• # question_answer 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

Let there be $n$ men participants. Then the number of games that the men play between themselves is $2\ .{{\ }^{n}}{{C}_{2}}$ and the number of games that the men played with the women is $2.\ (2n)$. $\therefore$$2.{{\ }^{n}}{{C}_{2}}-2\ .\ 2n=66$    (By hypothesis) $\Rightarrow$${{n}^{2}}-5n-66=0\Rightarrow n=11$ $\therefore$ Number of participants$=11\ \text{men}+2\ \text{women}=13$.