# Verbal Reasoning - Arithmetic Reasoning - Discussion

### Discussion :: Arithmetic Reasoning - Section 1 (Q.No.12)

12.

The 30 members of a club decided to play a badminton singles tournament. Every time a member loses a game he is out of the tournament. There are no ties. What is the minimum number of matches that must be played to determine the winner ?

 [A]. 15 [B]. 29 [C]. 61 [D]. None of these

Explanation:

Clearly, every member except one (i.e. the winner) must lose one game to decide the winner. Thus, minimum number of matches to be played = 30 - 1 = 29.

 Ananta said: (Nov 20, 2012) Is their any altranative method sir ?

 Jebas said: (Dec 1, 2012) Game can be divided into 4 sets. 1st set: 30 members can be alloted 15 games with 2 members each = 15 winners(15 matches) 2nd set: 15 winners can be separated into 14 + 1 members. 7 matches can be alloted for 14 members = 7 winners(7 matches) with 1 member remaining. 3rd set: 7 winners can be separated into 6 + 1 members. 3 matches can be alloted for first six members = 3 winners(3 matches). 1 match can be alloted for 2nd and 3rd set left out peoples = 1 winner(1 match). Totally 4 matches in 3rd set 4th set: Now we have 4 winners from which 2 semi final match and 1 final match can be played(3 matches) to decide the winner. Total matches played from 4 sets: 15+7+4+3 = 29.