Question

There were two women participating in a chess tournament. Every participant played two games with the other participates. The number of games that the men played among themselves proved to exceed by 66 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 1

The correct option is C 13

Let there be $n$ men participants.

Then the number of games that the men play between themselves is $2{\times }^n{C}_2$ and the number of games that the men played with the women is $2\times \left(2n\right)$.
$\therefore 2{\times }^n{C}_2-2\times 2n=66$ (by hypothesis)
or $n^2-5n-66=0$ or $n=11$
Hence, the number of participants is $11$ men + $2$ women $=13$.