Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 17

In a tournament of Chess having 150 entrants, a player is eliminated whenever he loses a match. It is given that no match results in a tie/draw. How many matches are played in the entire tournament?

  1. 151
  2. 150
  3. 149
  4. 148

Answer

149

  • Key fact: In a knockout tournament, each match eliminates exactly one player since there are no draws.

  • Starting with 150 entrants, to get 1 winner, exactly 149 players must be eliminated.

  • Option (a) 151: Would eliminate 151 players, impossible with only 150 entrants. Verdict: Incorrect.

  • Option (b) 150: Would eliminate 150 players, leaving no winner. Verdict: Incorrect.

  • Option (c) 149: Eliminates 149 players and leaves 1 champion. Verdict: Correct.

  • Option (d) 148: Would leave 2 players uneleminated, so tournament not complete. Verdict: Incorrect.

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