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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? CAT 2008

(1) 2 ≤ x ≤ 6                                                                        (2) 5 ≤ x ≤ 8
(3) 9 ≤ x ≤ 12                                                                       (4) 11≤ x ≤ 14
(5) 13 ≤ x ≤ 18

2.                     The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is: CAT 2006

(1) 7                                                                       (2) 13
(3) 14                                                                     (4) 18
(5) 20

3. If three positive real numbers x, y, z satisfy y – x = z – y and xyz = 4, then what is the minimum possible value of y? CAT 2004

1. 21/3                                                                                    2. 22/3
3 .21/4                                                                                                       4. 23/4

4. Extra: If p, q and r are the lengths of the sides of a triangle, then the range of the expression below is? P2 + q2 + r2 / (pq + rq + pr)

(1) (1,2)                                                                                (2) [1,2)
(3) (1,3)                                                                                (4) (-1/2,3)

5. Consider a sequence where the nth term, tn = n/(n+2), n = 1, 2, ….

The value of t3 x t4 x t5 x….x t53 equals: CAT 2006
(1) 2/495                                                              (2) 2/477
(3) 12/55                                                              (4) 1/1485
(5) 1/2970

6. If a1 = 1 and an+1 – 3an + 2 = 4n for every positive integer n, then

a100 equals? CAT 2005
1. 399 – 200                                                                          2. 399 + 200
3. 3100 – 200                                                                         4. 3100 + 200

7. Find the sum CAT 2008

(1) 2008 – 1/2008                                                              (2) 2007 – 1/2007
(3) 2007 – 1/2008                                                              (4)2008 – 1/2007
(5) 2008 – 1/2009

8. ABCDEF is a regular hexagon and angle AOF = 90°. FO is parallel to ED. What is the ratio of the area of the triangle AOF to that of the hexagon ABCDEF? CAT 2003

a) 1/12                                                                                  b) 1/6
c) 1/24                                                                                  d) 1/18

9. In the figure given below, AB is the chord of a circle with centre O.ABis extended to C such that BC =OB.The straight line CO is produced to meet the circle at D. If LACD = y degrees and LAOD = x degrees such that x = ky, then the value of k  is?

a) 3                                                                                         b) 2
c) 1                                                                                         d) 4

10. Let f(x) be a function satisfying f(x).f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)? CAT 2008
(1) 0                                                                                       (2) 1/4
(3) 1/2                                                                                   (4) 1
(5) Cannot be determined