Question

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 themselves 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. $[8,9]$
• B. $[10,12]$
• C. $(11,13]$
• D. $(14,17)$

Answer 1

The correct option is B $[10,12]$

$2w,xM$
$2$ ${}^x{C}_2-2\times 2x=66$
${}^x{C}_2-2x=33$
$x(x-1)-4x=66$
$x=11$