Quantitative Aptitude and Data Interpretation for the CAT and Other MBA Examinations

1064 Pages·2012·23.686 MB·English

by  Trishna Knowledge Systems

Quantitative Aptitude and
Data Interpretation
for the CAt and
Other MbA Entrance Examinations
Trishna Knowledge Systems
A division of
Triumphant Institute of Management Education Pvt. Ltd
00_TIME_FM.indd 1 11/04/12 1:18 PM
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 © Trishna Knowledge Systems, 2012
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 9788131774151
eISBN 9788131798836
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
00_TIME_FM.indd 2 11/04/12 1:18 PM
contents
Preface v–vi
PART-A (Quantitative Aptitude)
Chapter 1 Simple Equations A.3–A.24
Chapter 2 Ratio, Proportion and Variation A.25–A.46
Chapter 3 Numbers A.47–A.108
Chapter 4 Indices and Surds A.109–A.133
Chapter 5 Logarithms A.135–A.152
Chapter 6 Percentages A.153–A.177
Chapter 7 Profit and Loss – Partnership A.179–A.202
Chapter 8 Simple Interest – Compound Interest A.203–A.227
Chapter 9 Averages – Mixtures – Alligations A.229–A.256
Chapter 10 Quadratic Equations A.257–A.281
Chapter 11 Progressions A.283–A.307
Chapter 12 Time and Work A.309–A.335
Chapter 13 Time and Distance A.337–A.376
Chapter 14 Geometry and Mensuration A.377–A.431
00_TIME_FM.indd 3 11/04/12 1:18 PM
iv ■ CONTENTS
Chapter 15 Mensuration A.433–A.471
Chapter 16 Permutations and Combinations A.473–A.500
Chapter 17 Probability A.501–A.536
Chapter 18 Functions and Graphs A.537–A.591
Chapter 19 Trigonometry A.593–A.615
Chapter 20 Coordinate Geometry A.617–A.648
Chapter 21 Statistics A.649–A.669
Chapter 22 Special Equations A.671–A.690
Chapter 23 Inequalities and Modules A.691–A.715
Chapter 24 Number Systems A.717–A.736
Chapter 25 Operator Based Questions A.737–A.755
PART-B (Data Interpretation)
Chapter 1 Tables B.3–B.32
Chapter 2 Line Graphs B.33–B.56
Chapter 3 Bar Graphs B.57–B.86
Chapter 4 Pie Charts B.87–B.118
Chapter 5 Caselets B.119–B.134
Chapter 6 Network and 3D B.135–B.156
PART-C (Data Sufficiency)
Practice Exercises and Solutions C.3–C.94
PART-D (Practice Tests)
Practice Tests and Solutions D.3–D.52
00_TIME_FM.indd 4 11/04/12 1:18 PM
PReFAce
When you want to crack the CAT, one of the toughest competitive exams, then your preparation cannot be anything
short of top class. This is an exam where a mark can be the difference between success and rejection. For instance,
in CAT 2009 (conducted online), one needed to have scored enough to stand in or above the 95 percentile in each of
three sections, and in or above the 99.5 percentile overall, for an interview call from IIM Calcutta. Even if one stood
at the 99 percentile in Verbal Ability & Logical Reasoning, but lower than the 95 percentile in Quantitative Ability &
Data Interpretation, that would not have been good enough. No one would like to land up in a situation like that! Thus,
it is crucial that you not only achieve an excellent percentile overall, but also cross the cut-off in each of the sections
comfortably. This calls for preparation like a champion which in turn calls for guidance that is world class, that would
help you stay on course throughout your preparation, channelise your energies and, most importantly, build your skills
to master the unpredictable nature of the CAT. There was a time (in 1999), when there were 55 questions in DI & LR
alone, while, in 2011, the number of questions in each of the two sections of the test came down to 30. The nature of
questions has undergone a major shift from being calculation and observation based to being either purely logic based
or a fine blend of logic and calculations. The intensity of the exam has, thus, increased significantly. To get right on
top of all these aspects and to conquer them, you need to prepare for all scenarios that you may possibly expect in the
exam, to be able to unleash your talent and potential. What you need, in fact, is the right companion in the form of
quality study material.
Welcome to the Trishna Book on Quantitative Ability & Data Interpretation for the CAT! The book deals with the
various types of questions one is likely to face in the Quantitative Ability & Data Interpretation section of CAT. The sec-
tion accounts for half of the total marks in the CAT and a nearly equal percentage of the total marks in other management
entrance exams as well.
A notable feature of this book is the large number of solved examples provided in each chapter, followed by a number
of exercises. The basics and the solved examples are presented in a lucid manner, so that, with the solving of examples, the
concepts are easily understood. The detailed solutions given for each of these examples will not only help in comprehend-
ing the concepts involved, but will also help you get a good idea about the different models of problems in each chapter.
Once you go through all the solved examples, working out the exercises becomes easier. Care has also been taken to cover
a very wide range of problems in each chapter—including models of problems that have been appearing over the last few
years in a number of competitive exams.
Following the basics and the solved examples in every chapter, there are three exercises. The first exercise has rela-
tively easy questions, the second exercise has questions that are of a moderate level of difficulty, and the third exercise
has questions of a high level of difficulty. The first exercise is meant as the starting point for everybody, (even those who
would like to look at only the top institutes in the country), and would bring you up to the level required for the average
entrance exams. The second exercise would help you upgrade your ability and would help you cope with the exams that
00_TIME_FM.indd 5 11/04/12 1:18 PM
vi ■ PREFACE
are considered good and reasonably tough. The third exercise is meant to hone your skills and make you ready for the
toughest of exams – like the CAT.
After all the topics have been covered - in each of Quantitative ability, Data Sufficiency and Data Interpretation - the
book presents a number of practice tests of various levels of difficulty. Towards the end of the book there are five practice
tests on the lines of the CAT. These tests will help the student test his or her level of learning and to really get a feel of the
actual exam. They will also enable the student to hone his or her test taking skills and strategies, which, by themselves, are
a very important aspect in taking any management entrance exam.
In picking this book, you’ve made a sound choice. At Triumphant Institute of Management Education Pvt. Ltd. we
train graduates for National level entrance examinations like CAT, MAT, XAT, NIMCET, SNAP; International Level
examinations like GRE, GMAT, TOEFL, IELTS; and all major state level MBA/MCA entrance examinations. For students
in the Senior Secondary and Intermediate courses we offer training for National level examinations like IIT-JEE, AIEEE
and for local Engineering and Medical entrance tests. We also offer the IIT-Foundation course and preparatory courses for
examinations conducted by school boards.
The collective experience of the dedicated team at our institute, which has been gained over the last 20 years by train-
ing more than 9.5 lakh of students for a range of courses, allows us to say, confidently, that nobody understands the needs
of students and the nature of entrance examinations better than we do.
Another important feature of this book is that it is not authored by any single individual. It is prepared by a team of
faculty members at Triumphant Institute of Management Education Pvt. Ltd. the number 1 institute for CAT and
other Management Entrance Exams in India. All the faculty members who are involved in designing this book are very
experienced in teaching students preparing for various competitive exams and in preparing study material for such exams.
The essence of the combined knowledge of such an experienced team is what lies in your hands. We are sure that you will
find the book very useful in your preparation. The book has been prepared keeping in mind the needs of a cross-section of
students preparing for various competitive exams – from those who are who are keen on only the top notch institutes in the
country to those who may want to settle for local level institutes. As indicated earlier, the book contains exercises that will
help you practice not only for the very difficult exams but also for the not-so-difficult exams.
This book, in a nutshell, is useful not just for all those who are preparing for CAT and other management entrance
exams but also for those who want to build their skill-sets, overall, to understand and interpret data and chart a course to a
successful career at the global level.
The Editorial Team
Trishna Knowledge Systems
00_TIME_FM.indd 6 11/04/12 1:18 PM
p a r t
a
QUANTITATIVE APTITUDE
01_Simple Equations.indd 1 11/04/12 12:05 PM
This page is intentionally left blank.
01_Simple Equations.indd 2 11/04/12 12:05 PM
c h a p te r
1
SIMPLE EQUATIONS
There will be linear equations of one or two unknowns invariably in every problem. A linear equation is one where
each variable occurs only in its first power and not in any higher powers. Sometimes we get three equations in three
unknowns. In general, we need as many equations as the variables we will have to solve for. So, for solving for the values
of two unknowns, we need two equations (or two conditions given in the problem) and for solving for the values of three
unknowns, we need three equations (and hence, the problem should give three conditions from which we can frame three
equations). Solving the equations by itself is not a difficult task. The most important part of the problem is framing the
equation/equations. Once the equations are framed, solving them is very easy. In this chapter, we will deal with problems
involving as many equations (of first degree) as the number of unknowns. Later on, we will look at equations of second
degree (Quadratic Equations) and linear equations where the number of equations will be less than that of the number of
variables (in the chapter Special Equations).
ONE EQUaTION IN ONE UNKNOWN
An equation like 2x 1 4 5 26 is an equation in one unknown. We have only one variable x whose value we have to find
out. The steps in solving this are:
Step I: Take all quantities added to (or subtracted from) the x term (term with the unknown) to the right side with a
change of sign.
i.e., 2x 5 26 2 4 5 22.
Step II: Take the co‑efficient of x from left hand side and divide right hand side with this term to get the value of x.
i.e., x 5 22/2 5 11. Therefore, x 5 11.
TWO EQUaTIONS IN TWO UNKNOWNS
A set of equations like
2x 1 3y 5 8 ‑‑‑‑‑‑ (1)
5x 1 4y 5 13 ‑‑‑‑‑‑ (2)
is called a system of simultaneous equations in two unknowns. Here, we have two variables (or unknowns) x and y whose
values we have to find out. This can be done using the two given equations. The steps for this are as follows:
Step I: U sing both the equations we first eliminate one variable (so that we can then have one equation in one unknown).
01_Simple Equations.indd 3 11/04/12 12:05 PM