## Previous Year Paper

### CAT-2008-Previous Years Paper

Question
19 out of 25

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules:

A. If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

B. If the number of players, say it, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n-1) players are grouped into (n-l)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one 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+l)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

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 one bye.

 A If Question can be answered 1mm A alone but not from B alone. B If Question can be answered from B alone but not from A alone. C If Question can be answered from either of A or B alone. D If Question can be answered from A and B together but not from any of them alone. E If Question cannot be answered even from A and B together.

Ans. D

Using statement A alone, if there are 83 if there are 83 players, the number of players in each subsequent round will be as follows:

 Round Players 1 83 2 42 3 21 4 11 5 6 6 3 7 2 â Final

The champion plays in the final and so can play either 6 or 7 matches (depending on whether he gets a bye or not). Hence no unique answer.

Using statement B alone, we can draw no conclusion without knowing the number of rounds. With both the statement together, we can say that the champion plays 6 matches. Hence, (d).