How to Prepare for Quantitative Aptitude for CAT (2014)

Preface

Preface to the Sixth Edition

With the evolution of the CAT in its online avatar, I felt the need to create a comprehensive and updated book that caters to CAT aspirants. Some of its salient features are given below.

1. Questions from this book:Over the past decade, it has been noticed that a minimum of 10–20% questions in CAT and other major management entrance examinations have been directly taken from the questions provided in this book. Furthermore, it has been seen that between 2003 (when the book was first released) to 2013, 80–90% of the questions in CAT and other top management entrance tests were covered in this book.

The CAT having gone online saw no change in this trend. Many questions in each of the test papers that the CAT has administered in its online avatar since 2009 have been covered in this book.

In fact, 2009 onwards, the onset of the CAT online pattern has created a significant shift in terms of the CAT preparation process. This is because, 2009 was the first year where there were multiple CAT papers to study, analyse and base our writing and preparation process on. In subsequent years, with the increase of the CAT window, the number of papers every year has gone up to around 30–40 papers. Thus, I am now richer by the experience of around 150 plus test papers when it comes to understanding what I need to provide to my readers for their preparation. It is on the basis of this rather rich insight that I have based the changes in this edition. (Note: Similar changes have been incorporated in my other books How to prepare for Verbal Ability and Reading Comprehension for the CAT, How to Prepare for Data Interpretation for the CAT, and How to Prepare for Logical Reasoning for the CAT).

2. Not too many changes in the pattern:Looking rationally into the paper patterns of the 150 plus CAT papers in the past period, there have not been too many changes with regard to the pattern of the examination as compared to previous years. While the QA in the initial years of Online CAT examination (between 2009–2010) was slightly on the easier side, the standard of the questions from 2011 onwards has become pretty much ‘CAT standard’. Hence, the LOD I, LOD II and LOD III scheme of questions followed in this book is even more relevant now than ever before.

In fact, in the near future, the CAT is expected to shift to an adaptive format (like the GMAT) where every test-taker would get a different set of questions. In the adaptive format in the future, question banks of varying difficulty levels would be loaded into the computers and questions would appear for the student one-by-one. The difficulty level of the next question would increase if the previous one has been answered correctly and vice versa.

In order to do this, the examiners would need to build a database of questions which would be parallel to the LOD scheme followed in this book. These factors make this book and the content within all the more relevant for CAT aspirants.

How does Merging Quantitative Aptitude & Data Interpretation change the preparation process?

As you must be aware, the CAT 2011 introduced a new pattern shift by reducing the number of sections from 3 to 2. Before CAT 2011, there used to be three sections containing 20 questions each in the CAT exam namely:

Section 1: Quantitative Aptitude

Section 2: Verbal Ability & Reading Comprehension

Section 3: Data Interpretation & Logical reasoning.

In the new pattern the number of sections was reduced to 2 sections containing 30 questions each, namely

Section 1: Quantitative Aptitude & Data Interpretation

Section 2: Verbal Ability & Logical reasoning.

In many ways, this does not really change your process of preparation. This is because, even though, on the surface the number of sections was changed, the actual number of questions under each category remained the same. In other words, while the three-section CAT used to have 20 questions on Quantitative Aptitude, 20 questions on Verbal Ability and Reading Comprehension, 10-12 questions on Data Interpretation and 8-10 questions on Logical Reasoning, the new two-section examination has 20 questions on Quantitative Aptitude and 10 questions on Data Interpretation merged together under one section, while the 20 questions on Verbal Ability and Reading Comprehension and the 10 questions on Logical reasoning were merged together under the other section.

Thus, the emphasis of your preparation does not really need to change at all. The only change that might occur is in the way you may want to strategise to use the time available to you in each section in order to beat your competition.

3. The need for greater variety in your preparation: Prior to the CAT going online, preparing for QA used to be a battle for Blocks 1, 4, 5 and 6. Even out of these, if someone did Blocks I and V well, he stood a strong chance at QA section.

However, as explained in details in the introductory note to the online CAT, the new avatar of this exam requires the aspirant to be much more balanced in the context of portion coverage.

4. The tougher level of the CAT exam: As already stated above, the quality of questions asked in the CAT over the past couple of years has become extremely good—requiring an upgradation of your grasp of concepts and understanding of each particular topic to a level not required before. This shift has necessitated that we do more through this book.
5. 5. I have also come to know that many readers use this book for their preparation of other important management entrance exams (like XAT, IIFT, CMAT, MAT, SNAP, etc). So now, I have also included/modified the contents so that aspirants of the above exams need not look for any resource beyond this book for strengthening their hold on the quantitative aptitude section.

Apart from management entrance examinations, the book also has relevance for aspirants of UPSC and state civil services, Bank PO exams, GATE, Engineering Placement exams, etc. In short the scope of this book has considerably widened to cover the entire subject of quantitative aptitude that finds a resonance for all career aspirants.

The book you now hold in your hand has always been written keeping in mind the avowed objective of developing your quantitative intelligence to a point where you can quickly scale the height of preparation in each chapter of the portion.

Key features:

The book is now totally in sync with the new trend and pattern of the examination.

Ultimately the endeavour is to provide a one-stop solution for CAT and MBA exam aspirants to tackle the QA section of all major management entrance exams—an endeavour I feel I have managed to do pretty well.

Through this book, I am confident of giving you—the reader—an invaluable resource for enhancing your QA section score drastically. Contained in this book is the very best advisory for each and every question type. Your job is simple—to ensure that you follow the process contained in this advisory.

KEY POINTS FOR YOUR PREPARATION

Outline and Strategy

The first aspect I would like to deal with here is to focus on helping you with the formulation of your strategy with respect to the portion to be covered for the Quantitative Aptitude section of the various management entrance exams including the CAT, XAT, CMAT, IIFT, and other examinations.

Let us start by trying to understand some of the key areas in Quantitative Aptitude (QA).

Tackling each portion

My experience shows that very often students look at the vast number of chapters and concepts to be studied for QA and get disheartened. This is especially true for students who do not have a strong traditional background in Mathematics. Indeed if you were to look at it with a chapter-wise approach, you can easily define the course to be studied by dividing it into 20+ chapters—preparation for which is such a long-drawn effort that it ends up draining the student’s energy enthusiasm and motivation.

It is in this context and for this precise reason that I have divided this book into six manageable blocks—the approach being rationalising the chapters and grouping them according to the amount of shared concepts these chapters have amongst each other.

The outline as defined in the index to this book would divide your work into 6 major areas to prepare for. For your convenience and strategising I have put down the relative importance of each of these six blocks into perspective:

Block I: Number Systems and Progressions

Importance: Very High for CAT, XAT, IIFT, FMS & High for MAT, CMAT, SNAP, IRMA, etc.

Block II: Averages and Alligations

Importance: Low for QA in CAT, XAT, IIFT, but High for Data Interpretation as a lot of questions in DI are based on the concepts of averages and alligations. Also High for MAT, CMAT, IRMA, NMIMS, etc.

Block III: Percentages, Ratio, Proportion and Variation, Time and Work, Time, Speed and Distance. (Subsidiary but almost redundant chapters in this block – Interest and Profit & Loss)

Importance: Moderate to High for QA in CAT, XAT, IIFT, and Very High for Data Interpretation (DI) as DI is almost entirely based on the concept of Percentages and Ratio and Proportions. Very High for MAT, CMAT, IRMA, NMIMS, etc.

Block IV: Geometry, Mensuration and Coordinate Geometry

Importance: Very High for CAT, XAT. Average for MAT, CMAT, SNAP, IRMA, IIFT, etc.

Block V: Functions, Inequalities, Logs and Quadratic Equations

Importance: Very High for CAT, XAT. Low for MAT, CMAT, IRMA, NMIMS, etc.

Block VI: Permutations and Combinations, Probability and Set Theory

Importance: Very High for CAT, XAT, IIFT etc. Average for MAT, CMAT, IRMA etc.

Based on the experience of the online CAT, the strategic preparation imperative for you should be to do at least four blocks and if possible up to 6 blocks “really well”.

What does it mean to prepare a block “really well”? This is something I feel needs emphasis here.

Well what I mean to say is that do not just focus on studying the theory in each of these areas but develop an intuitive knowledge of all problem scenarios which emerge out of each block.

Only then would you be able to reach a situation in the exam—that when the question presents itself to you in the exam—you would have had the logic for the same worked out before hand. This is something that can make a huge difference to your chances in the CAT.

Analysing Your Knowledge Level

The first thing you need to focus on is an analysis of your knowledge level in each of these seven parts. In each of the above areas, first analyse your level of knowledge/ability. In order to do so the typical question you should ask yourself is: For the next 100 questions I face in each of these areas, how many would I be able to handle comfortably?

Think of a number as an answer to this question for each of the six blocks.

Based on your answer, the following analysis would provide you a thumb rule which would tell you how much of a knowledge issue you have:

1.90+: You know pretty much every question type and variant in the area. You should focus your energies on other aspects rather than knowledge improvement in the area.

2.80+: Maybe you need to increase your exposure to questions a little bit; around 200–300 more questions in that area would be sufficient.

3.60–80+: You have a significant knowledge issue in the area. You might need to go back to the basics, but it is less likely to be a theory issue but more of an exposure to questions issue.

4.<60: You need to work on both theory and exposure to questions.

Needless to say, the target and objective for preparations has to be to reach the 90+ range as explained above in any block you intend to do “really well”.

Looking beyond Ability (Quick Reflexes)

A common frustrating experience for test-takers while taking the test is to not being able to solve a known question/logic and subsequently, not being able to score marks in questions which they knew.

In order to handle this problem, you would need to work on your reactions and reflexes when faced with QA questions. Once you have solved your knowledge/ability issue in a particular block, your next step is to improve your reactions and reflexes while solving a question. Needless to say you would need to do this block wise.

So obviously the main issue is how to improve reflexes and reactions.

(a)For every block, once you have solved the LODs and the Pre-Assessment/Review tests, the most crucial exercise in this context would be a comprehensive revision and review of each and every question you have solved in that block. Solve every question of every LOD and Pre-Assessment/Review test again and review the logic/process of problem solving used. This need to be done to the point where you almost “recollect” the logic of the question and are able to recognise the same if it is used again in a different context/problem.

(b)A thorough revision on the theory of the block.

1. Improve your ability to select what you know and leave what you do not

In the context of an examination where the required scores for 99 percentile would be 60–70% attempts with 100% accuracy, it is easy to see that perfect knowledge is perhaps not needed in order to crack the CAT. Hence, even if you have around 60–70% knowledge of the questions in an average test, you are perhaps good enough to crack the exam. A good way to test whether you have sufficient knowledge would be to pick up 10–20 test papers and divide your QA section into blocks of 5 questions each. Then test your knowledge by looking at the average number of questions you know. If on an average for every 5 QA test questions that you pick up, if you know more than 3, then the prognosis would be that you have adequate knowledge for cracking the CAT. Thus, while you may want to move towards knowing 5 out of 5 in this context, there are other things that you should focus on—developing your ability to decide on whether you are going to be able to solve a question while reading it for the first time. This would help you stop fishing during the test. (Fishing can be described as the activity of trying to solve a question without knowing whether you would actually complete the question.)

Your mind should give you a clear indication of whether you would be able to do the last step in a question, before you start doing it. In that sense you should be able to clearly define three types of outcomes when you finish reading a question for the first time:

(a)I see a clear flowchart and the steps are manageable—Obviously you need to go on and solve these questions.

(b)I see a clear flowchart but the steps are too lengthy—In this case you need to see where you stand in your test-time and attempt-wise.

(c)I do not see a clear flowchart but I can try as I see a starting point—This is potentially the most dangerous situation for you in the duration of the test, as once you get sucked into a question, there is a strong tendency to lose track of the time you are using up while trying the question. My advice is that while taking the test you should not even start doing such questions.

(d)I see no flowchart and no starting point to the question—Obviously you should leave such questions and in fact if these are limited to around 20–30% of the paper there is no problem and you need not worry about them.

2. Focus on thorough knowledge of ‘problem scenarios’ rather than theoretical learning

To illustrate this, I would like to start with a few examples.

Consider the following string of 3 questions. Before I come to my main point here, I would like you to start by solving these questions before looking at the explanations provided:

1.A boy starts adding consecutive natural numbers starting from 1. After some time he reaches a total of 1000 when he realises that he has double counted a number. Find the number double counted.

2.A boy starts adding consecutive natural numbers starting from 1. He reaches a total of 575 when he realises that he has missed a number. What can be said about the number missed?

3.Find the 288^th term of the series: ABBCCCDDDDEEEEEFFFFFFG....

We can now start to look at each of these 3 questions:

1.Consider the fact that when you add numbers as stated above (1+2+3+4+......) the result is known as a triangular number. Hence, numbers like 1, 1+2=3, 1+2+3=6 and so on are triangular numbers. This question asks us to consider the possibility of making the mistake of double counting a number. So instead of 1+2+3+4 if you were to do by error 1+2+3+3+4 you would realise that the number you would get would be 13 which would be more than 10 (which should have been your correct addition) and less than 15 (the sum of 1 to 5) which is the next triangular number. And the double counted value could be achieved by spotting 10 as the immediately lower value—and the difference between 10 and 13 would give you the required double counted number.

To carry forward this logic into the given question, we should realise that we are just bothered about finding the last triangular number below 1000—and in trying to work this out is where we really apply our intelligence.

Before one writes about that though, one fully realises that a lot of readers (especially aspirants with an engineering background at this point are thinking about n × (n + 1)/2. Knowing that process, one chooses to write about the alternate way to think about in this question.

1 + 2 + 3 + 4 ... + 10 = 55;

Hence, we can easily see that 11+12+13+14+15+...+20 would equal 155 and the sum of 21 to 30 would equal 255 and so on.

Thus, in trying to find the last triangular number below 1000 we can just do: 55+155+255+355 = 820 (which is the sum of the first 40 natural numbers) and since we have still not reached close to 1000 we start by adding more numbers as: 820 + 41 + 42 + 43 + 44 = 990 and the difference between 990 and 1000 is 10 which is the required answer.

2.For this question we would just need to carry the learning from the previous question forward and realise that when we miss a number, we actually get a total which is lower than the correct total. Hence, if we want to find the number missed all we need to do is to find the first triangular number greater than 575. This can be got simply by 55+155+255+31+32+33+34 = 595, so the number missed has to be 20.

3.In this question all you would need to notice is that in the series ABBCCCDDDDEEEEEF...

A ends after the first term; B ends after the third (1+2) term; C ends after the sixth (1+2+3) term and so on. So we can infer that what we are looking at is how many numbers need to be added before we get to a number just below 288. So 55 + 155+21+22+23 gives us 276 which pretty much means that the 24^th alphabet (i.e. x) would be running in this series when we reach the 288^th term.

So looking at the three questions above and the solutions, one wants the reader to only answer one specific question:

How much does knowing the first question and developing your thought ability and your intelligence help you in solving the second and the third one? I hope you see the connection. For your information, the three questions presented above were asked in CAT 2001, CAT 2002 and CAT 2003!!!

CONCLUDING NOTE

You sit in front of your CAT question paper and the first question comes in front of you. If you have identified the logic of the question or seen the question itself earlier, your entire QA preparation is fructified. In fact, every question/logic (that you would face in your test) which you have seen earlier represents a triumph of your preparation process. It is for this very reaction that you prepare for an aptitude exam like the CAT. Any other preparation is quite worthless.

Your battle for CAT would be won if you get a “YES I KNOW THIS PATTERN/LOGIC” reaction to 50–60% of the questions in your test.

Contained in this book is the finest collection questions which you would hope to find anywhere. Remember, each question solved needs to be a learning experience—one that is to be kept in your mind for future problem solving. Adopt this approach with the problems contained in this book and I am quite confident that you would KNOW over 50% of your actual CAT test paper since you have already solved something like that before!!

All The BEST !!!!!!

ARUN SHARMA

Preface to the First Edition

Over the last few years, as a trainer of CAT and other aptitude tests, I have felt the need for a comprehensive book on the subject. Students appearing for the CAT and other aptitude tests usually struggle for appropriate study material to prepare for this vital section of the examination.

This book comes as a humble attempt to fulfil this gap.

Structure of the book

The book is divided into 19 chapters and five test papers. Each chapter is divided into three broad parts:

(a)Theory

(b)Solved examples

(c)Chapter end exercises (LODs I, II & III), with answer key

The questions in the chapter end exercises have been categorised into three levels of difficulty, viz, Level of Difficulty I, Level of Difficulty II and Level of Difficulty III.

Level of Difficulty I (LOD I): These are the basic types of questions pertaining to the chapter. A majority of the MBA entrance tests would test the student with LOD I questions. Tests which ask LOD I questions include MAT, IMT, IRMA, IIFT, NIFT, CET Maharashtra, Bank PO examinations, BBA, BCA, Law, and so on. Besides, there are about 10 questions of LOD I type in the CAT nowadays.

Level of Difficulty II (LOD II): These are questions, which are more advanced than the LOD I questions. These questions test all basic as well as applied concepts in the chapter. LOD II questions are closest to the difficulty levels of the CAT. Hence, the objective of LOD II questions should be to:

(a)Clearly understand the concept which underlies the question.

(b)Create a judgment of time required for different mental processes.

(c)Identify the time guzzlers.

(d)Reinforce application of a method in mental processes through the question.

(e)Learn to flowchart complex questions.

Level of Difficulty III (LOD III): LOD III questions build on the previous questions and are a step beyond the LOD II questions. Although they are also normally more difficult than the average CAT question, approximately 5–10 LOD III questions could be asked in the CAT every year. Hence, the learning objectives at LOD III are to:

(a)Learn applications of the basic concepts at the highest level.

(b)Sharpen the flowcharting skills learnt at LOD II.

(c)Use each question as a learning opportunity.

One should not be disheartened if he/she is unable to solve LOD III questions. These questions are extremely tough and uncommon in the CAT and other aptitude tests. Questions in actual tests will appear very simple and elementary if one can solve LOD III questions.

Approach Taken in Writing This Book

In my experience, the ‘math skill’ of students appearing for CAT can be classified into three levels:

Level 1: Students who are weak at Mathematics

Level 2: Students who are average at Mathematics

Level 3: Students who are strong at Mathematics

This book has been written keeping in mind all the three kinds of students.

From my experience I have given below my perspective of what one should aim for (based on the category that he/she belongs to). It is important to clearly understand the starting level and accordingly define strategy for the QA section.

Level 1: Students who are weak at mathematics: Typically, these are students who were weak at mathematics in school and/or have left mathematics after their 10th or 12th class. They face a mental block in mathematics and have problems in writing equations. They also have severe problems in understanding mathematical language and are unable to convert the mathematical language into mathematical equations. They make mistakes even in interpretation of the most basic statements in mathematics (leave alone the complex statements). Besides, these students also have problems in solving equations. They suffer from the insecurity of knowing that they are unable to solve most problems which they face.

Level 2: Students who are average at mathematics: These students lie between the Level 1 and Level 3 students.

Level 3: Students who are strong at mathematics: These are the students who have got strong, structured and logical thinking ability. They not only understand the basic repetitive statements in mathematics but also complex statements. They are able to create their own flowcharts to arrive at solutions of these complex mathematical situations.

There are two alternative approaches that a student can take in solving this book.

Approach 1: “Start with basic concepts, solved examples then move on to LOD I, then LOD II in the chapter. Do not go into LOD III in the chapter in the first go. Complete all 19 chapters and then re-start with Chapter1 – review the basic concepts, resolve LOD I and LOD II, then move on to LOD III. This approach is advocated for students who are weak to average in mathematics (i.e. students of Level 1 and Level 2).

After completing the theory and practice exercises of the book for a second time, go to the practice sets 1–5 provided at the end of book. Set a time limit of 40 minutes for each set and take the tests. The questions contained in the sets are questions which have appeared in the CAT over the last 5 years (based on memory).”

Approach 2: “Start with the basic concepts, solved examples and then go through the exercises of LOD I, LOD II and LOD III. This is recommended for students who have strong concepts in mathematics (Level 3 students).”

Then go to the 5 practice tests given at the end of the book and take them one by one (time limit of 40 minutes for each test).”

An Important Point

Each of the questions contained in the LOD I, LOD II and LOD III exercises in the chapters have immense learning value. Hence, the approach that one takes while solving the questions should be one of learning. The reader should try to clearly understand the interpretation of each sentence used in the construction of the questions.

In other words the learning in every chapter should not be restricted to the solved examples or the theory contained in the chapter, but should continue through each of the questions contained in the exercises.

In conclusion, this is a book which is unique in approach and coverage. Any CAT aspirant who goes through the questions contained in this book in the manner advised in this book would get a distinct advantage when he/she faces the CAT.