Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct ? I. The result of the match between P and Q is a draw with the score 0 – 0. II. The number of goals scored by R against Q is 1. Which of the statements given above is/are correct ?
- (a) I only
- (b) II only
- (c) Both I and II ✓ UPSC's answer
- (d) Neither I nor II
Why the answer is (c)
• Three matches are played (P–Q, Q–R, R–P) and every team scores exactly one goal in the whole tournament.
• Points: P's 3 must be one win + one draw, R's 1 must be one draw + one loss, and Q's 2 is a win + a loss or two draws. Q cannot beat P, because P could then reach at most 2 points.
• Pattern A — P beats Q, P draws with R, Q beats R — fits the points but not the goals: P must spend its only goal beating Q, so P–R is 0–0 and R's goal comes against Q; Q–R then ends 1–1, not a Q win. So pattern A is impossible.
• Pattern B — P draws with Q, P beats R, Q draws with R. If P–Q were 1–1, P would have no goal left to beat R, so P–Q is 0–0; P then beats R 1–0, and Q–R is 1–1.
• So P–Q was a 0–0 draw (Statement I correct) and R scored 1 goal against Q (Statement II correct) — option (c).
Why the other options are wrong
- (a) I only
- Statement II is also correct, so 'I only' is incomplete.
- (b) II only
- Statement I is also correct, so 'II only' is incomplete.
- (d) Neither I nor II
- Both statements I and II are correct based on the unique solution derived from the points and goal constraints.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.