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1. The total cost of 2 pencils, 5 erasers and 7 sharpeners is Rs.30,
while 3 pencils and 5 sharpeners cost Rs.15 more than 6 erasers. By
what amount (in Rs.) does the cost of 39 erasers and 1 sharpener
exceed the cost of 6 pencils?
(1) 20
(2) 30
(3) It does not exceed
(4) Cannot be determined

2. If the roots of the equation (x + 1) (x + 9) + 8 = 0 are a and b, then
the roots of the equation (x+ a) (x+ b) - 8 = 0 are
(1) 1 and 9
(2) -4 and -6
(3) 4 and 6
(4) Cannot be determined

3. What is the remainder when 7
700
is divided by 100?
(1) 1
(2) 61
(3) 41
(4) 21

4. Balram, the local shoe shop owner, sells four types of footwear -Slippers (S), Canvas Shoes (C), Leather Shoes (L) and Joggers (J).
The following information is known regarding the cost prices and
selling prices of these four types of footwear:
(i) L sells for Rs.500 less than J, which costs Rs.300 more than S,
which, in turn, sells for Rs.200 more than L.
(ii) L costs Rs.300 less than C, which sells for Rs.100 more than S,
which, in turn, costs Rs.100 less than C.
If it is known that Balram never sells any item at a loss, then which
of the following is true regarding the profit percentages earned by
Balram on the items L, S, C and J represented by l, s, cand j
respectively?
(1) l≥ c≥ s≥ j
(2) c≥ s≥ l≥ j
(3) l≥ s≥ c≥ j
(4) s≥ l≥ j≥ c

6. A sequence of 4 digits, when considered as a numberin base 10
is four times the number it represents in base 6. What is the sum of
the digits of the sequence?
(1) 7
(2) 6
(3) 9
(4) 8

7. Some friends planned to contribute equally to jointly buy a CD
player. However, two of them decided to withdraw atthe last minute.
As a result, each of the others had to shell out one rupee more than
what they had planned for. If the price (in Rs.) ofthe CD player is an
integer between 1000 and 1100, find the number of friends who
actually contributed?
(1) 21
(2) 23
(3) 44
(4) 46

8. I assigned a value for n and started the program. If the robot
finally came back to O and stopped, what is the total distance that it
has covered?
(1) 180 m
(2) 360 m
(3) 720 m
(4) Cannot be determined

9. For how many values of n in the intervals [1, 60] does the robot
cover less than 1000 m, before it stops?
(1) 19
(2) 60
(3) 355
(4) Infinite

0. If N = 888Dup to 100 digits, what is the remainder when N is
divided by 625?
(1) 128
(2) 138
(3) 338
(4) 388

11. If [log
101] + [log102] + [log103] + [log104] + ...... + [log10n] = n,
where [x] denotes the greatest integer less than or equal to x, then
(1) 96 ≤ n< 104
(2) 104 ≤ n< 107
(3) 107 ≤ n< 111
(4) 111 ≤ n< 116

13. A regular polygon has an even number of sides. If the product
of the length of its side and the distance between two opposite
sides is of its area, find the number of sides it has.
(1) 6
(2) 8
(3) 20
(4) 16

14. There are three cities A, B and C, not on the same straight road.
Two buses P and Q start simultaneously from A and Brespectively
towards C. By the time Q reaches C, P is exactly halfway to C.
Immediately after Q reaches C, it starts travellingtowards A and it

crosses P at a point 165 km from A. The ratio of the speeds of P and
Q is 3 : 5. Assume that the roads joining A to C, Bto C and B to A
are all straight roads. If B is twice as far as from A as it is from C
and P would take to cover the distance from A to B,how much
time would Q take to cover the distance from C to A?
(1)
(2) 3 hours
(3)
(4) 4 hours

15. Two positive real numbers, a and b, are expressed as the sum
of mpositive real numbers and npositive real numbers respectively
as follows:
a= s1
+ s2
+ D..+ s mand
b= t
1
+ t
2
+ D..+ t
n
If [a] = [s1
] + [s2
] + D.. + [sm] + 4 and [b] = [t
1
] + [t
2
] + D. + [t
n
] + 3,

where [x] denotes the greatest integer less than or equal to x, what
is the minimum possible value of m+ n?
(1) 6
(2) 10
(3) 8
(4) 9

16. Consider two figures A and D that are defined in the co-ordinate
plane. Each figure represents the graph of a certain function, as
defined below :
A: | x| - | y| = a
D: | y| = d

If the area enclosed by A and D is 0, which of the following is a
possible value of (a, d)?
(1) (2, 1)
(2) (-2, 1)
(3) (-2, 3)
(4) (2, 3)

17. A natural number n is such that 120 n ≤ 240. If HCF of n and 240
is 1, how many values of nare possible?
(1) 24
(2) 32
(3) 36
(4) 40

19. If the sum to infinity of the series 2 + (2 - d)2/3 + (2 + d) 4/9 + (2
+ 3d) 8/27 + D.. is 5/2, what is the value of d?
(1) 7/12
(2) -7/12
(3) -5/12
(4) 5/12

20. The first n natural numbers, 1 to n, have to be arranged in a row
from left to right. The nnumbers are arranged such that there are an
odd number of numbers between any two even numbers as well as
between any two odd numbers. If the number of ways in which this
can be done is 72, then find the value of n.
(1) 6
(2) 7
(3) 8
(4) More than 8


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Previous year CAT Exam paper