CAT 2008 — QA Question 24
Each question is followed by two statements, A and B. Answer each question using the following instructions:
Mark option (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark option (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark option (3) if the question can be answered by using either statement alone.
Mark option (4) if the question can be answered by using both the statements together but not by either of the statements alone.
Mark option (5) if the question cannot be answered on the basis of the two statements.
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 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.
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.
Answer & solution
- A
1
- B
2
- C
3
4
- E
5
From statement (A) alone:
The entry list for the tournament consists of 83 players.
In round 1, 1 of the 83 players gets a bye and directly moves on to the next round.
∴ 42 players move on to round 2.
Similarly, 21 players move on to round 3, 11 players move on to round 4, 6 players move on to round 5, 3 players move on to round 6, 2 players move on to round 7.
The winner of the tournament would have played one match in each of the rounds; i.e. a total of 7 matches, provided he doesn’t get a bye.
However, we are not told whether or not the champion received a bye at some point in the tournament.
∴ We cannot answer the question on the basis of statement (A) alone.
From statement (B) alone:
The champion received one bye.
From this statement, we cannot find the number of matches played by the champion.
∴ We cannot answer the question on the basis of statement (B) alone.
From both the statements (A) and (B) together:
The champion must have played 7 matches if he did not receive any bye.
But it is given that the champion has got one bye in the tournament.
∴ He must have played only 6 matches.
∴ We can answer the question using both the statements (A) and (B) together.
Hence, option (d).