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CAT 2005 — QA Question 5

Forming a committeeEasy

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is

Answer & solution

  • 200

  • B

    216

  • C

    235

  • D

    256

Solution

Let there be g girls and b boys.

Number of games between two girls = gC2​​​​​​​
∴ g(g – 1)/2 = 45 
⇒ g2 – g – 90 = 0
⇒ (g – 10)(g + 9) = 0
Since the number of girls cannot be negative, ∴ g = 10

Number of games between two boys = bC2
∴ b(b – 1)/2 = 190
⇒ b2 – b – 380 = 0
⇒ (b + 19)(b – 20) = 0
⇒ b = 20

∴ Number of games in which one player is a boy and the other is a girl = 10 × 20 = 200

Hence, option (a).

CAT 2005 QA Q5: In a chess competition involving some boys and girls of a school, every student had to play exactly one game w — Solution | TheCATExam