# . In a chess tournament, all participants were to play one game with the other

Two players fell ill after having played 3 games each. If total number of games played in the tournament is equal to 84, then total number of participants in the beginning was equal to:

A. 10

B. 15

C. 12

D. 14

Ans: B

Sol: Let there were ‘n’ players in the beginning. Total number of games to be played was played to nC2 and each

player would have played (n – 1) games. Thus,

nC2 – ((n – 1) + (n – 1) – 1) + 6 = 84

n2 – 5n – 150 = 0

n = 15
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