UPSC Prelims 2025 CSAT, question 50

Topic: Arrangements and puzzles

Q50

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 IICorrect answer
(d) Neither I nor II

Solution.

Answer: (c) Both I and II

In a 3-team round-robin ( $3$ matches: $P$ - $Q$ , $P$ - $R$ , $Q$ - $R$ ) where each team scores exactly $1$ goal: $P$ has $3$ points ( $1$ win, $1$ draw, $0$ losses) and $R$ has $1$ point ( $0$ wins, $1$ draw, $1$ loss); since total wins equal total losses ( $1$ win and $1$ loss overall), $Q$ 's $2$ points must come from $2$ draws ( $0$ wins, $2$ draws, $0$ losses).
Statement I is correct: since $Q$ drew both its matches, $P$ 's win was against $R$ ( $1$ - $0$ , using $P$ 's only goal) and $P$ drew with $Q$ ; since $P$ had $0$ goals left for the $P$ - $Q$ match, the $P$ - $Q$ draw must have been $0$ - $0$ .
Statement II is correct: since $Q$ - $R$ was a draw and both $Q$ and $R$ scored $0$ goals in their matches against $P$ , both $Q$ and $R$ must have scored their $1$ tournament goal against each other in a $1$ - $1$ draw.