UPSC Prelims 2006 · General Studies
Question 60: Basic Numeracy
In a tournament each of the participants was to play one match against each of the other participants. 3 players fell ill after each of them had played three matches and had to leave the tournament. What was the total number of participants at the beginning, if the total number of matches played was 75 ?
AnswerThe answer is (d).
Let n be the number of participants at the start. The three who fell ill had played three matches each, 9 matches in all. The other n - 3 players all finished their round-robin among themselves: (n - 3)(n - 4)/2 matches. So (n - 3)(n - 4)/2 + 9 = 75, giving (n - 3)(n - 4) = 132 = 12 x 11, so n - 3 = 12 and n = 15. Check: 66 + 9 = 75.
Why each option is right or wrong
- (a) n = 8 would give only 10 + 9 = 19 matches.
- (b) n = 10 would give 21 + 9 = 30 matches.
- (c) n = 12 would give 36 + 9 = 45 matches.
- (d) Correct: n = 15 gives 66 + 9 = 75 matches.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.