1 Dear Student, The wait is finally coming to an end!! As you already know, the final frontier

192 Pages·2010·8.32 MB·English

Dear Student,
The wait is finally coming to an end!! As you already know, the final frontier: CAT 2010
is scheduled to be conducted starting 27 th October 2010. We are sure that all the hard work
and efforts that you have put in the last few months will pay rich dividends on the D-day.
Being anxious about what the test may have in store for you is natural at this stage. But
do not let this anxiety affect how you will finally perform in the CAT.
“CAT 500 series” is a special booklet from IMS to support you in your final lap before the
CAT. This booklet comprises 500 “must-solve questions” that have been statistically chosen
from select SimCATs* of 2009 and 2010. If you can solve these questions correctly and
in the target time (average 2.5 min), then you can be rest assured that you are on the right
path to acing CAT 2010.
* SimCATs have historically and statistically proven to be closest to the actual CAT. Refer
Chart on the left to view the statistical representations for CAT and SimCAT data.
To ensure an “effective preparation”, the 500 Questions are classified into two levels:
1. Score Enhancers: Questions that have been solved correctly by a majority of the
Top 10 percentilers who attempted them
(These are questions that are must attempts to break into the Top 10 percentile)
2. Score Maximisers: Questions that have been attempted by a majority of the Top 10
percentilers but solved incorrectly
(These are questions that will differentiate the best from the rest)
The questions have been classified into 10 sections on an area-wise basis: Arithmetic, Algebra,
Geometry, Modern Math, Verbal Ability, Verbal reasoning, Reading Comprehension, Data In-
terpretation, Logical Reasoning and Data Sufficiency.
How to use this booklet:
1. Plan your schedule for solving the questions in this booklet in a systematic manner.
And more importantly, stick to it.
a. To attempt every question and analyse how to solve it in the most effective way,
you should be spending about 8 minutes on an average on each of the questions
– this translates to a total time of about 4000 min, i.e. approx 65 hours
b. We recommend that you spend 3-4 hours daily for this purpose – this means you
should complete the booklet in around 20 days
c. If you do not have enough time on hand, first focus on completing questions from
your areas of weakness and then, time permitting, move to those from your areas
of strength.
2. If you need any help in solving the questions in this booklet, refer to the explanatory
answers provided at the end of the booklet (refer Pg 132)
3. For further assistance/guidance on how to solve these questions in the most efficient
manner, feel free to contact our centres and register for “CAT 500 Helpline” sessions.
Wish you all the best for Success in the CAT and other tests that you will be taking this
season.
Stay Focussed.
Vinayak KUDVA
National Product Manager,
Test prep, IMS
1
The Last Mile
All endeavor calls for the ability to tramp the last mile, shape the last plan, endure the last
hour’s toil.
Step 1: Believe that you can tramp the last mile!!
Life’s races aren’t won by the biggest, the fastest or the strongest. It’s inevitable that one day
it will be won by the person WHO BELIEVES HE CAN!!
Step 2: Have a fresh outlook: Rejuvenate and Focus on your goal – acing CAT 2010
- Imagine you have just started your prep.
- Imagine the last comprehensive test you took was your first test.
- Remember that at this stage, you have nothing to lose and everything to gain.
Step 3: For every test you take:
- Set the desired target score to get the coveted IIM call.
- Take the test to find your actual score.
- Analyse how you can bridge the gap between your actual score and desired score
Step 4: Bridge the Gap
- List all areas that require improvement.
- Rate the impact each of the areas can have on the score and prioritise accordingly
- areas with a higher weightage in the test must be tackled first.
- Spend about 3-4 hours everyday and work on two to three critical areas.
- Ensure that you can solve the “Score enhancer” and “Score maximiser” questions that
have been identified.
Finally, a few tips for the D-Day:
1. Stay calm and focused. Do not stress yourself by worrying.
2. On the eve the CAT, sleep early and ensure that you are fresh the next day.
3. Ensure that you have the Admit Card and any other document(s) as specified in your
admit card.
4. Before the test, read the instruction page carefully - see if there are any major changes
in the test structure and if the changes warrant a change in your test strategy.
5. While taking the test, read the questions and the directions for every question very
carefully. Also be careful while clicking the right option.
6. Mentally break the test into shorter tests-carry the success in one mini-test to the
next, but leave any failure behind.
DO NOT GIVE UP AT ANY STAGE DURING THE TEST. For all you know, you may perform
relatively better than the others.
2
1.PROBLEM SOLVING
a.ARITHMETIC
Score Enhancer............................................................................................................5
Score Maximiser..........................................................................................................8
b.ALGEBRA
Score Enhancer............................................................................................................11
Score Maximiser..........................................................................................................12
c.GEOMETRY
Score Enhancer............................................................................................................13
Score Maximiser..........................................................................................................15
d.MODERN MATHEMATICS
Score Enhancer............................................................................................................17
Score Maximiser..........................................................................................................19
2.DATA INTERPRETATION *....................................................................................21
3.DATA SUFFICIENCY
Score Enhancer................................................................................................................39
Score Maximiser..............................................................................................................40
4.LOGICAL REASONING *.........................................................................................45
5.VERBAL ABILITY
Score Enhancer................................................................................................................53
Score Maximiser..............................................................................................................63
6.READING COMPREHENSION * ............................................................................80
Explanatory Answers............................................................................................................132
· *Questions will be classified as “Score Enhancer” and “Score Maximiser” as per the set.
3

PROBLEM SOLVING
Arithmetic
“Score Enhancer “
DIRECTIONS for questions 1 to 19: Choose the 6. An ant travels along the edges of a cube shown
correct alternative. below. It travels along the longest path from
A to F at 2 cm/s and travels back to A at
1. What is the remainder when ((55) 15!)188 is 1 cm/s taking the shortest route. It does not
divided by 17? cross any vertex more than once and com-
pletes the journey in 120 seconds. What is
1) 1 2) 16
3) 3 4) 5 the length of each side of the cube?
5) 15
H G
2. Let n = 999 ... 99 be an integer consisting of
a string of 2009 nines. Find the sum of digits F
E
of n2.
1) 18072 2) 18081
3) 18090 4) 18080 D C
5) 18073
A B
3. A group of 10 workers can plough a field in
20 days. This group starts the work and after 1) 12 cm. 2)15 cm.
every 2 days, 2 additional workers join the 3) 24 cm. 4)20 cm.
group. The capacity of each worker is the
same. In how many days will the field be
7. A mixture of liquids A and B contains 70%
ploughed?
of B by weight. Liquid C is added till the final
1) 11 2) 12 solution contains 12% by weight of A. What
3) 14 4) 15 is the ratio (by weight) of B to C in the final
5) 13 mixture?
1) 7 : 15 2)3 : 11
11 11 11 11 3) 7 : 25 4)1 : 5
4. Find x, where x = + + + +
3 8 15 24
8. In a computer program, the current values
11 11 11 11 11
+ + + + . of a and b are 5 and 8 respectively. It then
35 48 63 80 99
executes the following code 100 times.
1) 7.2 2)11
{
3) 14.4 4)6.6
Step 1: New value of a = Sum of the present
values of a and b;
5. Which is the largest of the following num-
Step 2: New value of a= The difference between
- 1 - 1 - 1 - 1
the present values of a and b;
bers: 55 , 66 , 77 , 88 ?
Step 3: New value of b= The difference between
- 1 - 1 the present values of a and b;
1) 55 2) 66
}
- 1 - 1
3) 77 4) 88 What are the final values of a and b?
1) a = 5, b = 8 2)a = 8, b = 5
3) a = 5, b = 2 4)a = 5, b = 3
5
PROBLEM SOLVING
9. Considering all the natural numbers which 15. A mutual fund gives 21% per annum com-
lie between 1000 and 7770 (not including pound interest. Another investment gives the
either), in which place does the digit 7 appear same earning in 5 years under simple interest
the most? as the mutual fund gives in two years. What
is the rate of interest of simple interest?
1) Units 2)Tens
3) Hundreds 4)Thousands 1) 8.4% 2)8.82 %
3) 9.28 % 4)11.61%
10. Find the sum of the last two digits of (2 3
+ 33 + 43) 16. The cruise liner “Queen Alice” is 380 m long
and travels at a speed of 32 kmph in still
1) 9 2)12
water. The frigate “Lord Harry” is 180 m long
3) 1 4) 18
and travels at 40 kmph in still water. The
two ships pass each other in the Atlantic ocean,
traveling in opposite directions, in a region
11. If k = [ ] ×[ ] × [ ] × [ ] . . . × [ ] × [ ],
where there is current of 8m/s. How long
will it take them to pass each other?
where [ ] is the greatest integer d” a, then
1) 20 sec 2)28 sec
the number of zeroes at the end of k is
3) 42 sec
1) 21 2) 32
4) Cannot be determined
3) 33 4) 18
17. Distance between two points P and Q is 1200
12. On buying a camera, the shopkeeper gives
meters. Car A starts from P and travels on
three rolls of film free. On buying a camera
a straight line at a speed of 15m/s to reach
and six rolls of film, the shopkeeper gives
Q. Then, it reverses its direction immediately
additional four rolls of film free. If the
to travel back to P. If car B starts from P
equivalent discount is the same in both cases,
towards Q, four seconds later than car A at
then how many rolls will be equal in value
a speed of 10m/s, what distance from Q will
to a camera?
these two cars meet?
1) 12 2) 15
1) 936 m 2)991 m
3) 18 4) 24
3) 264 m 4)209 m
18. Find the value of the following expression:
13. Find the remainder when (3! + 6! + 12! +
24! + 48! + 96!) is divided by 66.
24· 4n1+2+n 1 - 1
1) 0 2) 1 ·
3) 33 4) 65 42·-· 842n4n122(n+2) 1-- +
1) 22n+1 + 2 2) 1
3) –1 4) 2n
14. A mixture of liquids P, Q and R, contains
the three in the ratio 2 : 4 : 7 respectively.
P and Q are added till the ratio becomes 19. What is the remainder when 924 is divided
7 : 4 : 2. Find the ratio of the amounts of by 79?
P and Q added.
1) 0 2) 1
1) 49 : 16 2)9 : 4 3) 47 4)67
3) 5 : 2 4)7 : 4
6
PROBLEM SOLVING
DIRECTIONS for questions 20 and 21: Answer 23. f(n) is defined as the sum of all the divisors
the questions on the basis of the data given of a natural number ‘n’.
below.
If f(n) < 2n, then the number ‘n’ is called
a deficient number.
The factorial of a natural number ‘n’ (or n!) is defined
as the product of all natural numbers less than or If f(n) > 2n, then the number ‘n’ is called
equal to ‘n’. an abundant number.
Given: m = 1! + 2! + 3! + 4! + …. + 99! + 100!
Which of the following pairs of numbers
comprises one abundant and one deficient
20. Find the last two digits of ‘m’.
number?
1) 3 2) 9
1) 7, 28 2)6, 64
3) 13 4)19
3) 42, 84 4)32, 42
21. Find the remainder, when ‘m’ is divided by
DIRECTIONS for question 24: Answer the ques-
168.
tions on the basis of the data given below.
1) 33 2)129
3) 153 4)67
DIRECTIONS for questions 22 and 23: Answer
the questions independently of each other.
22. Alok started one hour after Bimol from city
P towards city Q and crossed Bimol at a
distance of 10 km from P. After reaching city ACEG is a square park divided into two parts by its
Q, Alok immediately started moving back to diagonal. The only paths available for cycling in this
city P along the same route. On the way back, park are the boundary of the park, the diagonal and
he again met Bimol, who still needed 1 hour two identical circles placed in the two halves. Each
and 12 minutes to reach city Q. Find the of the circular paths has a radius of 1 km and they
distance between city P and city Q if Alok touch the side of the square at B, D, F and H and
and Bimol travelled at a constant speed the diagonal of the square at point K. Amit cycles
throughout the journey and Alok’s speed was
along these paths at a constant speed of 2 km/hr.
5 km/hr.
1) 30 km 2)28 km
24. Find the ratio of time taken by Amit to cycle
3) 34 km 4)20 km
along the path B-K-F to the time taken to cycle
along the path B-H-K-D-F.
1) 2 : 3 2)1 : 2
3) 3 : 5 4)4 : 5
7
PROBLEM SOLVING
Arithmetic
“Score Maximiser“
DIRECTIONS for questions 25 and 26: Choose DIRECTIONS for questions 28 to35: Choose the
the correct alternative. correct alternative.
25. Shakuntala challenges Dushyant - “Identify 28. How many numbers in the set
the ages of my three younger brothers. No
(cid:236) 99!96!93!6!3! (cid:252)
two are of the same age and the sum of their (cid:237) ,,,..., , (cid:253) are divisible by 24?
ages is 35.” “This is certainly not enough in- (cid:238) 96!93!90!3!0! (cid:254)
formation. Give me some more clues”, said
1) 20 2)17
Dushyant. “Okay”, she replied, “The age of
3) 16 4)21
each one is a prime number and if I tell you
the age of the middle one, then you would
easily get the ages of the others.” What is 29. It is known that: “Integer n is not prime if
the age of the eldest brother? k is an odd number divisible by 3”. Which
of the following can be logically concluded
1) 17 years 2) 19 years
from this?
3) 23 years 4) 29 years
5) Cannot be determined 1) If n is prime then k is an even number
not divisible by 3.
26. A function f is defined as f(n) = 6 n + 8n for 2) If k is not an odd number divisible by
all integers n. Find the remainder when f(83) 3 then n is prime.
is divided by 49.
3) If n is prime and k is divisible by 3 then
1) 7 2) 42 k must be divisible by 6.
3) 0 4) 14 4) If k is divisible by 3 and n is not prime
5) 35 then k is not divisible by 6.
DIRECTIONS for question 27: Refer to the data 30. The time for a pendulum’s swing is directly
below and answer the questions that follow. proportional to the square root of its length.
A pendulum 21 cm long is found to swing
M children (1 to M) are standing in a circle facing 30 times per minute. How many swings per
each other wearing different caps. In the first round minute will be made by a pendulum 28/3
each passes his cap to the child on his left. In the cm long?
next round each one passes the cap he now has
1) 45 2)20
to the second child on his left. In the next round
each one passes the cap he has to the third child 40
3) 4)80
on his left and so on. They stop when the first child 3
gets his original cap back for the first time.
31. How many pairs of integers (x, y) exist such
27. If M = 44 then after how many rounds will that x2 + 4y 2 < 100?
they stop?
1) 95 2)90
1) 12 2)22 3) 159 4)180
3) 33 4)32
32. How many numbers between 300 and 400
are such that the number equals the sum of
the cubes of its digits?
1) 0 2) 1
3) 2 4) 3
8
PROBLEM SOLVING
2
34. If u = for n > 1, then find the value
n n2- 1
of u + u + … + u .
2 3 100
1) 1.15 2)1.24
3) 1.36 4)1.48
33.
35. In the last summer vacation, Akshay was given
an assignment of writing down numbers from
100 to 1000. Despite all his brilliance and
intelligence, Akshay always gets confused
ACEG is a square park divided into two parts between the digits ‘6’ and ‘9’. As a result,
by its diagonal. The only paths available for he ends up interchanging them.
cycling in this park are the boundary of the
How many numbers did he write correctly
park, the diagonal and two identical circles
in his assignment?
placed in the two halves. Each of the circular
paths has a radius of 1 km and they touch 1) 343 2)353
the side of the square at B, D, F and H and 3) 448 4)449
the diagonal of the square at point K. Amit
cycles along these paths at a constant speed
of 2 km/hr.
How much extra time will Amit take to cycle
along the path B-C-K-G-F than to cycle along
the path B-C-D-E-F?
1) 2 hrs 2)3.5 hrs
3) 0.5 hrs 4)0.2 hrs
9