CAT Quant Practice Problems

Question: 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 :

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

(2) If the number of players, say n, 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–1)/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+1)/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.

(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 one bye.

Q can be answered from A alone but not from B alone.
Q can be answered from B alone but not from A alone.
Q can be answered from A alone as well as from B alone.
Q can be answered from A and B together but not from any of them alone.
Q cannot be answered even from A and B together.
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