April 3, 2012

CAT 2013 Challenge!

Can you solve these questions within 2 minutes and without using pen… If yes all the best for your CAT 2013.. If not then join our free CAT 2013 kick off class and learn how to solve CAT questions with shortcuts…

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