Question
Question: There were two women participating in a chess tournament. Every participant played two games with th...
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by 66 the number of games that the men played with the women. The number of participants is –
A
6
B
11
C
13
D
None of these
Answer
13
Explanation
Solution
Let number of men be n.
\ No. of games between males = 2 (nC2)
No. of games between players of opposite sex
= 2 (n × 2) = 4n
\ By the given condition,
2 . nC2 – 4n = 66
Ž n(n – 1) – 4n = 66
Ž n2 – 5n – 66 = 0
Ž n = 11 (Q n = –6 is impossible)
\ No. of participants = 11 + 2 = 13.