Common Admission Test or CAT is a entrance exam for management courses. CAT is conducted by IIMs every year and holds a very reputed position when aspirants talk about MBA Entrance Examinations in India.

Here I’m giving you few questions for CAT exam:

1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
(1) 2 ≤ x ≤ 6
(2) 5 ≤ x ≤ 8
(3) 9 ≤ x ≤ 12
(4) 11≤ x ≤ 14
(5) 13 ≤ x ≤ 18

Directions for Questions 2 and 3:
Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a ≠ 0. It is known that f (5) = −3f (2) and that 3 is a root of f(x) = 0.

2. What is the other root of f(x) = 0?
(1) −7
(2) − 4
(3) 2
(4) 6
(5) cannot be determined

3. What is the value of a + b + c?
(1) 9
(2) 14
(3) 13
(4) 37
(5) cannot be determined
4. The number of common terms in the two sequences 17, 21, 25, … , 417 and 16, 21, 26, … , 466 is
(1) 78
(2) 19
(3) 20
(4) 77
(5) 22
5. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 60
(2) 75
(3) 45
(4) 90
(5) 72

DIRECTIONS for questions 1 to 7: Answer the questions independently of each other.

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?

(1) 21
(2) 23
(3) 44
(4) 46