May 20, 2010

Quantitative Ability Question of the Day

QUESTION:-
64 people play a badminton tournament. A person is held to be knocked out if he loses two matches. In a round, all people play a match. A person will always play the person he has played in the previous round provided that person has not been knocked out. The winner is the last person left at the end of all the rounds.

What is the maximum possible number of matches needed to be played before the winner is crowned?

OPTIONS
1) 96
2) 97
3) 126
4) 127
5) 128

Solution

We can see that the maximum possible number of matches will be achieved when the maximum possible matches happen between the opponents in the first round, because all 64 people play that round.
This will happen when the 32 people who win the first round, all lose their second round matches (to the same opponents, by the rule of the tournament). After this, 32 people will lose in the third round, and will necessarily be out of the tournament, since this will be their second loss in the tournament. 96 matches have been played till now.
At the end of the third round, we have 32 players, each of whom have lost a single match and will be out of the tournament if they lose one more.
So, every match played after the third round will necessarily result in one player being knocked out.
Since we have one player left at the end, 32 – 1 = 31 matches will have to be played to crown a winner.
∴ Total number of matches = 96 + 31 = 127.
Hence, option 4.

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