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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 7700 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, c and j
respectively?
(1) l ≥ c ≥ s ≥ j
(2) c ≥ s ≥ l ≥ j
(3) l ≥ s ≥ c ≥ j
(4) s ≥ l ≥ j ≥ c
5. In the figure below, P, Q and R are points on a circle with centre
O. The tangent to the circle at R intersects secant PQ at T. If QRT =
55° and QTR = 25°, find POQ.
(1) 110°
(2) 100°
(3) 90°
(4) 50°
6. A sequence of 4 digits, when considered as a number in 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 at the 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.) of the CD player is an
integer between 1000 and 1100, find the number of friends who
actually contributed?

Q: 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

Answer: (3)

Q: 9 For how many value 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

Answer: (3)

DIRECTIONS for questions 10 to 20: Answer the questions independently of each other.

Q: 10. If N = 888…up to 100 digits, what is the remainder when N is divided by 625?

(1) 128

(2) 138

(3) 338

(4) 388

Answer: (2)

Q: 11. If
 
 
 
 
where [x] denotes the greatest integer less than or equal to x, then

(1)

(2)

(3)

(4)

Answer: (3)

Q: 12 In the figure below, BD = 8 cm and DC = 6 cm. AE : ED = 3 : 4. If AF =12 cm, find AC (in cm).

Q 12 Find the AC in cm
Q 12 Find the AC in Cm

(1) 28

(2) 38

(3) 44

(4) 40

Answer: (4)

Q: 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 ¼ th of its area, find number of sides it has

(1) 6

(2) 8

(3) 20

(4) 16

Answer: (4)

Q: 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 B respectively towards C. By the time Q reaches C, P is exactly halfway to C. Immediately after Q reaches C, it starts travelling towards 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, B to C and B to A are all straight roads. If B is twice as far 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)

(4) 4 hours

Answer: (1)

Q: 15. Two positive real numbers, a and b, are expressed as the sum of m positive real numbers and n positive real numbers respectively as follows:



If

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

Answer: (4)

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

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)

Answer: (2)

Q: 17. A natural number n is such that 120 n≤240. If HCF of n and 240 is 1, how many values of n are possible?

(1) 24

(2) 32

(3) 36

(4) 40

Answer: (2)

Q: 18. If

(1) 24/90

(2) 242/900

(3) 245/900

(4) 200/729

Answer: (4)

Q: 19 If the sum to infinity of the series 2 +(2-d) 2/3+ (2 + d) 4/9 + (2 + 3d) 8/27 + ……▭ is 5/2, what is the value of d?

(1) 7/12

(2) -7/12

(3) -5/12

(4) 5/12

Answer: (2)

Q: 20. The first n natural numbers, 1 to n, have to be arranged in a row from left to right. The n numbers 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

Answer: (1)


CAT Exam sample question paper
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