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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 :

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

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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.
answered Apr 2, 2015 by Limitsofawesomeness
 

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