Chess competition games between boys and girls

CAT 2005 Slot 1 · QA · Easy · Combinatorics

All CAT 2005 Slot 1 questionsMore Combinatorics questionsAll CAT QA

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

  1. A.

    200

  2. B.

    216

  3. C.

    235

  4. D.

    256

Answer

A

Explanation

Let there be gg girls and bb boys. Number of games between girls =(g2)=45  ⟹  g(g−1)2=45  ⟹  g=10= \binom{g}{2} = 45 \implies \frac{g(g-1)}{2} = 45 \implies g = 10. Number of games between boys =(b2)=190  ⟹  b(b−1)2=190  ⟹  b=20= \binom{b}{2} = 190 \implies \frac{b(b-1)}{2} = 190 \implies b = 20. Number of games between one boy and one girl =b×g=20×10=200= b \times g = 20 \times 10 = 200.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace