Indian Institue of Management 2008 COMMON APTITUDE TEST (CAT ) - Question Paper

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+1)/2 players move on to the next round. T he process is continued till the final round, which obviously is played ranging from 2 players. The winner in the final round is the champion of the tournament.

15. Q: what is the number of matches played by the champion?
A: the entry list for the tournament consists of 83 players.
B: the champion received 1 bye.

15. Q: if the number of players, say n, in the 1st round was ranging from 65 and 128, then what is the exact value of n?
16.
A: Exactly 1 player received a bye in the entire tournament
B: 1 player received a bye while moving on to the 4th round from the 3rd round.

17. the integers 1,2,….,40 are written on a blackboard, the subsequent operation is then repeated 39 times.: in every repetition, any 2 numbers, say a and b currently on the blackboard are erased and a new number a+b-1 is written. What will be the number left on the board at the end?
(1) 820 (2) 821 (3) 781 (4) 819 (5) 780

18. Consider a square ABCD with midpoints E,F,G,H of AB,BC,CD AND DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 1200. what is the ratio of the area of ABQCDP to the remaining area inside ABCD?
(1) 4v2/3 (2) 2+v3 (3) 10-3v3/9 (4) 1+1/v3 (5) 2v3-1

19. Consider obtuse-angled triangles with sides eight cm, 15cm, and x cm. if x is an integer, then how many such triangles exist?
(1) five (2) 21 (3) 10 (4)15 (5) 14

20. Three consecutive positive integers are raised to the first, 2nd and 3rd powers respectively and then added. The sum so found is a perfect square whose square root equals the total of the 3 original integers. Which of the subsequent best defines the minimum, say m of these 3 integers?
(1) 1=m=3 (2) 4=m=6 (3) 7=m=9 (4) 10=m=12 (5) 13=m=15



Directions for ques. 21 and 22:

Five horses, Red, white, grey, black, and spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get 4 times the bet amount and those betting on the horse that came in 2nd get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 and Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

Earning:   Approval pending.