CAT Exam Model Paper 1 with solutions for free online practice

Question : 100 of 100

Marks: +1, -0

Serena and Venus were only two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that men played between themselves proved to exceed by 66, compared to the number of games the men played with women. How many participants were there?.

Your Answer:

Validate

Solution:

Let the number of men participating in the tournament be n. Since every participant played two games with every other participant. Therefore the total number of games played among men is

2 ×^ { n } C _ { 2 } = n ( n - 1 )

And the number of games played with each woman = 2n.
but since there are two women, hence the total number of games men played with 2 women = 2 × 2n = 4n
∴ {n(n − 1)} − 4n = 66
⇒

n ^ { 2 } - 5 n - 66 = 0

⇒n = 11 ( ∵ < 0, is not possible)
∴ Number of participants = 11 men + 2 women = 13.

Go to Question:

Prev Question