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

Correct  option (B) (B) [10, 12)

Let the number of men who participated be n. See Fig. 

Number of matches men played with women = 2(n + n) = 4n

Number of matches men played among themselves = 2ⁿC₂

Now, according to the question,

Therefore, the number of men is 11, which lies in the interval (10, 12).