## Previous Year Paper

### CAT-2008-Previous Years Paper

Question
20 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.

If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?

A: Exactly one player received a bye in the entire tournament.

B: One player received a bye while moving on to the fourth round from the third round

 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 we get various possible cases. We can see that 7 rounds have to be played. The bye could have occurred in any of the first 6. Let us look at the table below now:

 Round Bye in Round 1 Round 2 Round 3 Round 4 Round 5 Round 6 1 127 126 124 120 112 96 2 64 63 62 60 56 47 3 32 32 31 30 28 24 4 16 16 16 15 14 12 5 8 8 8 8 7 6 6 4 4 4 4 4 3 7 2 2 2 2 2 2

Using Statement B alone, we cannot say anything as other players too might have received byes. Using both together we can say that the number of players is 124.

Hence, (d).