Question

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. 12

Answer 1

The correct option is C 13

$\therefore 2n_{c_2}-2.2n=66$ (By hypothesis)
$\Rightarrow n^2-5n-66=0\Rightarrow n=11$
$\therefore$ Number of participants = 11 men + 2 women =13.