the justification of their respective views. 31. According to your understanding of the author’s arguments, which countries are more likely to allow abortion?

1.  India and China 2.  Australia and Mongolia 3.  Cannot be inferred from the passage 4.  Both (1) and (2)

32. Which amongst these was not a reason for banning of abortions by 1900? 1. Medical professionals stressing the health and safety of women. 2. Influx of eastern and southern European immigrants. 3.  Control of unlicensed medical practitioners. 4.  A tradition of matriarchal control. 33. A pro-life woman would advocate abortion if:

1.  The mother of an unborn child is suicidal. 2.  Bearing a child conflicts with a woman’s career prospects. 3.  The mother becomes pregnant accidentally. 4.  None of the above

34. Pro-choice women object to the notion of the home being the “women’s sphere” because they believe: 1. That the home is a “joint sphere” shared between men and women. 2. That reproduction is a matter of choice for women. 3.  That men and women are equal. 4.  Both (2) and (3) 35. Two health tragedies affecting US society in the 1960s led to

1.  A change in attitude to women’s right to privacy. 2.  Retaining the anti-abortion laws with some exceptions. 3.  Scrapping of anti-abortion laws. 4.  Strengthening of the pro-life lobby.

3.10 

  CAT Papers

36. Historically, the pro-choice movement has got support from ________ among others. 1.  Major patriarchal religions 2.  Countries with low population density 3.  Medical profession 4.  None of the above

PASSAGE  3 The conceptions of life and the world which we call ‘philosophical’ are a product of two factors: one, inherited religious and ethical conceptions; the other, the sort of investigation which may be called ‘scientific’, using this word in its broadest sense. Individual philosophers have differed widely in regard to the proportions in which these two factors entered into their systems, but it is the presence of both, in some degree, that characterizes philosophy. ‘Philosophy’ is a word which has been used in many ways, some wider, some narrower. I propose to use it in a very wide sense, which I will now try to explain. Philosophy, as I shall understand the word, is something intermediate between theology and science. Like theology, it consists of speculations on matters as to which definite knowledge has, so far, been unascertainable; but like science, it appeals to human reason rather than to authority, whether that of tradition or that of revelation. All definite knowledge-so I should contend-belongs to science; all dogma as to what surpasses definite knowledge belongs to theology. But between theology and science there is a ‘No man’s Land’, exposed to attack from both sides; this ‘No Man’s Land’ is philosophy. Almost all the questions of most interest to speculative minds are such as science cannot answer, and the confident answers of theologians no longer seem so convincing as they did in former centuries. Is the world divided into mind and matter, and if so, what is mind and what is matter? Is mind subject to matter, or is it possessed of independent powers? Has the universe any unity or purpose? Is it evolving towards some goal? Are there really laws of nature, or do we believe in them only because of our innate love of order? Is man what he seems to the astronomer, a tiny lump of carbon and water impotently crawling on a small and unimportant planet? Or is he what he appears to Hamlet? Is he perhaps both at once? Is there a way of living that is noble and another that is base, or are all ways of living merely futile? If there is a way of living that is noble, in what does it consist, and how shall we achieve it? Must the good be eternal in order to deserve to be valued, or is it worth seeking even if the universe is inexorably moving towards death? Is there such a thing as wisdom, or is what seems such merely the ultimate refinement of folly? To such questions no answer can be found in the laboratory. Theologies have professed to give answers,

all to definite; but their definiteness causes moderm minds to view them with suspicion. The studying of these questions, if not the answering of them, is the business of philosophy. Why, then, you may ask, waste time on such insoluble problems? To this one may answer as a historian, or as an individual facing the terror of cosmic loneliness. The answer of the historian, in so far as I am capable of giving it, will appear in the course of this work. Ever since men became capable of free speculation, their actions in innumerable important respects, have depended upon their theories as to the world and human life, as to what is good and what is evil. This is as true in the present day as at any former time. To understand an age or a nation, we must understand its philosophy, and to understand its philosophy we must ourselves be in some degree philosophers. There is here a reciprocal causation: the circumstances of men’s lives do much to determine their philosophy, but, conversely, their philosophy does much to determine their circumstances. There is also, however, a more personal answer. Science tells us what we can know, but what we can know is little, and if we forget how much we cannot know we may become insensitive to many things of very great importance. Theology, on the other hand, induces a dogmatic belief that we have knowledge, where in fact we have ignorance, and by doing so generates a kind of impertinent insolence towards the universe. Uncertainty, in the presence of vivid hopes and fears, is painful, but must be endured if we wish to live without the support of comforting fairy tales. It is not good either to forget the questions that philosophy asks, or to persuade ourselves that we have found indubitable answers to them. To teach how to live without certainty, and yet without being paralyzed by hesitation, is perhaps the chief thing that philosophy, in our age, can still do for those who study it. 37. The purpose of philosophy is to:

1.  Reduce uncertainty and chaos. 2.  Help us to cope with uncertainty and ambiguity. 3.  Help us to find explanations for uncertainty. 4.  Reduce the terror of cosmic loneliness.

38. Based on this passage what can be concluded about the relation between philosophy and science?

1.  The two are antagonistic. 2.  The two are complementary. 3. There is no relation between the two. 4. Philosophy derives from science.

39. From reading the passage, what can be concluded about the profession of the author? He is most likely not to be a:

CAT 2002  1.  Historian 3.  Scientist

2.  Philosopher 4.  Theologian

40. According to the author, which of the following statements about the nature of the universe must be definitely true?

1.  The universe has unity. 2.  The universe has a purpose. 3.  The universe is evolving towards a goal. 4.  None of the above.

PASSAGE  4 Cells are the ultimate multi-taskers: they can switch on genes and carry out their orders, talk to each other, divide in two and much more, all at the same time. But they couldn’t do any of these tricks without a power source to generate movement. The inside of a cell bustles with more traffic than Delhi roads, and, like all vehicles, the cell’s moving parts need engines. Physicists and biologists have looked “under the hood” of the cell and laid out the nuts and bolts of molecular engines. The ability of such engines to convert chemical energy into motion is the envy of nanotechnology researchers looking for ways to power molecule-sized devices. Medical researchers also want to understand how these engines work. Because these molecules are essential for cell division, scientists hope to shut down the rampant growth of cancer cells by deactivating certain motors. Improving motor-driven transport in nerve cells may also be helpful for treating diseases such as Alzheimer’s, Parkinson’s or ALS, also known as Lou Gehrig’s disease. We wouldn’t make it far in life without motor proteins. Our muscles wouldn’t contract. We couldn’t grow, because the growth process requires cells to duplicate their machinery and pull the copies apart. And our genes would be silent without the services of messenger RNA, which carries genetic instructions over to the cell’s protein-making factories. The movements that make these cellular activities possible occur along a complex network of threadlike fibers, or polymers, along which bundles of molecules travel like trams. The engines that power the cell’s freight are three families of proteins, called myosin, kinesin and dynein. For fuel, these proteins bum molecules of ATP, which cells make when they break down the carbohydrates and fats from the foods we eat. The energy from burning ATP causes changes in the proteins’ shape that allow them to heave themselves along the polymer track. The results are impressive: In one second, these molecules can travel between 50 and 100 times their own diameter. If a car with a 5-foot-wide engine were as efficient, it would travel 170 to 340 kmph. Ronald Vale, a researcher at the Howard Hughes Medical Institute and the University of California at San Fran-

  3.11

cisco, and Ronald Milligan of the Scripps Research Institute have realized a long-awaited goal by reconstructing the process by which myosin and kinesin move, almost down to the atom. The dynein motor, on the other hand, is still poorly understood. Myosin molecules, best known for their role in muscle contraction, form chains that lie between filaments of another protein called actin. Each myosin molecule has a tiny head that pokes out from the chain like oars from a canoe. Just as rowers propel their boat by stroking their oars through the water, the myosin molecules stick their heads into the actin and hoist themselves forward along the filament. While myosin moves along in short strokes, its cousin kinesin walks steadily along a different type of filament called a microtubule. Instead of using a projecting head as a lever, kinesin walks on two “legs.” Based on these differences, researchers used to think that myosin and kinesin were virtually unrelated. But newly discovered similarities in the motors’ ATP-processing machinery now suggest that they share a common ancestor - molecule. At this point, scientists can only speculate as to what type of primitive cell-like structure this ancestor occupied as it learned to bum ATP and use the energy to change shape. “We’ll never really know, because we can’t dig up the remains of ancient proteins, but that was probably a big evolutionary leap,” says Vale. On a slightly larger scale, loner cells like sperm or infectious bacteria are prime movers that resolutely push their way through to other cells. As L. Mahadevan and Paul Matsudaira of the Massachusetts Institute of Technology explain, the engines in this case are springs or ratchets that are clusters of molecules, rather than single proteins like myosin and kinesin. Researchers don’t yet fully understand these engines’ fueling process or the details of how they move, but the result is a force to be reckoned with. For example, one such engine is a spring like stalk connecting a single-celled organism called a vorticellid to the leaf fragment it calls home. When exposed to calcium, the spring contracts, yanking the vorticellid down at speeds approaching 3 inches (8 centimeters) per second. Springs like this are coiled bundles of filaments that expand or contract in response to chemical cues. A wave of positively charged calcium ions, for example, neutralizes the negative charges that keep the filaments extended. Some sperm use spring like engines made of actin filaments to shoot out a barb that penetrates the layers that surround an egg. And certain viruses use a similar apparatus to shoot their DNA into the host’s cell. Ratchets are also useful for moving whole cells, including some other sperm and pathogens. These engines are filaments that simply grow at one end, attracting chemical building blocks from nearby. Because the other end is anchored in place, the growing end pushes against any barrier that gets in its way. Both springs and ratchets are made up of small units that each move just slightly, but collectively produce a

3.12 

  CAT Papers

powerful movement. Ultimately, Mahadevan and Matsudaira hope to better understand just how these particles create an effect that seems to be so much more than the sum of its parts. Might such an understanding provide inspiration for ways to power artificial nano-sized devices in the future? “The short answer is absolutely,” says Mahadevan. “Biology has had a lot more time to evolve enormous richness in design for different organisms. Hopefully, studying these structures will not only improve our understanding of the biological world, it will also enable us to copy them, take apart their components and re-create them for other purposes.”

c. Cells, together, generate more power than the sum of power generated by them separately. d. Vorticellid and the leaf fragment are connected by a calcium engine.

41. According to the author, research on the power source of movement in cells can contribute to:

b. Growth processes involve a routine in a cell that duplicates their machinery and pulls the copies apart.

1. Control over the movement of genes within human systems. 2.  The understanding of nanotechnology. 3.  Arresting the growth of cancer in a human being. 4.  The development of cures for a variety of diseases. 42. The author has used several analogies to illustrate his arguments in the article. Which of the following pairs of words are examples of the analogies used?

a.  Cell activity and vehicular traffic. b.  Polymers and tram tracks. c.  Genes and canoes. d.  Vorticellids and ratchets.

1.  (a) and (b) 3.  (a) and (d)

2.  (b) and (c) 4.  (a) and (c)

43. Read the five statements below: a, b, c, d, and e. From the options given, select the one which includes a statement that is not representative of an argument presented in the passage. a. Sperms use spring like engines made of actin filament. b.  Myosin and kinesin are unrelated. c. Nanotechnology researchers look for ways to power molecule-sized devices. d.  Motor proteins help muscle contraction. e.  The dynein motor is still poorly understood. 1.  a, b and c 3.  a, d and e

2.  c, d and e 4.  a, c and d

44. Read the four statements below: a, b, c, and d. From the options given, select the one which includes only statement(s) that are representative of arguments presented in the passage. a.  Protein motors help growth processes b. Improved transport in nerve cells will help arrest tuberculosis and cancer

1.  (a) and (b) but not (c)

2.  (a) and (c) but not (d)

3.  (a) and (d) but not (b)

4.  (c) and (d) but not (b)

45. Read the four statements below: a, b, c, and d. From the options given, select the one which include statement(s) that are representative of arguments presented in the passage. a.  Myosin, kinesin and actin are three types of protein

c.  Myosin molecules can generate vibrations in muscles. d. Ronald and Mahadevan are researchers at Massachusetts Institute of Technology. 1.  (a) and (b) but not (c) and (d) 2.  (b) and (c) but not (a) 3.  (b) and (d) but not (a) and (c) 4.  (a), (b) and (c) but not (d)

PASSAGE  5 If translated into English, most of the ways economists talk among themselves would sound plausible enough to poets, journalists, business people, and other thoughtful though non-economical folk, Like serious talk any where among boat designers and baseball fans, say—the talk is hard to follow when one has not made a habit of listening to it for a while. The culture of the conversation makes the words arcane. But the people in the unfamiliar conversation are not Martians. Underneath it, all (the economist’s favourite phrase) conversational habits are similar. Economics uses mathematical models and statistical tests and market arguments, all of which look alien to the literary eye. But looked at closely they are not so alien. They may be seen as figures of speech-metaphors, analogies, and appeals to authority. Figures of speech are not mere frills. They think for us. Someone who thinks of a market as an “invisible hand” and the organization of work as a “production function” and his coefficients as being “significant,” as an economist does, is giving the language a lot of responsibility. It seems a good idea to look hard at his language. If the economic conversation were found to depend a lot on its verbal forms, this would not mean that economics would be not a science, or just a matter of opinion, or some sort of confidence game. Good poets, though not scientists, are serious thinkers about symbols; good historians, though

CAT 2002  not scientists, are serious thinkers about data. Good scientists also use language. What is more (though it remains to be shown) they use the cunning of language, without particularly meaning to. The language used is a social object, and using language is a social act. It requires cunning (or, if you prefer, consideration), attention to the other minds present when one speaks. The paying of attention to one’s audience is called “rhetoric,” a word that I later exercise hard. One uses rhetoric, of course, to warn of a fire in a theatre or to arouse the xenophobia of the electorate. This sort of yelling is the vulgar meaning of the word, like the president’s “heated rhetoric” in a press conference or the “mere rhetoric” to which our enemies stoop. Since the Greek flame was lit, though, the word has been used also in a broader and more amiable sense, to mean the study of all the ways of accomplishing things with language: inciting a mob to lynch the accused, to be sure, but also persuading readers of a novel that its characters breathe, or bringing scholars to accept the better argument and reject the worse. The question is whether the scholar—who usually fancies himself an announcer of “results” or a stater of “conclusions” free of rhetoric—speaks rhetorically. Does he try to persuade? It would seem so. Language, I just said, is not a solitary accomplishment. The scholar doesn’t speak into the void, or to himself. He speaks to a community of voices. He desires to be heeded, praised, published, imitated, honoured, en-Nobled. These are the desires. The devices of language are the means. Rhetoric is the proportioning of means to desires in speech. Rhetoric is an economics of language, the study of how scarce means are allocated to the insatiable desires of people to be heard. It seems on the face of it a reasonable hypothesis that economists are like other people in being talkers, who desire listeners whey they go to the library or the laboratory as much as when they go to the office on the polls. The purpose here is to see if this is true, and to see if it is useful: to study the rhetoric of economic scholarship. The subject is scholarship. It is not the economy, or the adequacy of economic theory as a description of the economy, or even mainly the economist’s role in the economy. The subject is the conversation economists have among themselves, for purposes of persuading each other that the interest elasticity of demand for investment is zero or that the money supply is controlled by the Federal Reserve. Unfortunately, though, the conclusions are of more than academic interest. The conversations of classicists or of astronomers rarely affect the lives of other people. Those of economists do so on a large scale. A well known joke describes a May Day parade through Red Square with the usual mass of soldiers, guided missiles, rocket launchers. At last come rank upon rank of people in gray business suits. A bystander asks, “Who are those?” “Aha!” comes the reply, “those are economists: you have no idea what damage they can do!” Their conversations do it.

  3.13

41. According to the passage, which of the following is the best set of reasons for which one needs to “look hard” at an economist’s language? a. Economists accomplish a great deal through their language. b.  Economics is an opinion-based subject. c.  Economics has a great impact on other’s lives. d.  Economics is damaging. 1.  (a) and (b) 3.  (a) and (c)

2.  (c) and (d) 4.  (b) and (d)

47. In the light of the definition of rhetoric given in the passage, which of the following will have the least element of rhetoric?

1.  An election speech. 2. An advertisement jingle. 3.  Dialogues in a play. 4.  Commands given by army officers.

48. 

As used in the passage, which of the following is the closest meaning to the statement “The culture of the conversation makes the words arcane”?

1.  Economists belong to a different culture. 2.  Only mathematicians can understand economists. 3. Economists tend to use terms unfamiliar to the lay person, but depend on familiar linguistic forms. 4.  Economists use similes and adjectives in their analysis. 49. As used in the passage, which of the following is the closest alternative to the word ‘arcane’? 1.  Mysterious 3.  Covert

2.  Secret 4.  Perfidious

50.  Based on your understanding of the passage, which of the following conclusions would you agree with? 1. The geocentric and the heliocentric views of the solar system are equally tenable. 2. The heliocentric view is superior because of better rhetoric. 3.  Both views use rhetoric to persuade. 4.  Scientists should not use rhetoric.

  SECTION  II There are 50 questions in this section. All the questions carry equal marks. 51. If there are 10 positive real numbers n1 R(x, y) 76. Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is 1.  56

2.  255

3.  1024

4.  Not unique

77. When 2256 is divided by 17, the remainder would be 1.  1

2.  16

3.  14

4.  None of these

2 2 78. The number of real roots of the equation ___ ​ Ax ​ + _____ ​ x B–  1   ​ = 1, where A and B are real numbers not equal to zero simultaneously, is

81. After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number? 1.  80

2.  75

3.  41

4.  53

82. Six persons are playing a card game. Suresh is facing Raghubir who is to the left of Ajay and to the right of Pramod. Ajay is to the left of Dhiraj. Yogendra is to the left of Pramod. If Dhiraj exchanges his seat with Yogendra and Pramod exchanges with Raghubir, who will be sitting to the left of Dhiraj? 1.  Vogendra

2.  Raghubir

3.  Suresh

4.  Ajay

Direction for questions 83 and 84:  Answer the questions based on the following information. A boy is asked to put one mango in a basket when ordered ‘One’, one orange when ordered ‘Two’, one apple when ordered Three, and is asked to take out from the basket one mango and an orange when ordered Four. A sequence of orders is given as: 1 2 3 3 2 1 4 2 3 1 4 2 2 3 3 1 4 1 1 3 2 3 4 83. How many total oranges were in the basket at the end of the above sequence? 1.  1

2.  4

3.  3

4.  2

84. How many total fruits will be in the basket at the end of the above order sequence?

1.  None

2.  1

1.  9

2.  8

3.  2

4.  1 or 2

3.  11

4.  10

79. At a bookstore, ‘MODERN BOOK STORE’ is flashed using neon lights. The words as individually flashed at 1 ​ s, 4​ __ 1 1 __ the intervals of 2​ __ 2 4 ​ s and 5​ 8 ​ s respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is 1.  49.5s

2.  73.5s

3.  1744.5s

3.  855s

80. Three pieces of cakes of weight 4 __ ​ 12 ​ lb, 6 __ ​ 34  ​lb and 7 __ ​ 15 ​ lb respectively are to be divided into parts of equal weight. Each part must be as heavy as possible. If one such part is served to each guest, then what is the maximum number of guests that could be entertained? 1.  54

2.  72

3.  20

3.  None of these

Direction for questions 85 and 86:  Answer the questions based on the following information. Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. 85. How many four-letter computer passwords can be formed using only the symmetric letters (no repetition allowed)? 1.  7,920

2.  330

3.  14,640

4.  4,19,430

86. How many three-letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

CAT 2002  1.  990

2.  2,730

3.  12,870

4.  15,600

  3.17

91. If u, v, weighted average and m are natural numbers such that um +vm = wm, then which one of the following is true?

87. A train approaches a tunnel AB. Inside the tunnel is a cat located at a point that is __ ​ 38 ​ of the distance AB measured from the entrance A. When the train whistles, the cat runs. If the cat moves to the entrance of the tunnel A, the train catches the cat exactly at the entrance. If the cat moves to the exit B, the train catches the cat at exactly the exit. The speed of the train is greater than the speed of the cat by what order?

1.  m > min(u, v, w) 2. m > max(u, v, w) 3.  m < min(u, v, w) d. None of these

1.  3 : 1

2.  4 : 1

92. In how many ways is it possible to choose a white square and a black square on a chessboard so that the squares must not lie in the same row or column?

3.  5 : 1

4.  None of these

1.  56

2.  896

3.  60

4.  768

88. A piece of string is 40 cm long. It is cut into three pieces. The longest piece is three times as long as the middle-sized and the shortest piece is 23 cm shorter than the longest piece. Find the length of the shortest piece. 1.  27

2.  5

3.  4

4.  9

89. Three travellers are sitting around a fire, and are about to eat a meal. One of them has 5 small loaves of bread, the second has 3 small loaves of bread. The third has no food, but has 8 coins. He offers to pay for some bread. They agree to share the 8 loaves equally among the three travellers, and the third traveller will pay 8 coins for his share of the 8 loaves. All loaves were the same size. The second traveller (who had 3 loaves) suggests that he will be paid 3 coins, and that the first traveller be paid 5 coins. The first traveller says that he should get more than 5 coins. How much should the first traveller get? 1.  5

2.  7

3.  1

4.  None of these

B

In the above figure, ACB is a right-angled triangle. CD is the altitude. Circles are inscribed within the ∆ACD and ∆BCD. P and Q are the centres of the circles. The distance PQ is ___ 1.  5 2. ​√50 ​  3.  7

4.  8

1.  13

2.  127

3.  559

4.  All of these

1    94. If pqr = 1, the value of the expression _________ ​   ​ 1 + p – q–1 1 1 _________ _________ + ​     ​  + ​     ​  is equal to 1 + q + r–1 1 + r + p–1 1 p+q+r 2   ________ ​ p + 1q + r ​  3.  1

4.  p–1 + q–1 + r–1

95. It takes six technicians a total of 10 h to build a new server from Direct Computer, with each working at the same rate. If six technicians start to build the server at 11 am, and one technician per hour is added beginning at 5 pm, at what time will the server be completed? 1.  6.40 pm

2.  7 pm

3.  7.20 pm

4.  8 pm

96. Davji Shop sells samosas in boxes of different sizes. The samosas are priced at Rs 2 per samosa up to 200 samosas. For every additional 20 samosas, the price of the whole lot goes down by 10 paise per samosa. What should be the maximum size of the box that would maximise the revenue?

90.

A

93. 76n – 66n, where n is an integer > 0, is divisible by

1.  240

2.  300

3.  400

4.  None of these

97. Three small pumps and a large pump are filling a tank. Each of the three small pumps work at __ ​ 32 ​  the rate of the large pump. If all four pumps work at the same time, they should fill the tank in what fraction of the time that it would have taken the large pump alone? 4 ​   1 ​  1. ​ __ 2. ​ __ 7 3 3 ​  2 ​   3. ​ __ 4. ​ __ 3 4

  CAT Papers

3.18 

Direction for questions 98 to 100: Answer the questions based on the following diagram. A

E

F

N

4. Dhanraj isn’t an engineer and received more admission offers than Ashish. 5.  The doctor got the most number of admission offer. 101. Which one of the following statement is necessary true? 1. Ashish is a chartered accountant and got offer for admission in three NIIMs.

D

B

C

O

H

I

K

G

2.  Dhanraj is doctor and got admission in one NIM.

L

M

In the above diagram, ∠ABC=90°= ∠DCH= ∠DOE= ∠EHK= ∠FKL= ∠GLM = ∠LMN AB = BC = 2CH = 2CD = EH = FK = 2HK = 4KL = 2LM = MN 98. The magnitude of ∠FGO= 1.  300

2.  450

3.  600

4.  None of these

99. What is the ratio of the areas of the two quadrilaterals ABCD to DEFG? 1.  1 : 2

2.  2 : 1

3.  12 : 7

4.  None of these

100. How many numbers greater than 0 and less than a million can be formed with the digits 0, 7 and 8?

3. Sameer is an economist who got admission offer in two NIIMs. 4. Felix is not an engineer didn’t get any offer for admission. 102. Five boys went to a store to buy sweets. One boy had Rs 40, another boy had Rs 30. two other boys had Rs 20 each. The remaining boy has Rs 10.Below are some more facts about the intital and final Cash position. 1.  Allam started more than Jugraj. 2.  Sandeep spent Rs 1.50 more than Duljeet. 3. Ganesh started with more money than just only one other person. 4.  Duljeet started with 2/3 of what Sandeep started with. 5.  Allam spent the most, but didn’t end with the least. 6. Jugraj spent the least and ended with more than Allam or Duljeet. 7.  Ganesh spent Rs 3.50.

1.  486

2.  1084

8.  Allam spent 10 times more than what Ganesh did.

3.  728

4.  None of these

In the choices given below, all statement except are false. Which one of the following statementscan be true?

  SECTION  III Direction for questions 101 to 106: Answer the question independently. Four students—Ashish, Dhanraj, felix and Sameer sat for the common entrance exam for management(CEEM).One student got admission offer from three NIIMs (National institute of management),another from two NIIMs, the third from one NIM, while the fourth got none. Below are the some of the facts about who got admission offers from how many NIIMs and what is there educational background

1.  Allam started with Rs 40 and ended with Rs 9.50. 2.  Sandeep started with Rs 30 and ended with Rs 1 3.  Ganesh started with Rs 20 and ended with Rs 4. 4.  Jugraj started with Rs 10 and ended with Rs 7.

2. The one who got offer for admission in two NIIMs isn’t Dhanraj nor is he Chartered Accountant.

103. In a hospital, there was 200 diabetes,150 hyperglycemia and 150 gastroenteritis patients. Of these, 80 patients were treated for both diabetes and Hyperglycemia. 60 patients were enteritis. Some of these patients had all the three diseases. Doctor Dennis treats with only gastroenteritis. Doctor Paul is a generalist. Therefore, he can treat patient with multiple diseases. Patients always prefer specialist for their disease. If Doctors Dennis has 80 patients, then the other three doctor can be arrangement in terms of number of patients treated as

3.  Sameer is an economist.

1.  Paul>Gerard>Hormis

1. The one who is an engineer didn’t get as many admission as Ashish.

CAT 2002  2.  Paul>Hormis>Gerard 3.  Gerard>Paul>Hormis 4.  None of these

each flight is 2/3 of the passenger who waited in the waiting hall for both the flights put together. Half the passenger who boarded flight A are women. After boarding for flight A, 60 per cent of the waiting hall became empty. For every 20 of those who are still waiting in the hall for flight B, there is one air-hostess in flight A. What is the ratio of empty seat in flight B to the number of air-hostesses in flight A?

104. Three children won the prizes in the Bournvita quiz contest. They are from the school: Loyala, Convent and Little flower which are located in different cities. Below are some of the facts about the schools, the children and the city they are from,

1.  10 : 1

2.  5 : 1

1.  One of the contestant is Vipin.

3.  20 : 1

4.  1 : 1

2.  Loyala schools contestant didn’t come first.

  3.19

3.  Little flowers contestant was named Riaz.

Direction for questions 107 to 110: Answer the question based on the information given below.

4.  Convent school is not in Hyderabad.

A country has following types of traffic signals.

5.  The contestant from Pune is not from Loyala school.

3 red lights = Stop

6.  The contestant from Bangalore did not come first.

2 red light = turn left

7.  Convent contestant name is not Balbir.

1 red light = turn right

Which of the following statements is true?

3 green lights = go at 100km/h speed

1. First prize: Riaz (Little flowers), 2nd prize: Vipin (Convent), 3rd prize: Balbir (Loyala)

2 green lights = go at 40 km/h speed

2. 1st prize: Vipin( Convent), 2nd prize: Riaz (Little Flowers), 3rd prize: Balbir (Loyala) 3. 1st prize: Riaz (Little flowers), 2nd prize: Balbir (Loyala), 3rd prize: Vipin (Convent) 4. 1st prize : Vipin (Convent), 2nd prize: Balbir (Loyala), 3rd prize : Riaz (Little flower) 105. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boy. If we play the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, if we play the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of younger boy. The mother of the younger boy is younger to his father by 3 years. Then, what is the age of the younger boy. 1.  3 3.  2

2.  4 4.  None of these

106. Flights A and B are scheduled from an airport within the next one hour. All the booked passenger of the two flights are waiting in the boarding hall after check-in. The hall has a seating capacity of 200, out of which 10 per cent remained vacant. 40 per cent of the waiting passengers are ladies. When boarding announcement came, passengers of flight A left the hall and boarded the flight. Seating capacity of

1 green light = go at 20kn/h speed A motorist starts at a point on a road and follows all traffic signals. His car is heading towards the north. He encounters the following signals (the time mentioned in each case below is applicable after crossing the previous signal). Starting point—1 green light After half an hour , 1st signal- 2 red and 2 green lights. After 15 mins, 2nd signal- 1 red light After half an hour, 3rd signal- 1 red and 3 green lights After 24 mins, 4th signals- 2 red and 2 green lights After 15 min. 5th signals- 3 red lights 107. The total distance travelled by the motorists from the starting point till the last signal is 1.  90 km 2.  100 km 3.  120 km 4.  None of these 108. What is the position (Radial distance) of the most motorists when he reaches the last signal? 1. 45 km directly north of the starting point. 2.  30 km directly to the east of the starting point. 3.  50 km away to the north-east of the starting point. 4.  45 km away to the north-west of the starting point.

3.20 

  CAT Papers

109. After the starting point, if the first signal were one red and 2 green light, what would be the final position of the motorist?

111. What percentage of cities located within 10º east and 40º east (20º east and 40ºeast) lie in the southern hemisphere?

1.  30 km to the west and 20 km to the south.

1.  15%

2.  20%

2.  30 km to the west and 40 km to the north

3.  25%

4.  30%

3. 50 km to the east and 40 km to the north 4.  Directly 30 km to the east 100. If at the starting point, the car was heading towards south, what would be the final position of the motorist? 1.  30 km to the east and 40 km to the south 2.  50 km to the east and 40 km to the south 3.  30 km to the west and 40 km to the south 4.  50 km to the west and 20 km to the north Direction for questions 111 to 113:  Answer these question based on the table given below. The following table provides data on the different countries and location of their capitals. (The data may not match the actual latitude, longitude). Answer the following question on the basis of this table. S.No.

Country

Capital

Latitude Longitude

1

Argentina

Buenos Aires

34.30 S

58.20 E

2

Australia

Canberra

3.15 S

149.08 E

3

Austria

Vienna

48.12 N

16.22 E

4

Bulgaria

Sofia

42.45 N

23.20 E

5

Brazil

Brasilia

15.47 S

47.55 E

6

Canada

Ottawa

45.27 N

75.42 E

7

Cambodia

Phnom Penh

11.33 N

104.55 E

8

Ecuador

Quito

0.15 S

78.35 E

9

Ghana

Accra

5.35 N

0.6 E

10

Iran

Tehran

35.44 N

51.30 E

11

Ireland

Dublin

53.20 N

6.18 E

12

Libya

Tripoli

32.49 N

13.07 E

13

Malaysia

Kuala Lumpur

3.9 N

101.41 E

14

Peru

Lima

12.05 S

77.0 E

15

Poland

Warsaw

52.13 N

21.0 E

16

New-Zealand

Wellington 41.17 S

174.47 E

17

Saudi-Arabia

Riyadh

24.41 N

46.42 E

18

Spain

Madrid

40.25 N

3.45 W

19

Sri-Lanka

Colombo

6.56 N

79.58 E

20

Zambia

Lusaka

15.28 S

28.16 E

112. The number of cities whose name begins with consonant and are in the northern hemisphere in the table? 1. Exceeds the number of cities whose names begin with a consonant and are in the southern hemisphere by 1. 2. Exceeds the number of cities whose name begins with a consonant and are in southern hemisphere by 2. 3. Is less than the number of cities whose name begins with a consonant and are in the east of the meridian by 1. 4. Is less than the no. of countries whose name begins with a consonant and are in the east of the meridian by 3. 113. The ratio of the number of countries whose names start with vowels and located in the southern hemisphere, to the number of countries, the name of whose capital cities start with a vowel in the table above is 1.  3 : 2

2.  3 : 3

3.  3 : 1

4.  4 : 3

Direction for questions 114 to 121:  Each item is followed by two statements, A and B. answer each question using the following instruction. Choose 1 if the question can be answered by one of the statement alone but not by the other. Choose 2 if the question can be answered by using other statement alone. Choose 3 if the question can be answered by using both the statements together, but cannot be answered by using other statement alone. Choose 4 if the question cannot be answered by either of the statements 114. In a hockey match, the Indian team was behind by 2 goals with 5 mins remaining. Did they win the match? 1. Deepak Thakur, the Indian striker, score three goals in the last 5 mins of the match. 2.  Korea scored a total of three goals in the match. 1.  1

2.  2

3.  3

4.  4

CAT 2002  115. Four student were added to a dance class. Would the teacher be able to divide her students evenly into a dance team (or teams) of 8? A. If 12 students were added, the teacher could put everyone in team of 8 without any left over. B. The number of students in the class is currently not visible by 8. 1.  1

2.  2

3.  3

4.  4.

  3.21

119. Is |x-2| < 1? A.  |x | 3 rounds

CAT 2002  71. (3)  x2 + 5y2 + z2 – 4yx + 2yz

(x2 + 4y2 – 4yx) + z2 + y2 – 2yz = 0



(x—2y)2 +(z—y)2 =0



It can be true only if x = 2y and z = y

  3.29

2 B2 – 1 ​ ⇒ A2(x-1) B2x = x2 - x _____ 78. (4)  __ ​ A x ​  + ​  x –1   

 This is a quadratic equation. Hence, number of roots = 2 or 1 (1 in the case when both roots are equal).

72. (2) Arithmetic mean is more by 1 .8 means sum is more by 18.

79. (2)  Because each word is lit for a second,

( 

)

5 49 17 7 21 __ 41   LCM ​ _​ 2  ​+1, __ ​ 4 ​  +1, __ ​ 8 ​  +1  ​= LCM _​ 2  ​, __ ​ 4 ​ ,  ​ 8 ​  =



So ba – ab = 18



b > a because sum has gone up, e.g. 31 - 13 = 18



Hence, b – a = 2

 

73. (3)  By trial and error:

LCM (​  7,21,49 )​ ​ __________    ​ HCM (​  2,4,8 )​

HCF ​( 9,27,36 )​ 9 27 __ 36 ​= 9/20 lb 80. (4) HCF ​( _​ 2 ​, __ ​ 4  ​,  ​ 5  ​  )​= __________ ​ LCM ​( 2,4,5 )​   



30 × 12 = 360 > 300



30 × 7.5 = 225 < 300



50 × 6 = 300.

total weight = 18.45 lb



Hence, he rented the car for 6 h.

18.45×20 Maximum number of guests = _______ ​  9  ​    = 41

= weight of each piece,

74. (4)  575 = – x

81. (4)  3(4(7x+4) + 1) + 2 = 84x + 53



1150 = n2 + n – 2x

  Therefore, remainder is 53.



n(n + 1) ≥ 1150

82. (3)



n + n ≥ 1150



The smallest value for it is n = 34.



For n = 34



40 = 2x ⇒ x = 20

75. (4)  x – 1 ≤ [x] ≤ x

Suresh is sitting to the left of Dhiraj.



2x + 2y – 3 ≤ L (x, y) ≤ 2x + 2y ⇒ a – 3 ≤ L ≤ a



2x + 2y – 2 ≤ R(x, y) ≤ 2x + 2y ⇒ a – 2 ≤ R ≤ a



Therefore, L ≤ R

83. (4)  Number of oranges at the end of the sequence =   Number of 2s – Number of 4s = 6 – 4 = 2 84. (3) Number of (1s + 2s + 3s) - 2(Number of 4s) = 19—8

Note: Choice (b) is wrong, otherwise choice (a) and choice (c) are also not correct. Choose the numbers to check. n(n + 1) 76. (1)  Number of regions ​ ______ ​ + 1 where n = Number of lines, 2    i.e., for 0 line

85. (1)  11 x 10 x 9 x 8 = 7920 86. (3) Total number of passwords using all letters - Total number of passwords using no symmetric letters   = (26 x 25 x 24)—(15 x 14 x 13) = 12870



We have region = 1.



For 1 line we have region = 2.



If can be shown as:

87. (2) Let tunnel = 8 km and speed of cat = 1 km/h   Time taken to reach entrance of tunnel by cat = 3 h   Time taken to reach exit of tunnel by cat = 5 h

Number of lines

0

1

2

3

4

5

...

10

Number of regions

1

2

4

7

11

16

...

56

Therefore, for n = 10, it is = 56 77. (1) (24)64 = (17-1)64 =17n+(—1)54 = 17n + 1 Hence, remainder =1

  Train will cover the sum (length of tunnel) = 2 h   Therefore, ratio of speeds of train and cat = 4 : 1   Speed of the train is greater by 3 : 1 than that of the cat. 88. (3)  Let the largest piece = 3x Middle = x   Shortest = 3x—23

3.30 

  CAT Papers

  or 3x + x + (3x—23) = 40   or x = 9   or the shortest piece = 3(9)—23 = 4   Check choices:   The shortest piece has to be < 20 cm.

92. (4) A black square can be chosen in 32 ways. Once a black square is there, you cannot choose the 8 white squares in its row or column. So the number of white squares available = 24   Number of ways = 32 × 24 = 768 93. (4)  76n – 66n   put n = 1

  27 is wrong choice.

  76 – 66 = (73 – 63) (73 + 63)

  The largest piece is a multiple of 3.

  This is a multiple of 73 + 63 = 559 and 7+6 = 13

  Or (23 + Shortest) should be a multiple of 3.

94. (3)  lf p=q = r= 1, then expression = 1

  Answer = 4 cm (Among other choices)

 Check the choice only, one choice gives the value of expression = 1.

89. (2)  Each traveller had __ ​  8 3   ​loaves.

8   First traveller has given 5–​ _3 ​loaves to the third.

8  Second traveller sacrificed only 3 – _​ 3 ​ = _​ 13 ​ rd of a loaf. So, first should get 7 coins.

95. (4) Total amount of work = 60 man-hours From 11 am to 5pm, 6 technicians = 36 man-hours From 5 pm to 6 pm, 7 technicians = 7 man-hours   From 6 pm to 7 pm, 8 technicians = 8 man-hours   From 7 am to 8 pm, 9 technicians = 9 man-hours

90. (2)

  Total = 60 man-hours 96. (2)  Number of samosas = 200 + 20n,   n is a natural number.   Price per samosa = Rs (2 - 0.ln)   Revenue = (200 + 20n)(2 – 0.ln) = 400 + 20n –2n2 (15)2 - x2 = (20)2 - (25 - x)2 ⇒ x = 9

  For maxima 20 – 4n = 0; by differentiation n = 5  ⇒ Maximum revenue will be at (200 + 20 x 5) = 300 samosas

⇒ BD =12 Area of ∆ ABD= _​ 12 ​×12×9=54

97. (2) Three small pumps = Two large pumps Three small + One large pumps

s = _​ 12 ​ (15 + 12 + 9) = 18

  = Three large pump ⇒ _​ 1 ​ 3

Area r1 = ____ ​  s   ​ ⇒ r1 = 3

98. (4)  It KL = 1,then lG = 1 and FI=2

Area of ∆BCD = _​ 12 ​= 16×12=96

  Hence, tanθ = _​ 21 ​= 2

s= _​ 12 ​​( 16+20+12 )​= 24

  Thus, θ none of 30. 45 and 600.

r2=____ ​ Area ​ ⇒ r2=4 s    in ∆PQM,

PM = r1 + r2 = 7 cm



QM = r2 – r1 = 1 cm

___

Hence, PQ = ​√ 50 ​ cm (Using Pythagoras Theorem)

99. (3) Area of quadrilateral ABCD = _​ 12 ​​( 2x + 4x )​×4x = 12x   Area of quadrilateral DEFG = _​ 12 ​(5x + 2x) x 2x = 7x 2 100. (3)  Number of ways for single digit = 2   2 digits = 2 × 3 = 6   3 digits = 2 ×3 × 3 = 18   4 digits = 2 × 3 × 3 × 3 = 54

91. (4)  um + vm = wm

  5 digits = 2 × 3 × 3 × 3 × 3 = 162

  u +v = w

  6 digits = 2 × 3 × 3 × 3 × 3 × 3 = 486

 Taking Pythagorean triplet 3, 4 and 5, we see in < mm (u, v, w)

  Total = 728

2

2

2

  Also 1 + 2’ = 3’ and hence in ≤ mm (u, v, w) 1

Alternatively, Total = (3 × 3 × 3 × 3 × 3 × 3) − 1 = 36 − 1 = 728

CAT 2002  Section  III

  Seating capacity of Flight _ ​ 23 ​ x 180 = 120

101. (3)  According to statement c.

  Number of people in Flight A = 100

  1 Ashish is not an engineer ,(2) Ashish has got more offers than engineers.

  For flight B = 180 – 100 = 80

  Therefore, Ashish did not have 0 offers  Now, we can put the above given information in the table like the one given below Profession

Names

  Thus, number of airhostesses for A = 4   Empty seats in flight B = 120 – 80 = 40   40: 4 = 10 :1

Solution 107–110

Offers 3

2

1

0

X profession

CA

Ashish

X

X

X

X

X engineer

MD

Dhanraj

√

X

X

X

X engineer

Economist

Sameer

X

√

X

X

X

X

X

√

Engineer

  3.31

1 07. S = Distance covered; v = Velocity (km/h) t = Time taken; s= v x t The total distance traveled by the motorists from the starting point till last signal is 10+10+20+40+10 = 90 km.

From statement IV, Dhanraj is not 0 and 1. 102. (4)    Option(c) is ruled out be statement VII.   Option (a) is ruled out by statement VII and VIII.  From statement IV, Sandeep had Rs 30 to start with and Daljeet Rs 20.

108. Applying Pythagoras theorem, for a right-angled triangle. B

 From statement II, Option (b) is not possible as Sandeep was left with Rs 1, he spent Rs 29. but according to (b) he spent Rs 1.50 more than Daljeet. But Daljeet had only Rs 20. Hence, option (d) is correct. 103. (4)  104. (3) Statements V and VI rule out the options (a) and (b). The contestants from Bangalore and Pune did not come first, so, school from Hyderabad can come first. Convent is not in Hyderabad which rules out option (d). 105. (3)  Only two combinations possible are: Younger

Older

2

4

3

9

A (BC)(BC) = (AB)(AB) + (AC)(AC) BC = √(AB)(AB) + (AC)(AC) = 50 km.

109. (3) For the case when 1st signal were 1 red and 2 green lights, the surface diagram will be as given below.

 Cubes of natural numbers are 1,8,27,64……. Here 64 and above is not possible as the age will go above 10. Only (b) and (c) satisfy the case of mother and father. 106. (1)  Total seats in the hall

200

  Seats vacant

20

  Total waiting

180

  Ladies

72

C

S

3.32 

  CAT Papers

TF= 50 km; ST = 40 km Going by the above figure, option (c) is correct, 50 km to the east and 40 km to the north. 111. (4)  Total five countries lie between 10 E and 40 E   Austria,  Bulgaria,  Libya,  Poland,  Zambia   N

N

N

N

S

_ ​ 15 ​ = 20%

112. (4) Number of cities whose names are starting with consonants and are located in the northern hemisphere = 10

118. (4) A gives 500 as median and b gives 600 as range. A and B together do not give average. Therefore, it cannot be answered from the given statements. 119. (2)  From statement A, we know that all -1 61/187. Statement (c) is again wrong. 131. (2) The Profitability of North African and middle east in 2000 = 356/530 = 0.67 The Profitability of Spain in 2000 = 225/43 = 5.23 The Profitability of the rest of Latin America in 2000 = 169/252, which is less than 1. The Profitability of far east in 2000 = 189/311 = 3510/29870 = 0.11 1997-98 => 3829/33168 = 0.11 1998-99 => 4265/36068 = 0.11

3.34 

  CAT Papers 1999-00 => 4839/42348 = 0.11 2000-01 => 5413/49638 = 0.11 So, Karnataka is the correct option and no further check is required.

147. (3) By looking at the table prepared while solving question (11), we see that Tamil Nadu has maintained a constant rank over the years in terms of its contribution to total tax collections. 148. (2)  Only R9

149. (4)  Statement (a) is not satisfied by R9. Statement (b) is not satisfied R2 and R3. Statement (c) is incorrect as there are 5 such reason R1, R2, R3, R4 and R11. Statement (d) is correct 150. (3)  All three R9, R10 and R11.

CAT 2003 Time Given = 120 minutes CAT 2003 has a total of 150 questions distributed in three sections. Each section has 50 questions. There is negative marking.

  SECTION  I Direction for questions 1 to 25: Each of the five passages given below is followed by five questions. Choose the best answer to each question.

Passage  I At first, it looks as though Panchayati Raj, the lower layer of federalism in our polity, is as firmly entrenched in our system as is the older and higher layer comprising the Union Government and the State. Like the democratic institutions at the higher level, those at the panchayat level, the panchayati Raj institutions ( PRIs), are written into and Protected by the Constitution. All the essential features , which distinguish a unitary system from a federal one , are as much enshrined at the lower as at the upper level of our federal system. But look closely and you will discover a fatal flaw. The letter of the Constitution as well as the spirit of the present polity have exposed the intra-State level of our federal system to a dilemma of which the inter-State and Union-State layers are free. The flaw has many causes. But all of them are rooted in an historical anomaly, that while the dynamics of federalism and democracy have given added strength to the rights given to the States in the Constitution, they have worked against the rights of panchayats. At both levels of our federal system, there is the same tussle between those who have certain rights and those

Total Marks = 150 Section I – 50 Ques. Section II – 50 Ques. Section III – 50 Ques.

who try to encroach upon them if they believe they can. Thus the Union Government was able to encroach upon certain rights given to the States by the Constitution. It got away with that because the single dominant party system, which characterized Centre- State relations for close upon two decades, gave the party in power at the Union level many extra-constitutional political levers. Second, the Supreme Court had not yet begun to extend the limits of its power. But all that has changed in recent times. The spurt given to a multi-party democracy by the overthrow of the Emergency in 1977 became a longterm trend later on because of the ways in which a vigorously democratic multi-party system works in a political society which is as assertively pluralistic as Indian society is. It gives political clout to all the various segments which constitute that society. Secondly, because of the linguistic reorganization of States in the 1950s, many of the most assertive segments have found their most assertive expression as States. Thirdly, with single-party dominance becoming a thing of the past at the Union level, government can be formed at that level only by multi-party coalitions in which State-level partiers are major players. This has made it impossible for the Union Government to do much about anything unless it also carries a sufficient number of State-level parties with it. Indian federalism is now more real than it used to be, but an unfortunate side-effect is that India’s panchayati Raj System, inaugurated with such fanfare in the early 1980s has becomes less real.

3.36 

  CAT Papers

By the time the PRIs came on the scene, most of the political space in our federal system had been occupied by the Centre in the first 30 years of Independence, and most of what was still left after that was occupied by the States in the next 20 year. PRIs might have hoped to wrest some space from their immediate neighbour, the States, just as the States had wrested some from the Centre. But having at last managed to checkmate the Centre’s encroachments on their rights, the States were not about to allow the PRIs to do some encroaching of their own. By the 1980s and early 1990s, the only national party left, the Congress, had gone deeper into a siege mentality. Finding itself surrounded by State-level parties, it had built walls against them instead of winning them over. Next, the States retaliated by blocking Congress proposals for Panchayati Raj in Parliament, suspecting that the Centre would try to use panchayats to by-pass State Governments. The suspicion fed on the fact that the powers proposed by the Congress for panchayats were very similar to many of the more lucrative powers of State Governments. Statelevel leaders also feared, perhaps, that if panchayat-level leaders captured some of the larger PRIs, such as districtlevel panchayats, they would exert pressure on State-level leaders through intra-State multi-party federalizm. It soon became obvious to Congress leaders that there was no way the Panchayati Raj amendments they wanted to write into the Constitution would pass muster unless Statelevel parties were given their pound of flesh. The amendments were allowed only after it was agreed that the power of panchayats could be listed in the Constitution. Illustratively they would be defined and endowed on PRIs by the State Legislature acting at its discretion. This left the door wide open for the States to exert the power of the new political fact that while the Union and State Governments could afford to ignore panchayats as long as the MLAs were happy, the Union Governments had to be sensitive to the demands of States- level parties. This has given State-level actors strong beachheads on the shores of the both inter-State and intra-State federalism. By using various administrative devices and non-elected parallel structures, State Government have subordinated their PRIs to the State administration and given the upper hand to State Governments officials against the elected heads of PRIs. Panchayats have become local agencies for implementing schemes drawn up in distant state capitals. And their own volition has been further circumscribed by a plethora of “Centrally-sponsored schemes.” These are drawn up by even more distant Central authorities but at the same time tie up local staff and resources on pain of the schemes being switched off in the absence of matching local contribution. The “foreign aid” syndrome can be clearly seen at work behind this kind of “grass roots development”.

1. Which of the following best captures the current state of Indian federalizm as described in the passage? 1. The Supreme Court has not begun to extend the limits of its power. 2. The multi-party system has replaced the single party system. 3. The Union, State and Panchayati Raj levels have become real. 4. There is real distribution of power between the Union and State level parties. 2. The central theme of the passage can be best summarized as: 1. Our grassroots development at the panchayat level is now driven by the “foreign aid” syndrome. 2. Panchayati Raj is firmly entrenched at the lower level of our federal system of governance. 3. A truly federal polity has not developed since PRIs have not been allowed the necessary political space. 4. The Union government and State–level parties are engaged in a struggle for the protection of their respective rights. 3. The sentence in the last paragraph, “And their own volition has been further circumscribed …”, refers to: 1. The weakening of the local institutions’ ability to plan according to their needs. 2. The increasing demands made on elected local leaders to match central grants with local contributions. 3. The empowering of the panchayat system as implementers of schemes from State capitals. 4. The process by which the prescribed Central schemes are reformulated by local elected leaders. 4. What is the “dilemma” at the intra-State level mentioned in the first paragraph of the passage? 1. Should the state government wrest more space from the Union, before considering the panchayati system? 2. Should rights similar to those that the States managed to get be extended to panchayats as well? 3. Should the single party system which has withered away be brought back at the level of the States? 4. Should the States get “their pound of flesh” before allowing the Union government to pass any more laws? 5. Which of the following most closely describes the ‘fatal flaw’ that the passage refers to?

CAT 2003  1. The ways in which the democratic multi-party system works in an assertively pluralistic society like India’s are flawed. 2. The mechanisms that our federal system uses at the Union government level to deal with States are imperfect. 3. The instruments that have ensured federalism at one level, have been used to achieve the opposite at another. 4. The Indian Constitution and the spirit of the Indian polity are fatally flawed.

Passage  II The endless struggle between flesh and the spirit found an end in Greek art. The Greek artists were unaware of it. They were spiritual materialists, never denying the importance of the body and ever seeing in the body a spiritual significance. Mysticism on the whole was alien to the Greeks, thinkers as they were. Thought and mysticism never go well together and there is little symbolism in Greek art. Athena was not a symbol of wisdom but an embodiment of it and her statues were beautiful grave women, whose seriousness might mark them as wise, but who were marked in no other way. The Apollo Belvedere is not a symbol of the sun, nor the Versailles Artemis of the moon. There could be nothing less akin to the ways of symbolism than their beautiful, normal humanity. Nor did decoration really interest the Greeks. In all their art they were preoccupied with what they wanted to express, not with ways of expressing it, and lovely expression, merely as lovely expression, did not appeal to them at all. Greek art is intellectual art, the art of men who were clear and lucid thinkers, and it is therefore plain art. Artists than whom the world has never seen greater, men endowed with the spirit’s best gift, found their natural method of expression in the simplicity and clarity which are the endowment of the unclouded reason. “Nothing in excess,” the Greek axiom of art, is the dictum of men who would brush aside all obscuring, entangling superfluity, and see clearly, plainly, unadorned, what they wished to express. Structure belong in an especial degree to the province of the mind in art, and architectonics were preeminently a mark of the Greek. The power that made a unified whole of the trilogy of a Greek tragedy, that envisioned the sure, precise, decisive scheme of the Greek status, found its most conspicuous expression in Greek architecture. The Greek temple is the creation, par excellence, of mind and spirit in equilibrium. A Hindoo temple is a conglomeration of adornment. The lines of the building are completely hidden by the decorations. Sculptured figures and ornaments crowd its surface, stand out from it in thick masses, break it up into a bewildering series of irregular tiers. It is not a unity but

  3.37

a collection, rich, confused. It looks like something not planned but built this way and that as the ornament required. The conviction underlying it can be perceived: each bit of the exquisitely wrought detail had a mystical meaning and the temple’s exterior was important only as a means for the artist to inscribe thereon the symbols of the truth. It is decoration, not architecture. Again, the gigantic temples of Egypt, those massive immensities of granite which look as if only the power that moves in the earthquake were mighty enough to bring them into existence, are something other than the creation of geometry balanced by beauty. The science and the spirit are there, but what is there most of all is force, unhuman force, calm but tremendous, overwhelming. It reduces to nothingness all that belongs to man. He is annihilated. The Egyptian architects were possessed by the consciousness of the awful, irresistible domination of the ways of nature; they had no thought to give to the insignificant atom that was man. Greek architecture of the great age is the expression of men who were, first of all, intellectual artists, kept within the visible world by their mind, but, only second to that, lovers of the human world. The Greek temple is the perfect expression of the pure intellect illumined by the spirit. No other great buildings anywhere approach its simplicity. In the Parthenon, straight columns rise to plain capitals; a pediment is sculptured in bold relief; there is nothing more. And yet-here is the Greek miracle- this absolute simplicity of structure is alone in majesty of beauty among all the temples and cathedrals and palaces of the world. Majestic but human, truly Greek. No superhuman force as in Egypt; no strange supernatural shapes as in India; the Parthenon is the home of humanity at ease, calm, ordered, sure of itself and the world. The Greeks flung a challenge to nature in the fullness of their joyous strength. They set their temples on the summit of a hill overlooking the wide sea, outlined against the circle of the sky. They would build what was more beautiful than hill and sea and sky and greater than all these. It matters not at all if the temple is large or small; one never thinks of the size. It matters not how much it is in ruins. A few white columns dominate the lofty height at Sunion as securely as the great mass of the Parthenon dominates all the sweep of sea and land around Athens. To the Greek architect man was the world. His mind could understand its laws; his spirit could discover its beauty. 6. Which of the following is not a characteristic of Greek architecture, according to the passage? 1.  A lack of excess. 2.  Simplicity of form. 3.  Expression of intellect. 4.  Mystic spirituality.

3.38 

  CAT Papers

7. From the passage, which of the following combinations can be inferred to be correct?

1.  Hindoo temple- power of nature. 2.  Parthenon-simplicity. 3.  Egyptian temple-mysticism. 4.  Greek temple-symbolism.

8. According to the passage, what conception of man can be inferred from Egyptian architecture?

1.  Man is the center of creation. 2.  Egyptian temples save man from unhuman forces. 3.  Temples celebrate man’s victory over nature. 4. Man is inconsequential before the tremendous force of nature.

9. According to the passage, which of the following best explains why there is little symbolism in Greek art? 1. The Greeks focused on thought rather than mysticism. 2. The struggle between the flesh and the spirit found an end in Greek art. 3.  Greek artists were spiritual materialists. 4. Greek statues were embodiments rather than symbols of qualities. 10. “The Greeks flung a challenge to nature in the fullness of their joyous strength.” Which of the following best captures the ‘challenge’ that is being referred to? 1. To build a monument matching the background colours of the sky and the sea. 2. To build a monument bigger than nature’s creations. 3. To build monuments that were more appealing to the mind and spirit than nature’s creations. 4. To build a small but architecturally perfect monument.

Passage  III While I was in class at Columbia, struggling with the esoterica du jour, my father was on a bricklayer’s scaffold not far up the street, working on a campus building. Once we met up on the subway going home—he was with his tools, I with my books. My father wasn’t interested in Thucydides, and I wasn’t up on arches. My dad has built lots of places in New York City he can’t get into: Colleges, condos, office towers. He made his living on the outside. Once the walls were up, a place took on a different feel for him, as though he wasn’t welcome anymore. Related by blood, we’re separated by class, my father and I. Being the white-collar child of a bluecollar parent means being the hinge on the door between

two ways of life. With one foot in the working-class, the other in the middle class, people like me are Straddlers, at home in neither world, living a limbo life. What drove me to leave what I knew? Born blue-collar, I still never felt completely at home among the tough guys and anti-intellectual crowd of my neighbourhood in deepest Brooklyn. I never did completely fit in among the preppies and suburban royalty of Columbia, either. It’s like that for Straddlers. It was not so smooth jumping from Italian old-world style to US professional in a single generation. Others who were the first in their families to go to college, will tell you the same thing: the academy can render you unrecognizable to the very people who launched you into the world. The ideas and values absorbed in college the mom-and-pop orthodoxy that passed for truth for 18 years. Limbo folk may eschew polyester blends for sea-isle cotton, prefer Brie to Kraft slices. They marry outside the neighbourhood and raise their kids differently. They might not be in church on Sunday. When they pick careers (not jobs), it’s often a kind of work their parents never heard of or can’t understand. But for the white-collar kids of blue-collar parents, the office is not necessarily a sanctuary. In Corporate America, where the rules are based on notions foreign to working-class people, a Straddler can get lost. Social class counts at the office, even though nobody likes to admit it. Ultimately, corporate norms are based on middle-class values, business types say. From an early age, middle-class people learn how to get along, using diplomacy, nuance, and politics to grab what they need. It is as though they are following a set of rules laid out in a manual that blue-collar families never have the chance to read. People born into the middle class to parents with college degrees have lived lives filled with what French sociologist Pierre Bourdieu calls ‘cultural capital’. Growing up in an educated environment, they learn about Picasso and Mozart, stock portfolios and crème brulee. In a home with cultural capital, there are network: someone always has an aunt or golfing buddy with the inside track for an internship or some entry-level job. Dinner-table talk could involve what happened that day to mom and dad at the law firm, the doctors’ office, or the executive suite. Middle-class kids can grow up with a sense of entitlement that will carry them through their lives. This ‘belongingness’ is not just related to having material means, it also has to do with learning and possessing confidence in your place in the world. Such early access and direct exposure to culture in the home is the more organic, ‘legitimate’ means of appropriating cultural capital, Bourdieu tells us. Those of us possessing ‘ill-gotten Culture’ can learn it, but never as well. Something is always a little off about us, like an engine with imprecise timing. There’s greater match between middle-class lives and the institutions in which the middle class works and

CAT 2003  operates-universities or corporations. Children of the middle and upper classes have been speaking the language of the bosses and supervisors forever. Blue-collar kids are taught by their parents and communities to work hard to achieve, and that merit is rewarded. But no blue-collar parent knows whether such things are true in the middle-class world. Many professional born to the working–class report feeling out of the place and outmanoeuvred in the office. Soon enough, Straddlers learn that straight talk won’t always cut. Resolving conflicts head-on and speaking your mind doesn’t always work, no matter how educated the Straddler is. In the working-class, people perform jobs in which they are closely supervised and are required to follow orders and instructions. That, in turn, affects how they socialize their children. Children of the working-class are brought up in a home in which conformity, obedience and intolerance for back talk are the norm—the same characteristics that make a good factory worker. 11. According to the passage, which of the following statements about ‘cultural capital’ is not true? 1. It socializes children early into the norms of middle class institutions. 2. It helps them learn the language of universities and corporations. 3. It creates a sense of enlightenment in middle-class children. 4. It develops bright kids into Straddlers. 12. According to the passage, the patterns of socializations of working-class children make them most suited for jobs that require. 1.  Diplomacy 2.  Compliance with orders. 3.  Enterprise and initiative. 4.  High risk taking. 13. When Straddlers enter white collar jobs, they get lost because: 1.  They are thrown into an alien value system. 2. Their families have not read the rules in corporate manuals. 3. They have no one to guide them through the corporate maze. 4.  They miss the ‘mom and pop orthodoxy’. 14. What does the author’s statement, “My father wasn’t interested in Thucydides, and I wasn’t up on arches”, illustrate? 1.  Organic cultural capital. 2.  Professional arrogance and social distance.

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3.  Evolving social transformation. 4.  Breakdown of family relationship. 15. Which of the following statements about straddlers does the passage not support explicitly? 1. Their food preferences may not match those of their parents. 2. They may not keep up some central religious practices of their parents. 3. They are at home neither in the middle class nor in the working-class. 4. Their political ideologies may differ from those of their parents.

Passage  IV Pure love of learning, of course , was a less compelling motive for those who became educated for careers other than teaching. Students of law in particular had a reputation for being materialistic careerists in an age when law was becoming known as “the lucrative science” and its successful practice the best means for rapid advancement in the government of both church and state. Medicine too had its profit-making attraction. Those who did not go on to law or medicine could, if they had been well trained in the arts, gain positions at royal courts or rise in the clergy. Eloquent testimony to the profit motive behind much of twelfth-century education was the lament of a student of Abelard around 1150 that “Christians educate their sons … for gain, in order that the one brother, if he be a clerk, may help his father and mother and his other brothers, saying that a clerk will have no heir and whatever he has will be ours and the other brothers.” With the opening of positions in law, government, and the church, education became a means for advancement not only in income but also in status. Most who were educated were wealthy, but in the twelfth century, more often than before, many were not and were able to rise through the ranks by means of their education. The most familiar examples are Thomas Becket, who rose from a humble background to become chancellor of England and then archbishop of Canterbury, and John of Salisbury, who was born a “plebeian” but because of his reputation for learning died as bishop of Chartres. The instances of Becket and John of Salisbury bring us to the most difficult question concerning twelfthcentury education: To what degree was it still a clerical preserve? Despite the fact that throughout the twelfth century the clergy had a monopoly of instruction, one of the outstanding medievalists of our day, R. W. Southern, refers with good reason to the institutions staffed by the clergy as “secular schools.” How can we make sense out of the paradox that twelfth-century schools were clerical and yet “secular”?

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Let us look at the clerical side first. Not only were all twelfth-century teachers except professional and craftsmen in church orders, but in northern Europe students in school had clerical status and looked like priests. Not that all really were priests, but by virtue of being students all were awarded the legal privileges accorded to the clergy. Furthermore, the large majority of twelfth-century students, outside of the possible exception of Italy, if not already priests became so after their studies were finished. For these reasons, the term “cleric” was often used to denote a man who was literate and the term “layman” one who was illiterate. The English word for cleric, clerk, continued for a long time to be a synonym for student or for a man who could write, while the French word clerc even today has the connotation of intellectual. Despite all this, twelfth-century education was taking on many secular qualities in its environment, goals, and curriculum. Student life obviously became more secular when it moved out from the monasteries into the bustling towns. Most students wandered from town to town in search not only of good masters but also of worldly excitement, and as the twelfth century progressed they found the best of each in Paris. More important than environment was the fact that most students, even though they entered the clergy, had secular goals. Theology was recognized as the “queen of the sciences,” but very few went on to it. Instead they used their study of the liberal arts as a preparation for law, medicine, government service, or advancement in the ecclesiastical hierarchy. This being so, the curriculum of the liberal arts became more sophisticated and more divorced from religion. Teaching was still almost exclusively in Latin, and the first book most often read was the Psalter, but further education was no longer similar to that of a choir school. In particular, the discipline of rhetoric was transformed from a linguistic study into instruction in how to compose letters and documents; there was a new stress on logic; and in all the liberal arts and philosophy texts more advanced than those known in the early Middle Ages were introduced. Along with the rise of logic came the translation of Greek and Arabic philosophical and scientific works. Most important was the translation of almost all the writings of Aristotle, as well as his sophisticated Arabic commentators, which helped to bring about an intellectual revolution based on Greek rationalism. On a more prosaic level, contact with Arabs resulted in the introduction in the twelfth century of the Arabic numeral system and the concept of zero. Though most westerners first resisted this and made crude jokes about the zero as an ambitious number “that counts for nothing and yet wants to be counted,” the system steadily made its inroads first in Italy and then throughout Europe, thereby vastly simplifying the arts of computation and record keeping.

16. According to the passage, which of the following is the most noteworthy trend in education in twelfthcentury Europe? 1.  Secularization of education. 2. Flowering of theology as the queen of the sciences. 3.  Wealthy people increasingly turning to education. 4.  Rise of the clergy’s influence on the curriculum. 17. What does the sentence “Christians educate their sons… will be ours and the other brothers” imply? 1. The Christian family was a close-knit unit in the twelfth century. 2. Christians educated their sons not so much for the love of learning as for material gain. 3. Christians believed very strongly in educating their sons in the Church. 4. The relationship between Christian parents and their sons was exploitative in the twelfth century. 18. According to the passage, twelfth century schools were clerical and yet secular because: 1. Many teachers were craftsmen and professionals who did not form part of the church. 2. While the students had the legal privileges accorded to the clergy and looked like priests, not all were really priests. 3. The term ‘cleric’ denoted a literate individual rather than a strict association with the church. 4. Though the clergy had a monopoly in education, the environment, objectives and curriculum in the schools were becoming secular. 19. According to the author, in the twelfth century, individuals were motivated to get higher education because it: 1. Was a means for material advancement and higher status. 2.  Gave people with wealth an opportunity to learn. 3. Offered a coveted place for those with a love of learning. 4. Directly added to the income levels of people. 20. According to the passage, what led to the secularization of the curriculum of the liberal arts in the twelfth century? 1.  It was divorced from religion and its influences. 2. Students used it mainly as a base for studying law and medicine. 3. Teaching could no longer be conducted exclusively in Latin. 4.  Arabic was introduced into the curriculum.

CAT 2003 

Passage  V The invention of the gas turbine by Frank Whittle in England and Hans von Ohain in Germany in 1939 signalled the beginning of jet transport. Although the French engineer Lorin had visualized the concept of jet propulsion more than 25 years earlier, it took improved materials and the genius of Whittle and von Ohain to recognize the advantage that a gas turbine offered over a piston engine, including speeds in excess of 350 miles per hour. The progress from the first flight of liquid propellant rocket and jet-propelled aircraft in 1939 to the first faster-than-sound (supersonic) manned airplane (the Bell X-1) in 1947 happened in less than a decade. This then led very rapidly to a series of supersonic fighters and bombers, the first of which became operational in the 1950s. World War II technology foundations and emerging Cold War imperatives then led us into space with the launch of Sputnik in 1957 and the placing of the first man on the moon only 12 years later-a mere 24 years after the end of World War II. Now, a hypersonic flight can take you anywhere in the planet in less than four hours. British Royal Air force and Royal Navy, and the air forces of several other countries are going to use a single-engine cousin to the F/A- 22 called the F-35 Joint Strike Fighter. These planes exhibit stealthy angles and coatings that make it difficult for radar to detect them, among aviation’s most cutting-edge advances in design. The V-22, known as tilt-rotor, part helicopter, part airplane, takes off vertically, then tilts its engine forward for winged flight. It provides speed, three times the payload, five times the range of the helicopters it’s meant to replace. The new fighter, F-22 Raptor, with more than a million parts, shows a perfect amalgamation of stealth, speed, avionics and agility. It seems conventional forms, like the Predator and Global Hawk are passé, the stealthier unmanned aerial vehicles (UAVs) are in. They are shaped like kites, bats and boomerang, all but invisible to the enemy radar and able to remain over hostile territory without any fear of getting grilled if shot down. Will the UAVs take away pilots’ jobs permanently? Can a computer-operated machine take a smarter and faster decision in a war-like situation? The new free-flight concept will probably supplement the existing air traffic control system by computers on each plane to map the altitude, route, weather and other planes; and a decade from now, there will be no use of radar any more. How much bigger can the airplanes get? In the ‘50s they got speed, in the ‘80s they became stealthy. Now, they are getting smarter thanks to computer automation. The change is quite huge: from the four-seater to the A380 airplane. It seems we are now trading speed for size as we build a new superjumbo jet, the 555 seater A380, which will fly at almost the same speed of Boeing 707, introduced half a century ago, but with an improved capacity, range, greater fuel economy. A few years down the line will come

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the truly larger model, to be known as 747X. In the beginning of 2005, the A380, the world’s first fully doubledecked superjumbo passenger jet, weighing 1.2 million pounds, may carry a load of about 840 passengers. Barring the early phase, civil aviation has always lagged behind the military technologies (of jet engines, lightweight composite materials etc.). There are two fundamental factors behind the decline in commercial aeronautics in comparison to military aeronautics. There is no collective vision of our future such as the one that drove us in the past. There is also a need for a more aggressive pool of airplane design talents to maintain an industry that continues to find a multibillion dollar-a-year market for its product. Can the history of aviation technology tell us something about the futures of aeronautics? Have we reached a final state in our evolution to a mature technology in aeronautics? Are the challenges of coming out with the ‘better, cheaper, faster’ designs somehow inferior to those that are suited for ‘faster, higher , further’? Safety should improve greatly as a result of the forthcoming improvements in airframes, engine, and avionics. Sixty years from now, aircraft will recover on their own if the pilot loses control. Satellites are the key not only to GPS(global positioning system) navigation but also to in-flight communication, uplinked weather, and even in-flight e-mail. Although there is some debate about what type of engines will power future airplanes-light turbines, turbocharged diesels, or both- there is little debate about how these power plants will be controlled. Pilots of the future can look forward to more and better on-board safety equipment. 21. According to the first paragraph of the passage, which of the following statements is not false? 1. Frank Whittle and Hans Von Ohain were the first to conceive of jet propulsion. 2. Supersonic fighter planes were first used in the Second World War. 3. No man had traveled faster than sound until the 1950s. 4. The exploitation of jet propulsion for supersonic aviation has been remarkably fast. 22. What is the fourth paragraph of the passage about? 1.  Stealth, speed, and agility of new aircraft. 2.  The way aircraft size has been growing. 3.  Use of computer automation in aircraft. 4. Super-jumbo jets that can take more than 500 passengers. 23. What is the most noteworthy difference between V-22 and a standard airplane? The V-22: 1.  Can take off vertically. 2.  Has winged flight.

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3.  Has excellent payload. 4.  Has a very high range.

4. Dr Malek will read a paper on criminalization of politics.

24. Why might radars not be used a decade from now?

29. Business

1. Stealth technology will advance so much that it is pointless to use radar to detect aircraft.

1.  I want to do an MBA before going into business. 2.  My wife runs profitable business in this suburb.

2. UAVs can remain over hostile territory without any danger of being detected.

3. If we advertise we will get twice as much business as we have now.

3. Computers on board may enable aircraft to manage safe navigation on their own.

4. How you spend money is as much my business as yours.

4.  It is not feasible to increase the range of radars. 25. According to the author, commercial aeronautics, in contrast to military aeronautics, has declined because, among other things, 1. Speed and technology barriers are more easily overcome in military aeronautics. 2. The collective vision of the past continues to drive civil and commercial aeronautics. 3. Though the industry has a huge market, it has not attracted the right kind of aircraft designers. 4. There is a shortage of materials, like light weight composites, used in commercial aeronautics.

30. Service 1.  Customers have to service themselves at this canteen. 2.  It’s a service lift; don’t get into it. 3.  I’m not making enough even to service the loan. 4. Joyti’s husband has been on active service for three months. Direction for questions 31 to 38:  There are two gaps in each of the following sentences. From the pairs of words given, choose the one that fills the gaps most appropriately. The first word in the pair should fill the first gap.

Direction for questions 26 to 30:  In each question, the word at the top of the table is used in four different ways, numbered 1 to 4. Choose the option in which the usage of the word is incorrect or inappropriate.

31. This simplified __________ to the decision- making process is a must read for anyone_________ important real estate, personal , or professional decisions.

26. Help

3.  Introduction, under

1.  This syrup will help your cold.

4.  Guide, facing

2.  I can’t help the colour of my skin.

32. Physicians may soon have ___to help paralyzed people move their limbs by bypassing the ____nerves that once controlled their muscles.

3.  Ranjit may help himself with the beer in the fridge. 4.  Do you really expect me to help you out with cash?

1.  Primer, maximizing 2.  Tract, enacting

1.  Instruments, detrimental 2.  Ways, damaged 3.  Reason, involuntary 4.  Impediments, complex

2.  Has she given you any reason for her resignation?



3.  There is little reason in your pompous advice. 4. How do you deal with a friend who doesn’t listen to a reason?

33. The Internet is a medium where users have nearly _____ choices and ______ constraints about where to go and what to do.

28. Paper



27. Reason 1.  Your stand is beyond all reason.

1. Your suggestions look great on the paper, but are absolutely impractical. 2. Do you know how many trees are killed to make a truckload of paper? 3. So far I have been able to paper over the disagreements among my brothers.

1.  Unbalanced, nonexistent 2.  Embarrassing, no 3.  Unlimited, minimal 4.  Choking, shocking

34. The best punctuation is that of which the reader is least conscious; for when punctuation, or lack of it, ________ _____ itself, it is usually because it __________.

CAT 2003 

1.  Obtrudes, offends 2.  Enjoins, fails 3.  Conceals, recedes 4.  Effaces, counts

35. The argument that the need for a looser fiscal policy to____demand outweighs the need to ____ budget deficits is persuasive. 1.  Assess, minimize 2.  Outstrip, eliminate 3.  Stimulate, control 4.  Restrain, conceal 36. The Athenians on the whole were peaceful and prosperous; they had _____ to sit at home and think about the universe and dispute with Socrates, or to travel abroad and ____the world. 1.  Leisure, explore 2.  Time, ignore 3.  Ability, suffer 4.  Temerity, understand 37. Their achievement in the field of literature is described as ____________; sometimes it is even called ______. 1.  Magnificent, irresponsible 2.  Insignificant, influential 3.  Significant, paltry 4.  Unimportant, trivial 38. From the time she had put her hair up, every man she had met had groveled before her and she had acquired a mental attitude towards the other sex which was a blend of ________and________. 1.  Admiration, tolerance 2.  Indifference, contempt 3.  Impertinence, temperance 4.  Arrogance, fidelity Direction for questions 39 to 46:  The sentences given in each questions, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given to construct a coherent paragraph. 39. A. The wall does not simply divide Israel from a putative Palestinian state on the basis of the 1967 borders. B. A chilling omission from the road map is the gigantic ‘separation wall’ now being built in the West Bank by Israel.

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C. It is surrounded by trenches, electric wire and moats; there are watchtowers at regular intervals. D. It actually takes in new tracts of Palestinian land, sometimes five or six kilometers at a stretch. E. Almost a decade after the end of South African apartheid, this ghastly racist wall is going up with scarcely a peep from Israel’s American allies who are going to pay for most of it. 1.  EBCAD 4.  ECADB

2.  BADCE

3.  AEDCB

40. A. Luckily the tide of battle moved elsewhere after the American victory at Midway and an Australian victory over Japan at Milne Bay. B.  It could have been no more than a delaying tactic. C. The Australian military, knowing the position was hopeless, planned to fall back to the south-east in the hope of defending the main cities. D. They had captured most of the Solomon Islands and much of New Guinea, and seemed poised for an invasion. E. Not many people outside Australia realize how close the Japanese got. 1.  EDCBA 4.  CDBAE

2.  ECDAB

3.  ADCBE

41. A.  Call it the third wave sweeping the Indian media. B. Now, they are starring in a new role, as suave dealmakers who are in a hurry to strike alliances and agreements. C. Look around and you will find a host of deals that have been inked or are ready to be finalized. D. Then the media barons wrested back control from their editors, and turned marketing warriors with the brand as their missile. E. The first came with those magnificent men in their mahogany chambers who took on the world with their mighty fountain pens. 1.  ACBED 4.  AEDBC

2.  CEBDA

3.  CAEBD

42. A. The celebrations of economic recovery in Washington may be as premature as that “Mission Accomplished” banner hung on the USS Abraham Lincoln to hail the end of the Iraq war. B. Meanwhile, in the real world, the struggles of families and communities continue unabated. C. Washington responded to the favourable turn in economic news with enthusiasm. D. The celebrations and high-fives up and down Pennsylvania Avenue are not to be found beyond the Beltway.

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  CAT Papers

E. When the third quarter GDP showed growth of 7.2 per cent and the monthly unemployment rate dipped to 6 per cent, euphoria gripped the US capital. 1.  ACEDB 3.  ECABD

2.  CEDAB 4.  ECBDA

43. A. To much of the Labour movement, it symbolizes the brutality of the upper classes. B. And to everybody watching, the current mess over foxhunting symbolizes the government’s weakness. C. To foxhunting’s supporters, Labour’s 1991 manifesto commitment to ban it symbolizes the party’s metropolitan roots and hostility to the countryside. D. Small issues sometimes have large symbolic power. E. To those who enjoy thundering across the countryside in red coats after foxes, foxhunting symbolizes the ancient roots of rural lives. 1.  DEACB 3.  CEADB

2.  ECDBA 4.  DBAEC

44. A. In the case of the King Merolchazzar’s courtship of the Princess of the Outer Isles, there occurs a regrettable hitch. B. She acknowledges the gifts, but no word of a meeting date follows. C. The monarch, hearing good reports of a neighbouring princess, dispatches messengers with gifts to her court, beseeching an interview. D. The princess names a date, and a formal meeting takes place; after that everything buzzes along pretty smoothly. E. Royal love affairs in olden days were conducted on the correspondence method. 1.  ACBDE 3.  ECDAB

2.  ABCDE 4.  ECBAD

45. A. Who can trace to its first beginnings the love of Damon for Pythias, of David for Jonathan, of Swan for Edgar? B.  Similarly with men. C. There is about great friendships between man and man a certain inevitability that can only be compared with the age-old association of ham and eggs. D. One simply feels that it is one of the things that must be so. E. No one can say what was the mutual magnetism that brought the deathless partnership of these wholesome and palatable foodstuffs about. 1.  ACBED 3.  ACEBD

2.  CEDBA 4.  CEABD

46. A Events intervened, and in the late 1930s and 1940s, Germany suffered from “over-branding”. B. The British used to be fascinated by the home of Romanticizm. C. But reunification and the federal government’s move to Berlin have prompted Germany to think again about its image. D. The first foreign package holiday was a tour of Germany organized by Thomas Cook in 1855. E. Since then, Germany has been understandably nervous about promoting itself abroad. 1.  ACEBD 3.  BDAEC

2.  DECAB 4.  DBAEC

Direction for questions 47 to 50:  Four alternative summaries are given below each text. Choose the option that best captures the essence of the text. 47. Some decisions will be fairly obvious—“no-brainers.” Your bank account is low, but you have a two-week vacation coming up and you want to get away to some place warm to relax with your family. Will you accept your ‘in-laws’ offer of free use of their Florida beachfront condo? Sure. You like your employer and feel ready to move forward in your career. Will you step in for your boss for three weeks while she attends a professional development course? Of course. A.  Some decisions are obvious under certain circumstances. You may, for example, readily accept a relative’s offer of free holiday accommodation. Or step in for your boss when she is away. B. Some decisions are no-brainers. You need not think when making them. Examples are condo offers from in-laws and job offers from bosses when you bank account is low or boss is away. C. Easy decisions are called “no-brainer” because they do not require any cerebral activity. Examples such as accepting free holiday accommodation abound in our lives. D. Accepting an offer from in-laws when you are short on funds and want a holiday is a no-brainer. Another no-brainer is taking the boss’s job when she is away. 1.  A 3.  C

2.  B 4.  D

48. Physically, inertia is a feeling that you can’t move; mentally, it is a sluggish mind. Even if you try to be sensitive, if your mind is sluggish, you just don’t feel anything intensely. You may even see a tragedy enacted in front of your eyes and not be able to respond meaningfully. You may see one person

CAT 2003  exploiting another, one group persecuting another and not be able to get angry. Your energy is frozen. You are not deliberately refusing to act; you just don’t have the capacity. A. Inertia makes your body and mind sluggish. They become insensitive to tragedies, exploitation, and persecution because it freezes your energy and decapacitates it. B. When you have inertia you don’t act although you see one person exploiting another or one group persecuting another. You don’t’ get angry because you are incapable. C. Inertia is of two types-physical and mental. Physical inertia restricts bodily movements. Mental inertia prevents mental response to events enacted in front of your eyes. D.  Physical inertia stops your body from moving; mental inertia freezes your energy, and stops your mind from responding meaningfully to events, even tragedies, in front of you. 1.  A 3.  C

2.  B 4.  D

49. Try before you buy. We use this memorable saying to urge you to experience the consequences of an alternative before you choose it, whenever this is feasible. If you are considering buying a van after having always owned sedans, rent one for a week or borrow a friend’s. By experiencing the consequences first hand, they become more meaningful. In addition, you are likely to identify consequences you had not even thought of before. May be you will discover that it is difficult to park the van in your small parking space at work, but that, on the other hand, your elderly father has a much easier time getting in and out of it. A. If you are planning to buy a van after being used to sedans, borrow a van or rent it and try it before deciding to buy it. Then you may realize that parking a van is difficult while it is easier for your elderly father to get in and out of it. B. Before choosing an alternative, experience its consequence if feasible. If, for example, you want to change from sedans to a van, try one before buying it. You will discover aspects you may never have thought of. C. Always try before you buy anything. You are bound to discover many consequences. One of the consequences of going in for a van is that it is more difficult to park than sedans at the office car park. D. We urge you to try products such as vans before buying them. Then you can experience consequences you have not thought of such as parking

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problems. But your father may find vans more comfortable than cars. 1.  A 3.  C

2.  B 4.  D

50. It is important for shipping companies to be clear about the objectives for maintenance and materials management—as to whether the primary focus is on service level improvement or cost minimization. Often when certain systems are set in place, the cost minimization objective and associated procedure become more important than the flexibility required for service level improvement. The problem really arises since cost minimization tends to focus on out of pocket costs which are visible, while the opportunity costs, often greater in value, are lost sight of. A. Shipping companies have to either minimize costs or maximize quality. If they focus on cost minimization, they will reduce quality. They should focus on service level improvement, or else opportunity costs will be lost sight of. B. Shipping companies should determine the primary focus of their maintenance and materials management. Focus on cost minimization may reduce visible costs, but ignore greater invisible costs and impair service quality. C. Any cost minimization program in shipping is bound to lower the quality of service. Therefore, shipping companies must be clear about the primary focus of their maintenance and materials management before embarking on cost minimization. D. Shipping companies should focus on quality level improvement rather than cost cutting. Cost cutting will lead to untold opportunity costs. Companies should have systems in place to make the service level flexible. 1.  A 3.  C

2.  B 4.  D

  SECTION  II Direction for questions 51 to 53:  Answer the questions on the basis of the information given below. The seven basic symbols in a certain numeral system and their respective values are as follows: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500 and M = 1000 In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times: the value of the numeral is the sum of the values of the symbols. For example, XXVII =

3.46 

  CAT Papers

10 + 10 + 5 + I + 1 = 27. An exception to the left-to-right reading occurs when a symbol is’ followed immediately by a symbol of greater value; then the smaller value is subtracted from the larger. For example, XLVI = (50 — 10) + 5 + 1 = 46. 51. The value of the numeral MDCCLXXXVII is 1.  1687 3.  1887

2.  1787 4.  1987

52. The value of the numeral MCMXC IX is 1.  1999 3.  1989

2.  1899 4.  1889

53. Which of the following represent the numeral for 1995? I.  MCMLXXV III.   MVD

II.  MCMXCV IV.  MVM

1.  Only I and II 2.  Only Ill and IV 3.  Only II and IV 4.  Only IV Direction for questions 54 to 56: Answer the questions on the basis of the information given below. Consider three circular parks of equal size with centres at A1, A2 and A3 respectively. The parks touch each other at the edge as shown in the figure (not drawn to scale). There are three paths formed by the triangles A1A2A3, B1B2B3 and C1C2C3 as shown. Three sprinters A, B, and C begin running from points A1, B1 and C1, respectively. Each sprinter traverses her respective triangular path clockwise and returns to her starting point.

55. Sprinter A traverses distance A1A2, A2A3 and A3A1 at an average speeds of 20, 30 and 15 respectively. B traverses   __ her entire path at a uniform speed of ​( 10 ​ √  3 ​ +20 )​. C traverses distances C C , C C and C3C1 at an average speed   __ 40  1 __2 2 ) 3 __ of ___ ​ 40     ​ ​    3 ​ +1, ​    ​​( ​ √ √ 3 3   3 ​ + 1  ​and 120 respectively. All speeds are in same unit. Where would B and C be respectively when A finishes her sprint?

1.  B1,C1 2.  B3,C3 3.  B1, C3 4.  B1, Somewhere between C3 and C1

56. Sprinters A, B and C traverse their respective paths at uniform speeds of u, v and w respectively. It is known that u2:v2:w2 is equal to Area A: Area B: Area C, where Area A, Area B and Area C are the areas of triangles A1A2A3, B1 B2B3, and C1C2C3 respectively. Where would A and C be when B reaches point B3?

1.  A2, C3 2.  A3, C3 3.  A3, C2 4. some where between A2 and A3, somewhere between C3 and C1

Direction for questions 57 to 59:  Answer the questions on the basis of the information given below.

Consider a cylinder of height h cm and radius r = _​ π2 ​ cm as shown in the figure (not drawn to scale). A string of a certain length, when wound on its cylindrical surface, starting at point A and ending at point B, gives a maximum of n turns (in other words, the string’s length is the minimum length required to wind n turns). 57. What is the vertical spacing between the two consecutive turns? 1.  __ ​ hn ​cm

h 3. ​ __   ​cm n2

54. Let the radius of each circular park be r, and the distances to be traversed by the sprinters A. B and C be a, b and c respectively. Which of the following is true?  

__

1.  b – a = c – b = 3​ √  3r ​   

2.  ___ ​   h__   ​ cm ​ √  n ​ 

4.  Cannot be determined

58. The same string, when wound on the exterior four walls of a cube of side n cm, starting at point C and ending at point D, can give exactly one turn (see figure, not drawn to scale). The length of the string is

D

__

2.  b – a = c – b =​ √  3r ​  __

3.  b = ____ ​ a +2  c   ​= 2 ​( 1 + ​ √  3 ​  )​  

__

4.  c = 2b – a = ​( 2 + ​ √  3 ​  )​  

C

CAT 2003   

__

 

1. ​ √  2 ​ n cm

___

2.  ​ √  17 ​ n cm ___

 

3.  n cm

4.  h=​ √  13 ​ n cm

59. In the set-up of the previous two questions, how is h related to n?  

__

 

1.  h = ​ √  2 ​ n 3.  h=n

___

2.  h = ​ √  17 ​ n   ___ 4.  h= ​ √  13 ​ n

Direction for questions 60 to 93: Answer the following questions independently. 60. There are 12 towns grouped into four zones with three towns per zone. It is intended to connect the towns with a telephone lines such that every two towns are connected with three direct lines if they belong to the same zone, and with only one direct line otherwise. How many direct telephone lines are required? 1.  72 3.  96

2.  90 4.  144

61. In the figure (not drawn to scale) given below, P is a point on AB such that AP: PB = 4 : 3. PQ is parallel to AC and QD is parallel to CP. In ∆ARC, ∠ARC = 90o and in ∠PQS, ∠PSQ = 90o. The length of QS is 6 cm. What is the ratio of AP: PD?

1.  10:3 3.  7:3

2.  2:1 4.  8:3

62. A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 min for the angle of elevation to change from 450 to 600. After how much more time will this car reach the base of the tower? __

 

__

__

2.  6​( ​ √  3 ​ +​ √  2 ​  )​   __ 4.  8​( ​ √  3 ​ –2 )​

1. ​( 5​ √  3 ​ + 1 )​   __ 3.  7​( ​ √  3 ​ –1 )​

 

 

63. In the figure (not drawn to scale) given below. If AD = CD= BC and ∠BCE = 96º, how much is the value of ∠DBC? C

α A

α

D

β

96˚

β

1.  32º 3.  64º

  3.47

2.  84º 4.  cannot be determined

64. If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the of ax2 + bx + 1 = 0 having real roots is 1.  10 3.  6

2.  7 4.  12

65. If log10x - log10 √x = 2 logx10, then the possible value of x is given by 1.  10 1 3. ​ ____    ​   1000

1 2. ​ ___ 100    ​ 4.  None of the

66. What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7? 1.  666

2.  676

3.  683

4.  777

67. An intelligence agency forms a code of two distinct digits selected from 0,1, 2, ..., 9 such that first digit of the code is non-zero. The code, handwritten on a slip, can however potentially create confusion when read upside down-for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise? 1.  80 3.  71

2.  78 4.  69

68. Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from square cloth piece of side a in the following steps: the original square of side a is divided into smaller squares, not necessarily of the same size, then a circle of maximum possible area is from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes: The ratio of the total area of scrap cloth generate in the former to that in the latter is  

__

1.  1:1 2. ​√  2 ​ : 1 n ​( 4–� )​ 4n–�   4. ​ ______  ​ 3. ​ ______ 4n– � ​   n​( 4– � )​ 69. In the figure below (not drawn to scale), rectangle ABCD is inscribed in the circle with centre at O.The length of side AB is greater than side BC. The ratio of the __area of the circle to   the area of the rectangle ABCD is � : ​ √ 3 ​ . The line segment DE intersects AB at E such that ∠ODC = ∠ADE.

  CAT Papers

3.48 

__

 

 

__

2.  1: ​ √  2 ​  4.  1:2

  1.  1: ​ √  3 ​__   3.  1:2 ​ √  3 ​  

70. If _​ 13 ​log3 M + 3log3 N = 1 + log0.008 5, then

9 1.  M = __ ​ N   ​ 3 3.  M3 = __ ​ N   ​  

9 2.  N = __ ​ M   ​ 3 4.  N9 = __ ​ M   ​

9

9

71. Using only 2,5,10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs 1.01 to three different persons? 1.  19 3.  17

2.  20 4.  18

77. If three positive real numbers x, y and z satisfy y - x = z - y and x y z = 4, then what is the minimum possible value of y? 1.  211/3 3.  21/4

2.  22/3 4.  23/4

78. In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes a tangent to the circle at point C. If ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is

72. The length of the circumference of a circle equals the perimeter of a triangle of equal sides, and also the perimeter of a square. The areas covered by the circle, triangle, and square are c, t and s, respectively. Then, 1.  s>t>c 3.  c>s>t

1.  1000 3.  800

2.  c>t>s 4.  s>c>t

2.  1500 4.  not possible to determine

73. What is the remainder when 496 is divided by 6?

9 __ 16 25 79. The infinite sum 1 + _​ 47 ​+ ​ __   ​+ ​    ​+​ __  ​+ ....equals 72 73 74

1.  0 3.  3

  27 a.​ ___ 14  ​

21 b. ​ __ 13 ​

49 c. ​ __ 27 ​

256 d. ​ ___ 147  ​

2.  2 4.  4

74. If x and y are integers, then the equation 5x + 19y = 64 has

1.  No solution for x < 300 and y < 0 2.  0no solution for x > 250 and y > - 100 3.  a solution for 250 < x < 300 4.  a solution for - 59 √ ​  n ​ 



  Therefore, statement B is true.

87. (2)  x = –|a|b

  Now a – xb = a – (-|a|b)b



  = a + |a|b2



  ∴ a – xb = a + ab2 ….. a ≥ 0 OR a – xb



  = a – ab2 …. A < 0



  = a(1+b2) = a(1-b2)



  Consider first case:



α + 3α + 4α + 5 = 0



α3 + 2α2 + 7α + 3 = 0



α2 – 3α + 2 = 0



  As a ≥ 0 and |b| ≥ 1, therefore (1+b2) is positive.



α=2, α = 1



  ∴ a (1 + b2) ≥ 0



  ∴ a – xb ≥ 0

3

2

​ n1 ​ < x ≤ 3 + _​ n1 ​  83. (3)  1– _

  Put n = 1



  Consider second case.



  ∴0 0 4.  minimized whenever a > 0, b< 0 57. Each family in a locality has at most two adults, and no family has less than 3 children. Consider­ing all the families together, there are more adults than boys, more boys than girls, and more girls than families, Then the minimum possible number of families in the locality is 1.  4

2.  5

3.  2

4.  3

58. The total number of integers pairs (x, y) satisfying the equation x + y = xy is 1.  0

2.  1

3.  2

4.  None of the above

1.  No solution for x. 2.  Exactly one solution for x. 3.  Exactly two distinct solutions for x. 4.  Exactly three distinct solutions for x. Direction for questions 63 and 64: Answer the questions on the basis of the information given below. f1(x)

= x

0≤x≤1



= 1

x≥1



= 0

Otherwise

f2(x)

= f1(–x) for all x

f3(x)

= – f2(x) for all x

f3(x)

= f3(–x) for all x

63. How many of the following products are necessarily zero for every x?

Part B Direction for questions 59 to 62: Answer the questions independently of each other. 59. Let C be a circle with centre P0 and AR be a diameter of C. Suppose P1 is the mid point of the line segment P0B, P2 is the mid-point of the line segment P1 B and so on. Let C1 C2 C3 be circles with diameters P0P1, P1P2, P2P3.. respectively. Suppose the circles C1 C2 C3 are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle is

f1(x)f2(x), f2(x)f3(x), f2(x)f4(x)? 1.  0

2.  1

3.  2

4.  3

64. Which of the following is necessarily true? 1.  f4(x) = f1(x) for all x 2.  f1(x) = –f3(—x) for all x 3.  f2(–x) = f4(x) for all x

1.  8 : 9

2.  9 : 10

4.  f1(x) + f3(x) = 0 for all x.

3.  10 : 11

4.  11 : 12

65. If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be:

60. Consider the sequence of numbers a1, a2, a3… to infinity where a1 = 81.33 and a2 = –19 and aj = aj–1

CAT 2004  __ 1.  3 – 2​√2 ​   __ 3.  7 – 4​√2 ​  

  3.77

__ 2.  4 – 2​√2 ​  __ 4.  6 – 4 ​√2 ​ 

69. In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If ∠CBE =65°, then what is the value of ∠DEC?

1.  Equal to the side of cube. 2.  Times the side of the cube. 3.  Times the side of the cube. 4.  Impossible to find from the given information. 66. In the adjoining figure, the lines represent one-way roads allowing travel only northwards or only westwards. Along how many distinct routes can a car reach point B from point A?

1.  15

2.  56

3.  120

4.  336

67. On a semicircle with diameter AD, chord BC is parallel to the diameter. Further, each of the chords AB and CD has length 2, while AD has length 8. What is the length of BC?

1.  35˚

2.  55˚

3.  45˚

4.  25˚

Direction for questions 70 and 71: Answer the questions on the basis of the information given below. In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60 percent of the total marks. 70. If group B contains 23 questions, then how many questions are there in Group C? 1.  1

2.  2

3.  3

4.  Cannot be determined

71. If group C contains 8 questions and group B carries at least 20 per cent of the total marks, which of the following best describes the number of questions in group B? 1.  11 or 12

2.  12 or 13

3.  13 or 14

4.  14 or 15

1.  7.5

2.  7

Direction for questions 72 and 73: Answer the questions independently of each other.

3.  7.75

4.  None of these

72. The remainder, when (1523 + 2323) is divided by 19, is

68. A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?

1.  4

2.  15

3.  0

4.  18

73. A new flag is to be designed with six vertical stripes using some or all of the colours yellow, green, blue and red. Then, the number of ways this can be done so that no two adjacent stripes have the same colour is 1.  12 × 81

2.  16 × 192

3.  20 × 125

4.  24 × 216

3.78 

  CAT Papers

Sub-section III–A

7 9. 1.  interest 3.  principal

Number of questions = 50

80.

Note:  Questions 74 to 83 carry half a mark each. All the other questions in Sub-section III–A carry one mark each.

1.  sanctions 3.  fees 81.

Direction for questions 74 to 83: Fill up the blanks, numbered [1], [2] … up to [10], in the two passages below with the most appropriate word from the options given for each blank.

1.  closed 3.  attached

Section  III

At that time the White House was as serene as a resort hotel out of season. The corridors were [1]. In the various offices, [2] gray men in waistcoats talked to one another in lowpitched voices. The only color, or choler, curiously enough, was provided by President Eisenhower himself. Apparently, his [3] was easily set off; he scowled when he [4] the corridors. 74. 1.  striking

2.  hollow

3.  empty

4.  white

75. 1.  quiet

2.  faded

3.  loud

4.  stentorian

76. 1.  laughter

2.  curiosity

3.  humour

4.  temper

77. 1.  paced

2.  strolled

3.  stormed

4.  prowled

“Between the year 1946 and the year 1955, I did not file any income tax returns.” With that [5] statement, Ramesh embarked on an account of his encounter with the Income Tax Department. “I originally owed Rs 20,000 in unpaid taxes. With [6] and [7], Rs 20,000 became Rs 60,000. The Income Tax Department then went into action, and I learned first hand just how much power the Tax Department wields. Royalties and trust funds can be [8]; automobiles may be [9], and auctioned off. Nothing belongs to the [10] until the case is settled.” 78. 1.  devious 3.  tactful

2.  blunt 4.  pretentious

2.  taxes 4.  returns 2.  refunds 4.  fines 2.  detached 4.  impounded

82. 1.  smashed 3.  dismantled

2.  seized 4.  frozen

83. 1.  purchaser

2.  victim

3.  investor

4.  offender

Direction for questions 84 to 86: Identify the incorrect sentence. 84. A.  Last Sunday, Archana had nothing to do. B. After waking up, she lay on the bed thinking of what to do. C.  At 11 o’clock she took shower and got ready. D.  She spent most of the day shopping. 1.  B and C

2.  C

3.  A and B

4.  B, C, and D

85. A. It was a tough situation and Manasi was taking pains to make it better. B. Slowly her efforts gave fruit and things started improving. C.  Everyone complemented her for her good work. D. She was very happy and thanked everyone for their help. 1.  A

2.  D

3.  B and C

4.  A and C

86. A.  Harish told Raj to plead guilty. B.  Raj pleaded guilty of stealing money from the shop. C. The court found Raj guilty of all the crimes he was charged with. D.  He was sentenced for three years in jail.

CAT 2004  1.  A and C

2.  B and D

3.  A, C, and D

4.  B, C, and D

Direction for questions 87 to 89:  Each statement has a part missing. Choose the best option from the four options given below the statement to make up the missing part. 87. Archaeologists believe that the pieces of red–ware pot-

tery excavated recently near Bhavnagar and ________ shed light on a hitherto dark 600-year period in the Harappan history of Gujarat.

1. Estimated with a reasonable certainty as being about 3400 years old, 2. Are estimated reasonably certain to be about 3400 years old, 3. Estimated at about 3400 years old with reasonable certainty, 4. Estimated with reasonable certainty to be about 3400 years old, 88. Many people suggest __________ and still others would like to convince people not to buy pirated cassettes 1. To bring down audiocassette prices to reduce the incidence of music piracy, others advocate strong legal action against the offenders, 2. Bringing down audiocassette prices to reduce the incidents of music piracy, others are advocating strong legal action against offenders, 3. Bringing down audiocassette prices to reduce the incidence of music piracy, others advocate strong legal action against offenders, 4. Audiocassette prices to be brought down to reduce incidence of music piracy, others advocate that strong legal action must be taken against offenders, 89. The ancient Egyptians believed _____________ so that when these objects were magically reanimated through the correct rituals, they would be able to function effectively. 1. That it was essential that things they portrayed must have every relevant feature shown as clearly as possible, 2. It was essential for things they portray to have had every relevant feature shown as clearly as possible, 3. It was essential that the things they portrayed had every relevant feature shown as clearly as possible, 4. That when they portrayed things, it should have every relevant feature shown as clearly as possible

  3.79

Direction for questions 90 to 92: In each question, the word at the top of the table is used in four different ways, numbered 1 to 4. Choose the option in which the usage of the word is incorrect or inappropriate. 90. FALLOUT 1. Nagasaki suffered from the fallout of nuclear radiation. 2. People believed that the political fallout of the scandal would be insignificant. 3. Who can predict the environmental fallout of the WTO agreements? 4. The headmaster could not understand the fallout of several of his good students at the Public examination. 91. PASSING 1.  She did not have passing marks in mathematics 2. The mad woman was cursing everybody passing her on the road. 3. At the birthday party all the children enjoyed a game of passing the parcel. 4. A passing taxi was stopped to rush the accident victim to the hospital 92. BOLT 1.  The shopkeeper showed us a bolt of fine silk. 2.  As he could not move, he made a bolt for the gate. 3.  Could you please bolt the door? 4. The thief was arrested before he could bolt from the scene of the crime. Direction for questions 93 to 95: The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 93. A. In the west, Allied Forces had fought their way through southern Italy as far as Rome. B. In June 1944, Germany’s military position in World War Two appeared hopeless. C. In Britain, the task of amassing the men and materials for the liberation of northern Europe had been completed. D. The Red Army was poised to drive the Nazis back through Poland. E.  The situation on the eastern front was catastrophic.

3.80 

  CAT Papers

1.  EDACB

2.  BEDAC

3.  BDECA

4.  CEDAB

94. A. He felt justified in bypassing Congress altogether on a variety of moves. B.  At times he was fighting the entire Congress. C. Bush felt he had a mission to restore power to the presidency. D.  Bush was not fighting just the democrats. E. Representative democracy is a messy business, and a CEO of the White House does not like a legislature of second guessers and time wasters. 1.  CAEDB

2.  DBAEC

3.  CEADB

4.  ECDBA

95. A.  The two neighbours never fought each other. B. Fights involving three male fiddler crabs have been recorded, but the status of the participants was unknown. C.  They pushed or grappled only with the intruder. D. We recorded 17 cases in which a resident that was fighting an intruder was joined by an immediate neighbour, an ally. E. We therefore tracked 268 intruder males until we saw them fighting a resident male. 1.  BEDAC

2.  DEBAC

3.  BDCAE

4.  BCEDA

Direction for questions 96 and 97: Four alternative summaries are given below each text. Choose the option that best captures the essence of the text. 96. The human race is spread all over the world, from the polar regions to the tropics. The people of whom it is made up eat different kinds of food, partly according to the climate in which they live, and partly according to the kind of food which their country produces. In hot climates, meat and fat are not much needed; but in the Arctic regions they seem to be very necessary for keeping up the heat of the body. Thus, in India, people live chiefly on different kinds of grains, eggs, milk, or sometimes fish and meat. In Europe, people eat more meat and less grain. In the Arctic regions, where no grains and fruits are produced, the Eskimo and other races live almost entirely on meat and fish. 1. Food eaten by people in different regions of the world depends on the climate and produce of the region, and varies from meat and fish in the Arctic to predominantly grains in the tropics.

2. Hot climates require people to eat grains while cold regions require people to eat meat and fish. 3. In hot countries, people eat mainly grains while in the Arctic, they eat meat and fish because they cannot grow grains. 4. While people in Arctic regions like meat and fish and those in hot regions like India prefer mainly grains, they have to change what they eat depending on the local climate and the local produce. 97. You seemed at first to take no notice of your school– fellows, or rather to set yourself against them because they were strangers to you. They knew as little of you as you did of them; this would have been the reason for their keeping aloof from you as well, which you would have felt as a hardship. Learn never to conceive a prejudice against others because you know nothing of them. It is bad reasoning, and makes enemies of half the world. Do not think ill of them till they behave ill to you; and then strive to avoid the faults which you see in them. This will disarm their hostility sooner than pique or resentment or complaint.

1. The discomfort you felt with your school fellows

was because both sides knew little of each other. You should not complain unless you find others prejudiced against you and have attempted to carefully analyze the faults you have observed in them.

2. The discomfort you felt with your school fellows was because both sides knew little of each other. Avoid prejudice and negative thoughts till you encounter bad behaviour from others, and then win them over by shunning the faults you have observed. 3. You encountered hardship amongst your school fellows because you did not know them well. You should learn to not make enemies because of your prejudices irrespective of their behaviour towards you. 4. You encountered hardship amongst your school fellows because you did not know them well. You should learn to not make enemies because of your prejudices unless they behave badly with you. Direction for questions 98 to 117: Each of the five passages given below is followed by a set of questions. Choose the best answer to each question.

PASSAGE  I Recently I spent several hours sitting under a tree in my garden with the social anthropologist William Ury, a Harvard University professor who specializes in the art of negotiation and wrote the bestselling book, Getting to Yes. He captivated me with his theory that tribalizm protects people from their

CAT 2004  fear of rapid change. He explained that the pillars of tribalizm that humans rely on for security would always counter any significant cultural or social change. In this way, he said, change is never allowed to happen too fast. Technology, for example, is a pillar of society. Ury believes that every time technology moves in a new or radical direction, another pillar such as religion or nationalism will grow stronger—in effect, the traditional and familiar will assume greater importance to compensate for the new and untested. In this manner, human tribes avoid rapid change that leaves people insecure and frightened. But we have all heard that nothing is as permanent as change. Nothing is guaranteed. Pithy expressions, to be sure, but no more than cliches. As Ury says, people don’t live that way from day-to-day. On the contrary, they actively seek certainty and stability. They want to know they will be safe. Even so, we scare ourselves constantly with the idea of change. An IBM CEO once said: ‘We only re-structure for a good reason, and if we haven’t re-structured in a while, that’s a good reason.’ We are scared that competitors, technology and the consumer will put us out of business—so we have to change all the time just to stay alive. But if we asked our fathers and grandfathers, would they have said that they lived in a period of little change? Structure may not have changed much. It may just be the speed with which we do things. Change is over–rated, anyway. Consider the automobile. It’s an especially valuable example, because the auto industry has spent tens of billions of dollars on research and product development in the last 100 years. Henry Ford’s first car had a metal chassis with an internal combustion, gasoline–powered engine, four wheels with rubber tyres, a foot operated clutch assembly and brake system, a steering wheel, and four seats, and it could safely do 18 miles per hour. A hundred years and tens of thousands of research hours later, we drive cars with a metal chassis with an internal combustion, gasoline–powered engine, four wheels with rubber tyres, a foot operated clutch assembly and brake system, a steering wheel, four seats—and the average speed in London in 2001 was 17.5 miles per hour! That’s not a hell of a lot of return for the money. Ford evidently doesn’t have much to teach us about change. The fact that they’re still manufacturing cars is not proof that Ford Motor Co. is a sound organization, just proof that it takes very large companies to make cars in great quantities —making for an almost impregnable entry barrier. Fifty years after the development of the jet engine, planes are also little changed. They’ve grown bigger, wider and can carry more people. But those are incremental, largely cosmetic changes. Taken together, this lack of real change has come to mean that in travel—whether driving or flying—time and

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technology have not combined to make things much better. The safety and design have of course accompanied the times and the new volume of cars and flights, but nothing of any significance has changed in the basic assumptions of the final product. At the same time, moving around in cars or aeroplanes becomes less and less efficient all the time. Not only has there been no great change, but also both forms of transport have deteriorated as more people clamour to use them. The same is true for telephones, which took over hundred years to become mobile, or photographic film, which also required an entire century to change. The only explanation for this is anthropological. Once established in calcified organizations, humans do two things: sabotage changes that might render people dispensable, and ensure industry-wide emulation. In the 1960s, German auto companies developed plans to scrap the entire combustion engine for an electrical design. (The same existed in the 1970s in Japan, and in the 1980s in France.) So for 40 years we might have been free of the wasteful and ludicrous dependence on fossil fuels. Why didn’t it go anywhere? Because auto executives understood pistons and carburettors, and would be loath to cannibalize their expertise, along with most of their factories. 98. Which of the following best describes one of the main ideas discussed in the passage? 1.  Rapid change is usually welcomed in society. 2.  Industry is not as innovative as it is made out to be. 3.  We should have less change than what we have now. 4.  Competition spurs companies into radical innovation. 99. According to the passage, which of the following statements is true? 1. Executives of automobile companies are inefficient and ludicrous. 2. The speed at which an automobile is driven in a city has not changed much in a century. 3. Anthropological factors have fostered innovation in automobiles by promoting use of new technologies. 4. Further innovation in jet engines has been more than incremental. 100. Which of the following views does the author fully

support in the passage?

1.  Nothing is as permanent as change. 2.  Change is always rapid. 3. More money spent on innovation leads to more rapid change. 4. Over decades, structural change has been incremental.

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101. According to the passage, the reason why we continued to be dependent on fossil fuels is that: 1.  Auto executives did not wish to change. 2.  No alternative fuels were discovered. 3.  Change in technology was not easily possible. 4. German, Japanese and French companies could not come up with new technologies.

PASSAGE  II The painter is now free to paint anything he chooses. There are scarcely any forbidden subjects, and today everybody is prepared to admit that a painting of some fruit can be as important as a painting of a hero dying. The Impressionists did as much as anybody to win this previously unheard–of freedom for the artist. Yet, by the next generation, painters began to abandon the subject altogether, and began to paint abstract pictures. Today the majority of pictures painted are abstract. Is there a connection between these two developments’? Has art gone abstract because the artist is embarrassed by his freedom? Is it that, because he is free to paint anything, he doesn’t know what to paint? Apologists for abstract art often talk of it as the art of maximum freedom. But could this be the freedom of the desert island? It would take too long to answer these questions properly. I believe there is a connection. Many things have encouraged the development of abstract art. Among them has been the artists’ wish to avoid the difficulties of finding subjects when all subjects are equally possible. I raise the matter now because I want to draw attention to the fact that the painter’s choice of a subject is a far more complicated question than it would at first seem. A subject does not start with what is put in front of the easel or with something which the painter happens to remember. A subject starts with the painter deciding he would like to paint such–and–such because for some reason or other he finds it meaningful. A subject begins when the artist selects something for special mention. (What makes it special or meaningful may seem to the artist to be purely visual—its colours or its form.) When the subject has been selected, the function of the painting itself is to communicate and justify the significance of that selection. It is often said today that subject matter is unimportant. But this is only a reaction against the excessively literary and moralistic interpretation of subject matter in the nineteenth century. In truth the subject is literally the beginning and end of a painting. The painting begins with a selection (I will paint this and not everything else in the world); it is finished when that selection is justified (now you can see all that I saw and felt in this and how it is more than merely itself).

Thus, for a painting to succeed it is essential that the painter and his public agree about what is significant. The subject may have a personal meaning for the painter or individual spectator; but there must also be the possibility of their agreement on its general meaning. It is at this point that the culture of the society and period in question precedes the artist and his art. Renaissance art would have meant nothing to the Aztecs—and vice versa. If, to some extent, a few intellectuals can appreciate them both today it is because their culture is an historical one: its inspiration is history and therefore it can include within itself, in principle if not in every particular, all known developments to date. When a culture is secure and certain of its values, it presents its artists with subjects. The general agreement about what is significant is so well established that the significance of a particular subject accrues and becomes traditional. This is true, for instance, of reeds and water in China, of the nude body in Renaissance, of the animal in Africa. Furthermore, in such cultures the artist is unlikely to be a free agent: he will be employed for the sake of particular subjects, and the problem, as we have just described it, will not occur to him. When a culture is in a state of disintegration or transition the freedom of the artist increases—but the question of subject matter becomes problematic for him: he, himself, has to choose for society. This was at the basis of all the increasing crises in European art during the nineteenth century. It is too often forgotten how many of the art scandals of that time were provoked by the choice of subject (Gericault, Courbet, Daumier, Degas, Lautrec, Van Gogh, etc.). By the end of the nineteenth century there were, roughly speaking, two ways in which the painter could meet this challenge of deciding what to paint and so choosing for society. Either he identified himself with the people and so allowed their lives to dictate his subjects to him; or he had to find his subjects within himself as painter. By people, I mean everybody except the bourgeoisie. Many painters did of course work for the bourgeoisie according to their copy– book of approved subjects, but all of them, filling the Salon and the Royal Academy year after year, are now forgotten, buried under the hypocrisy of those they served so sincerely. 102. In the sentence, “I believe there is a connection” (second paragraph), what two developments is the author referring to? 1. Painters using a dying hero and using a fruit as a subject of painting. 2. Growing success of painters and an increase in abstract forms. 3. Artists gaining freedom to choose subjects and abandoning subjects altogether. 4. Rise of Impressionists and an increase in abstract forms.

CAT 2004  103. When a culture is insecure, the painter chooses his subject on the basis of: 1.  The prevalent style in the society of his time. 2.  Its meaningfulness to the painter. 3.  What is put in front of the easel. 4.  Past experience and memory of the painter. 104. Which of the following views is taken by the author? 1. The more insecure a culture, the greater the freedom of the artist. 2. The more secure a culture, the greater the freedom of the artist. 3. The more secure a culture, more difficult the choice of subject. 4. The more insecure a culture, the less significant the choice of the subject. 105. Which of the following is NOT necessarily among the attributes needed for a painter to succeed: 1. The painter and his public agree on what is significant. 2. The painting is able to communicate and justify the significance of its subject selection. 3.  The subject has a personal meaning for the painter. 4. The painting of subjects is inspired by historical developments. 106. In the context of the passage, which of the following statements would NOT be true? 1. Painters decided subjects based on what they remembered from their own lives. 2. Painters of reeds and water in China faced no serious problem of choosing a subject. 3. The choice of subject was a source of scandals in nineteenth century European art. 4. Agreement on the general meaning of a painting is influenced by culture and historical context.

PASSAGE  III Throughout human history the leading causes of death have been infection and trauma. Modern medicine has scored significant victories against both, and the major causes of ill health and death are now the chronic degenerative diseases, such as coronary artery disease, arthritis, osteoporosis, Alzheimer’s, macular degeneration, cataract and cancer. These have a long latency period before symptoms appear and a diagnosis is made. It follows that the majority of apparently healthy people are pre-ill.

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But are these conditions inevitably degenerative? A truly preventive medicine that focused on the pre–ill, analysing the metabolic errors which lead to clinical illness, might be able to correct them before the first symptom. Genetic risk factors are known for all the chronic degenerative diseases, and are important to the individuals who possess them. At the population level, however, migration studies confirm that these illnesses are linked for the most part to lifestyle factors—exercise, smoking and nutrition. Nutrition is the easiest of these to change, and the most versatile tool for affecting the metabolic changes needed to tilt the balance away from disease. Many national surveys reveal that malnutrition is common in developed countries. This is not the calorie and/or micronutrient deficiency associated with developing nations (Type A malnutrition); but multiple micronutrient depletion, usually combined with calorific balance or excess (Type B malnutrition). The incidence and severity of Type B malnutrition will be shown to be worse if newer micronutrient groups such as the essential fatty acids, xanthophylls and flavonoids are included in the surveys. Commonly ingested levels of these micronutrients seem to be far too low in many developed countries. There is now considerable evidence that Type B malnutrition is a major cause of chronic degenerative diseases. If this is the case, then it is logical to treat such diseases not with drugs but with multiple micronutrient repletion, or ‘pharmaco–nutrition’. This can take the form of pills and capsules—‘nutraceuticals’, or food formats known as ‘functional foods’, This approach has been neglected hitherto because it is relatively unprofitable for drug companies— the products are hard to patent—and it is a strategy which does not sit easily with modern medical interventionism. Over the last 100 years, the drug industry has invested huge sums in developing a range of subtle and powerful drugs to treat the many diseases we are subject to. Medical training is couched in pharmaceutical terms and this approach has provided us with an exceptional range of therapeutic tools in the treatment of disease and in acute medical emergencies. However, the pharmaceutical model has also created an unhealthy dependency culture, in which relatively few of us accept responsibility for maintaining our own health. Instead, we have handed over this responsibility to health professionals who know very little about health maintenance, or disease prevention. One problem for supporters of this argument is lack of the right kind of hard evidence. We have a wealth of epidemiological data linking dietary factors to health profiles/disease risks, and a great deal of information on mechanism: how food factors interact with our biochemistry. But almost all intervention studies with micronutrients, with the notable exception of the omega 3 fatty acids, have so far produced conflicting or negative results. In other words, our science appears to have no predictive value. Does this invalidate the science? Or are we simply asking the wrong questions?

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Based on pharmaceutical thinking, most intervention studies have attempted to measure the impact of a single micronutrient on the incidence of disease. The classical approach says that if you give a compound formula to test subjects and obtain positive results, you cannot know which ingredient is exerting the benefit, so you must test each ingredient individually. But in the field of nutrition, this does not work. Each intervention on its own will hardly make enough difference to be measured. The best therapeutic response must therefore combine micronutrients to normalize our internal physiology. So do we need to analyse each individual’s nutritional status and then tailor a formula specifically for him or her? While we do not have the resources to analyse millions of individual cases, there is no need to do so. The vast majority of people are consuming suboptimal amounts of most micronutrients, and most of the micronutrients concerned are very safe. Accordingly, a comprehensive and universal program of micronutrient support is probably the most cost–effective and safest way of improving the general health of the nation. 107. Why are a large number of apparently healthy people deemed pre–ill? 1.  They may have chronic degenerative diseases. 2. They do not know their own genetic risk factors which predispose them to diseases. 3.  They suffer from Type–B malnutrition. 4. There is a lengthy latency period associated with chronically degenerative diseases 108. Type–B malnutrition is a serious concern in developed countries because: 1. Developing countries mainly suffer from Type–A malnutrition. 2.  It is a major contributor to illness and death. 3. Pharmaceutical companies are not producing drugs to treat this–condition. 4. National surveys on malnutrition do not include newer micronutrient groups. 109. Tailoring micronutrient–based treatment plans to suit individual deficiency profiles is not necessary because: 1.  It very likely to give inconsistent or negative results. 2. It is a classic pharmaceutical approach not suited to micronutrients. 3. Most people are consuming suboptimal amounts of safe–to–consume micronutrients. 4.  It is not cost effective to do so. 110. The author recommends micronutrient–repletion for large– scale treatment of chronic degenerative diseases because:

1.  It is relatively easy to manage. 2. Micronutrient deficiency is the cause of these diseases. 3.  It can overcome genetic risk factors. 4.  It can compensate for other lifestyle factors.

PASSAGE  IV Fifty feet away three male lions lay by the road. They didn’t .appear to have a hair on their heads. Noting the color of their noses (leonine noses darken as they age, from pink to black), Craig estimated that they were six years old—young adults. “This is wonderful!” he said, after staring at them for several moments. “This is what we came to see. They really are maneless.” Craig, a professor at the University of Minnesota, is arguably the leading expert on the majestic Serengeti lion, whose head is mantled in long, thick hair. He and Peyton West, a doctoral student who has been working with him in Tanzania, had never seen the Tsavo lions that live some 200 miles east of, the Serengeti. The scientists had partly suspected that the maneless males were adolescents mistaken for adults by amateur observers. Now they knew better. The Tsavo research expedition was mostly Peyton’s show. She had spent several years in Tanzania, compiling the data she needed to answer a question that ought to have been answered long ago: Why do lions have manes? It’s the only cat, wild or domestic, that displays such ornamentation. In Tsavo, she was attacking the riddle from the opposite angle. Why do its lions not have manes? (Some “maneless” lions in Tsavo East do have partial manes, but they rarely attain the regal glory of the Serengeti lions.) Does environmental adaptation account for the trait? Are the lions of Tsavo, as some people believe, a distinct subspecies of their Serengeti cousins? The Serengeti lions have been under continuous observation for more than 35 years, beginning with George Schaller’s pioneering work in the 1960s. But the lions in Tsavo, Kenya’s oldest and largest protected ecosystem, have hardly been studied. Consequently, legends have grown up around them. Not only do they look different, according to the myths, they behave differently, displaying greater cunning and aggressiveness. “Remember too,” Kenya: The Rough Guidness warns, “Tsavo’s lions have a reputation of ferocity.” Their fearsome image became well–known in 1898, when two males stalled construction of what is now Kenya Railways by allegedly killing and eating 135 Indian and African labourers. A British Army officer in charge of building a railroad bridge over the Tsavo River, Lt Col J. H. Patterson, spent nine months pursuing the pair before he brought them to bay and killed them. Stuffed and mounted, they now glare at visitors to the Field Museum in Chicago.

CAT 2004  Patterson’s account of the leonine reign of terror, The Man-Eaters of Tsavo, was an international best seller when published in 1907. Still in print, the book has made Tsavo’s lions notorious. That annoys some scientists. “People don’t want to give up on mythology,” Dennis King told me one day. The zoologist has been working in Tsavo off and on for four years. “I am so sick of this man-eater business. Patterson made a helluva lot of money off that story, but Tsavo’s lions are no more likely to turn man-eater than lions from elsewhere.” But tales of their savagery and wiliness don’t all come from sensationalist authors looking to make a buck. Tsavo lions are generally larger than lions elsewhere, enabling them to take down the predominant prey animal in Tsavo, the Cape buffalo, one of the strongest, most aggressive animals of Earth. The buffalo don’t give up easily: They often kill or severely injure an attacking lion, and a wounded lion might be more likely to turn to cattle and humans for food. And other prey is less abundant in Tsavo than in other traditional lion haunts. A hungry lion is more likely to attack humans. Safari guides and Kenya Wildlife Service rangers tell of lions attacking Land Rovers, raiding camps, stalking tourists. Tsavo is a tough neighbourhood, they say, and it breeds tougher lions. But are they really tougher? And if so, is there any connection between their manelessness and their ferocity? An intriguing hypothesis was advanced two years ago by Gnoske and Peterhans: Tsavo lions may be similar to the unmaned cave lions of the Pleistocene. The Serengeti variety is among the most evolved of the species—the latest model, so to speak—while certain morphological differences in Tsavo lions (bigger bodies, smaller skulls, and maybe even lack of a mane) suggest that they are closer to the primitive ancestor of all lions. Craig and Peyton had serious doubts about this idea, but admitted that Tsavo lions pose a mystery to science. 111. The book Man-Eaters of Tsavo annoys some scientists because 1.  It revealed that Tsavo lions are ferocious. 2. Patterson made a helluva lot of money from the book by sensationalizm. 3.  It perpetuated the bad name Tsavo lions had. 4.  It narrated how two male Tsavo lions were killed. 112. The sentence which concludes the first paragraph. “Now they knew better”, implies that 1. The two scientists were struck by wonder on seeing maneless lions for the first time. 2. Though Craig was an expert on the Serengeti lion, now he also knew about the Tsavo lions. 3. Earlier, Craig and West thought that amateur observers had been mistaken.

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4. Craig was now able to confirm that darkening of the noses as lions aged applied to Tsavo lions as well. 113. Which of the following, if true, would weaken the hypothesis advanced by Gnoske and Peterhans most? 1. Craig and Peyton develop even more serious doubts about the idea that Tsavo lions are primitive. 2. The maneless Tsavo East lions are shown to be closer to the cave lions. 3. Pleistocene cave lions are shown to be far less violent than believed. 4. The morphological variations in body and skull size between the cave and Tsavo lions are found to be insignificant. 114. According to the passage, which of the following has NOT contributed to the popular image of Tsavo lions as savage creatures? 1. Tsavo lions have been observed to bring down one of the strongest and most aggressive animals—the Cape buffalo. 2. In contrast to the situation in traditional lion haunts, scarcity of non–buffalo prey in the Tsavo makes the Tsavo lions more aggressive. 3. The Tsavo lion is considered to be less evolved than the Serengeti variety. 4. Tsavo lions have been observed to attack vehicles as well as humans.

PASSAGE  V The viability of the multinational corporate system depends upon the degree to which people will tolerate the unevenness it creates. It is well to remember that the ‘New Imperialism’ which began after 1870 in a spirit of Capitalism Triumphant, soon became seriously troubled and after 1914 was characterized by war, depression, breakdown of the international economic system and war again, rather than Free Trade, Pax Britannica and Material Improvement. A major reason was Britain’s inability to cope with the byproducts of its own rapid accumulation of capital; i.e., a class–conscious labour force at home; a middle class in the hinterland; and rival centres of capital on the Continent and in America. Britain’s policy tended to be atavistic and defensive rather than progressive—more concerned with warding off new threats than creating new areas of expansion. Ironically, Edwardian England revived the paraphernalia of the landed aristocracy it had just destroyed. Instead of embarking on a ‘big push’ to develop the vast hinterland of the Empire, colonial administrators often adopted policies to arrest the development of either a native capitalist class or a native proletariat which could overthrow them.

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As time went on, the centre had to devote an increasing share of government activity to military and other unproductive expenditures; they had to rely on alliances with an inefficient class of landlords, officials and soldiers in the hinterland to maintain stability at the cost of development. A great part of the surplus extracted from the population was thus wasted locally.

in most underdeveloped countries could survive without cheap labour since removing it (e.g. diverting it to public works projects as is done in socialist countries) would raise consumption costs to capitalists and professional elites.

The New Mercantilism (as the Multinational Corporate System of special alliances and privileges, aid and tariff concessions is sometimes called) faces similar problems of internal and external division. The centre is troubled: excluded groups revolt and even some of the affluent are dissatisfied with the roles. Nationalistic rivalry between major capitalist countries remains an important divisive factor. Finally, there is the threat presented by the middle classes and the excluded groups of the underdeveloped countries. The national middle classes in the underdeveloped countries came to power when the centre weakened but could not, through their policy of import substitution manufacturing, establish a viable basis for sustained growth. They now face a foreign exchange crisis and an unemployment (or population) crisis—the first indicating their inability to function in the international economy and the second indicating their alienation from the people they are supposed to lead. In the immediate future, these national middle classes will gain a new lease of life as they take advantage of the spaces created by the rivalry between American and non-American oligopolists striving to establish global market positions.

1. It was unable to deal with the fallouts of a sharp increase in capital.

The native capitalists will again become the champions of national independence as they bargain with multinational corporations. But the conflict at this level is more apparent than real, for in the end the fervent nationalizm of the middle class asks only for promotion within the corporate structure and not for a break with that structure. In the last analysis their power derives from the metropolis and they cannot easily afford to challenge the international system. They do not command the loyalty of their own population and cannot really compete with the large, powerful, aggregate capitals from the centre. They are prisoners of the taste patterns and consumption standards’ set at the centre. The main threat comes from the excluded groups. It is not unusual in underdeveloped countries for the top 5 per cent to obtain between 30 and 40 per cent of the total national income, and for the top one-third to obtain anywhere from 60 to 70 percent. At most, one-third of the population can be said to benefit in some sense from the dualistic growth that characterizes development in the hinterland. The remaining two-thirds, who together get only one-third of the income, are outsiders, not because they do not contribute to the economy, but because they do not share in the benefits. They provide a source of cheap labour which helps keep exports to the developed world at a low price and which has financed the urban-biased growth of recent years. In fact, it is difficult to see how the system

115. According to the author, the British policy during the ‘New Imperialism’ period tended to be defensive because

2.  Its cumulative capital had undesirable side-effects. 3.  Its policies favoured developing the vast hinterland. 4. It prevented the growth of a set-up which could have been capitalistic in nature. 116. The author is in a position to draw parallels between New Imperialism and New Mercantilism because 1. Both originated in the developed Western capitalist countries. 2. New Mercantilism was a logical sequel to New Imperialism. 3. They create the same set of outputs—a labour force, middle classes and rival centres of capital. 4.  Both have comparable uneven and divisive effects. 117. Under New Mercantilism, the fervent nationalism of the native middle classes does not create conflict with the multinational corporations because they (the middle classes) 1.  Negotiate with the multinational corporations. 2. Are dependent on the international system for their continued prosperity. 3.  Are not in a position to challenge the status quo. 4.  Do not enjoy popular support. 118. In the sentence, “They are prisoners of the taste patterns and consumption standards set at the centre.” (fourth paragraph), what is the meaning of ‘centre’? 1.  National government 2.  Native capitalists 3.  New capitalists 4.  None of the above

Sub-section III–B Number of Questions = 5 Note: Questions 119 to 122 carry two marks each. Direction for questions 119 and 120: The sentences given in each question, when properly

CAT 2004  sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph. 119. A. Experts such as Larry Burns, head of research at GM, reckon that only such a full hearted leap will allow the world to cope with the mass motorization that will one day come to China or India. B. But once hydrogen is being produced from biomass or extracted from underground coal or made from water, using nuclear or renewable electricity, the way will be open for a huge reduction in carbon emissions from the whole system. C. In theory, once all the bugs have been sorted out, fuel cells should deliver better total fuel economy than any existing engines. D. That is twice as good as the internal combustion engine, but only five percentage points better than a diesel hybrid. E. Allowing for the resources needed to extract hydrogen from hydrocarbon, oil, coal or gas, the fuel cell has an efficiency of 30 percent. 1.  CEDBA

2.  CEBDA

3.  AEDBC

4.  ACEBD

120. A. But this does not mean that death was the Egyptians’ only preoccupation. B.  Even papyri come mainly from pyramid temples. C. Most of our traditional sources of information about the Old Kingdom are monuments of the rich like pyramids and tombs. D. Houses in which ordinary Egyptians lived have not been preserved, and when most people died they were buried in simple graves. E. We know infinitely more about the wealthy people of Egypt than we do about the ordinary people, as most monuments were made for the rich. 1.  CDBEA

2.  ECDAB

3.  EDCBA

4.  DECAB

Direction for questions 121 to 123:  Four alternative summaries are given below each text. Choose the option that best captures the essence of the text. 121. Modern bourgeois society, said Nietzsche, was decadent and enfeebled—a victim of the excessive development of the rational faculties at the expense of will and instinct. Against the liberal–rationalist stress on the

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intellect, Nietzsche urged recognition of the dark mysterious world of instinctual desires—the true forces of life. Smother the will with excessive intellectualizing and you destroy the spontaneity that sparks cultural creativity and ignites a zest for living. The critical and theoretical outlook destroyed the creative instincts. For man’s manifold potential to be realized, he must forego relying on the intellect and nurture again the instinctual roots of human existence. 1. Nietzsche urges the decadent and enfeebled modern society to forego intellect and give importance to creative instincts. 2. Nietzsche urges the decadent and enfeebled modern society to smother the will with excessive intellectualising and ignite a zest for living. 3. Nietzsche criticizes the intellectuals for enfeebling the modem bourgeois society by not nurturing man’s creative instincts. 4. Nietzsche blames excessive intellectualization for the decline of modern society and suggests nurturing creative instincts instead. 122. Local communities have often come in conflict with agents trying to exploit resources, at a faster pace, for an expanding commercial–industrial economy. More often than not, such agents of resource–intensification are given preferential treatment by the state, through the grant of generous long leases over mineral or fish stocks, for example, or the provision of raw material at an enormously subsidized price. With the injustice so compounded, local communities at the receiving end of this process have no resource expert direct action, resisting both the state and outside exploiters through a variety of protest techniques. These struggles might perhaps be seen as a manifestation of a new kind of class conflict. 1. A new kind of class conflict arises from preferential treatment given to agents of resource – intensification by the state which the local community sees as unfair. 2. The grant of long leases to agents of resource– intensification for an expanding commercial–industrial economy leads to direct protests from the local community, which sees it as unfair. 3. Preferential treatment given by the state to agents of resource–intensification for an expanding commercial–industrial economy exacerbates injustice to local communities and leads to direct protests from them, resulting in a new type of class conflict. 4. Local communities have no option but to protest against agents of resource intensification and create a new type of class conflict when they are given raw material at subsidized prices for an expanding commercial–industrial economy.

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123. Although almost st all climate scientists agree that the Earth is gradually warming, they have long been of two minds about the process of rapid climate shifts within larger periods of change. Some have speculated that the process works like a giant oven freezer, warming or cooling the whole planet at the same time. Others think that shifts occur on opposing schedules in the Northern and Southern Hemispheres, like exaggerated seasons. Recent research in Germany examining climate patterns in the Southern Hemisphere at the end of the last Ice Age strengthens the idea that warming and cooling occurs at alternate times in the two hemispheres. A more definitive answer to this debate will allow scientists to better predict when and how quickly the next climate shift will happen.

schedules in different hemispheres; research will help find a definitive answer and better predict climate shifts in future. 2. Scientists have been unsure whether rapid shifts in the Earth’s climate happen all at once or on opposing schedules in different hemispheres; finding a definitive answer will help them better predict climate shifts in future. 3. Research in Germany will help scientists find a definitive answer about warming and cooling of the Earth and predict climate shifts in the future in a better manner. 4. More research rather than debates on warming or cooling of the Earth and exaggerated seasons in its hemispheres will help scientists in Germany predict climate changes better in future.

ANSWER KEYS

1. Scientists have been unsure whether rapid shifts in the Earth’s climate happen all at once or on opposing

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20.

4

21.

1

22.

1

23.

1

24.

1

25.

3

26.

4

27.

3

28.

1

29.

2

30.

2

31.

4

32.

3

33.

3

34.

4

35.

4

36.

2

37.

4

38.

4

39.

3

40.

2

41.

1

42.

2

43.

1

44.

2

45.

1

46.

1

47.

3

48.

4

49.

4

50.

2

51.

3

52.

4

53.

2

54.

2

55.

3

56.

4

57.

4

58.

3

59.

4

60.

3

61.

3

62.

2

63.

3

64.

2

65.

1

66.

2

67.

2

68.

4

69.

4

70.

1

71.

3

72.

3

73.

1

74.

3

75.

1

76.

4

77.

4

78.

2

79.

1

80.

4

81.

3

82.

2

83.

4

84.

1

85.

3

86.

2

87.

4

88.

3

89.

3

90.

4

91.

1

92.

2

93.

2

94.

4

95.

1

96.

1

97.

2

98.

2

99.

2

100.

4

101.

1

102.

3

103.

2

104.

1

105.

4

106.

1

107.

4

108..

2

109.

3

110.

2

111.

3

112.

3

113.

3

114.

3

115

1

116

4

117

2

118

4

119

1

120.

3

121.

4

122.

3

123.

2

CAT 2004 

  3.89

HINTS AND EXPLANATIONS Section  I



800 + 1600 + 2300 ________________ Average income of Bose = ​   ​      3

1. (1)  GPA of Preeti = 3.2



4700 ____ = ​   ​    3



F+D+X+D+Y _____________ i.e., ​   ​      = 3.2 5



Average income of Coomar



0+2+X+2+Y = 16



300 + 1100 + 1900 ____ 3300 ________________ = ​   ​      = ​   ​    3 3



X+Y= 12



1200 + 2800 ____ 4000 ___________ Average income of Dubey = ​   ​    = ​   ​    2 2



The only possible combination is A, A.



Thus, Coomer has the lowest income.



So Preeti obtained A grade in statistics.

6. (4) In the figure draw a line parallel to the expenditure and mid way between observations of each families’ Values.

2. (4) Tara got same grade in three courses. We know that Tara has got B grade in one of the subject and her GPA is 2.4. So B is the grade which Tara has scored in three of the subjects. So Tara has received the same Grade as Maanav. 3. (2)  GPA of Gouri is 3.8

i.e., 3+3+6+x+4 = 3.8 X 5.



16+ x = 18



X=2



So, the grade of Gouri in strategy is C.



Rahul’s grade in Strategy = (4.2 x 5 ) – 15 = 6, i.e., A.



Fazal’s grade in strategy = ( 2.4 x 5) – 8 = 4 i.e., B.

Hence, Gouri’s grade will be higher than that of Hari. 4. (3)  As Fazal’s GPA = 2.4

So D + F +B + P + D = 2.4 x 5



2 + 0 + 4 + P + 2 = 12



P=4



So, his grade in strategy is B.



Utkarsh has also scored grade B in Marketing.



So, for Utkarsh, X + B + F + C + A = 3x 5



X + 4 + 0+ 3+ 6 = 15



X=2



So, grade of Utkarsh in finance = D.

5. (3) Average income of Ahuja

700 + 1700 +1800 ____ 4200 _______________ = ​   ​      = ​   ​    3 3

7. (4) The figure shows the first member of Dubey family is on the line indicating income = expenditure. The second member is just above the line . 8. (1)  Look at the left most member of Ahuja’s family. Solutions for questions 9 to 12 When we compare table 1 and 2, university 4 corresponds to UK and university 6 corresponds to USA (after day 3 onwards values are concerned and university 8 corresponds to India and university 3 to Netherlands and now Indian or Netherlands can take university 1 or university 5. now university 2 and 7 belongs to either UK or Canada ( Only one ).

University

Day

Country

1

2

3

University 1

1

0

0

India/Netherlands

University 2

2

0

0

UK/Canada

University 3

0

1

0

Netherlands

University 4

0

0

2

UK

University 5

1

0

0

India/Netherlands

University 6

1

0

1

USA

University 7

2

0

0

UK/Canada

University 8

0

2

0

India

13. (2) In the year 1999, total number of Naya Mixer grinder = 124 Nnumber of Naya new mixer grinder disposed = 20 per cent of 30 = 6

Number of mixer bought 124 = (50 + 24 + 50)

3.90 

  CAT Papers

14. (3)  Nnumber of Naya mixer grinder disposed in the 1999 = 6



Number of Naya mixer grinder disposed in the 2000 = 10

Even if we combine both the statements, we dont get a unique value.



Total disposed by the end of 2000 = 16

15. (4) Initial no. of Purana mixer grinder not available, hence can not be determined. 16. (1) 20 Purana mixer grinder purchased in the year 1999.

Statement B: It will not give us the solution.



Answer is (4)

Solutions for questions 27 to 30 Let us have a tabular presentation of the data given:

17. (4) Thailand and Japan because they have the maximum difference of 4 ranks ( 5 – 1 ). 18. (1) China because maximum difference between two parameters is 2. 19. (2)  Maximum difference = 4. 20. (4)  Japan and Malaysia 22. (1) Let us assume that A,B,C,D are 4 people getting a score of 10,8,6,4.

Pakistan

South Africa

Australia

K

28

51