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?
Answer & explanation
Answer: (c) Both I and II
The points force P to have one win and one draw and R one draw and one loss; the goal condition rules out Q winning a match, so Q drew both. P's only goal beat R 1–0, leaving P–Q at 0–0, and the Q–R draw must be 1–1 — so both statements hold.
- Three matches at 2 points each give 6 points (3 + 2 + 1 checks). Each team scored exactly one goal, so there were 3 goals in all.
- P's 3 points = one win + one draw. R's 1 point = one draw + one loss. Q's 2 points = one win + one loss, or two draws.
- If Q had a win and a loss: P's draw and R's draw must be the same match, P vs R, so P beat Q and Q beat R. P's only goal came against Q, so P–R was 0–0; Q's only goal came against R, so R scored in neither match — but R must score one goal. Impossible.
- So Q drew both of its matches, and P beat R.
- P's only goal was needed to beat R (1–0), so P–Q was 0–0. Q's only goal came in the drawn Q–R match, so it ended 1–1 and R's goal came against Q.
- Both statements are correct.
- ✓ I P scored only once and needed that goal to beat R, so P–Q was a 0–0 draw.
- ✓ II Q's single goal came in the Q–R match, which was a draw, so it ended 1–1 and R's one goal was against Q.
Remember · In tournament puzzles, list the win/draw/loss patterns from the points, then use goal totals to eliminate cases.
Question and answer: UPSC's official GS Paper II (2025, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·