Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants .If the number of games that the men played between them - selves exceeds the number of games that the men played with the women by 66 , then the number of men who participated in the tournament lies in the interval :

$(a)\;[8,9]\qquad(b)\;[10,12)\qquad(c)\;(11,13]\qquad(d)\;(14,17)$

Let there be x number of man and 2 women.
Since each men play with each other the combination will be x^C_2 , but there are two games for each then 2* x^C_2
Each man plays with the two women, number of ways would be 2x.
Given 2 * x^C_2 -2x =66
x^2-3x-66=0
integer x should lie between (b) to exceed games by 66.