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Chess competition games between boys and girls

CAT 2005 Slot 1 · Quantitative Ability · Easy · Combinatorics

This is an easy Quantitative Ability question from the CAT 2005 Slot 1 paper. It tests Combinatorics. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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.

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