Indian Institue of Management 2008 Entrance Exams Other Entrance Exams CAT - Question Paper

(b) If the number of players, say n, in any round is odd, then 1 of them is provided a bye, that is he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-1)/2 pairs. The players in every pair play amatch against every other and the winnermoves on to the next round. No player gets more than 1 bye in the entire tournament.

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.


16. 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?

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. 3 consecutive positive integers are raised to the first, 2nd and 3rd powers

Earning:   Approval pending.