There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by 52 the number of games they played with women. If each player played one game with each other, the number of men in the tournament, was

Question

There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by 52 the number of games they played with women. If each player played one game with each other, the number of men in the tournament, was (A) 10 (B) 11 (C) 12 (D) 13

Tardigrade Admin · Accepted Answer

Let there were n men playing in the tournament with 2 women. According to the given condition, nC2 - nC1 × 2C1 = 52 ⇒ (n(n-1)/2) - 2n = 52 ⇒ n2 - n - 4n = 104 ⇒ n2 - 5n -104 = 0 ⇒ n = 13.

Q. There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by $52$ the number of games they played with women. If each player played one game with each other, the number of men in the tournament, was

$10$

$11$

$12$

$13$

Let there were n men playing in the tournament with $2$ women. According to the given condition,
$^{n} C_{2} -^{n} C_{1} \times^{2} C_{1} = 52$
$\Rightarrow \frac{n ( n - 1 )}{2} - 2 n = 52$
$\Rightarrow n^{2} - n - 4 n = 104$
$\Rightarrow n^{2} - 5 n - 104 = 0$
$\Rightarrow n = 13$ .

Q. There were two women participants in a chess tournament. The number of games the men played between themselves exceeded by 52 the number of games they played with women. If each player played one game with each other, the number of men in the tournament, was

10

11

12

13