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UPSC 2006: 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 ?
(a)8
(b)10
(c)12
(d)15
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Not attemptedCorrect Answer: (d) 15
With n original players, total scheduled matches are n(n – 1)/2. Three players withdrew after playing 3 matches each. Let x be matches already played among the three; unplayed matches U = 3n – 15 + x. The actually played matches are 75, so n(n – 1)/2 – U = 75 ⇒ n² – 7n – 120 – 2x = 0. Only x = 0 yields an integer root, n = 15, matching option (d). The other options (8, 10, 12) do not satisfy the equation under any permissible x, so 15 was the original number of participants.
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Frequently Asked Questions
What is the correct answer to this UPSC 2006 Science & Technology question?▼
The correct answer is option (d): 15. Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Quantitative Aptitude question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 2006, GS Paper 1, as Question 60. It falls under Science & Technology > Quantitative Aptitude.
What is the difficulty level of this UPSC question?▼
This question is rated "difficult". It is a challenging question that demands deep subject knowledge and analytical thinking.
How many UPSC Prelims questions have been asked from Quantitative Aptitude?▼
UPSC has asked 178 questions from Quantitative Aptitude (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.