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 po…

Question

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.

1. A. I only
2. B. II only
3. C. Both I and II (Correct answer)
4. D. Neither I nor II

Correct Answer

Option C — Both I and II

Detailed Solution & Explanation

The correct answer is Both I and II.

Key Points

• Total matches = 3 (P vs Q, P vs R, Q vs R).
• Points: P=3, Q=2, R=1. Total = 6 = 3 wins worth 2 pts each → all results are decisive (no draws)... but P=3 must come from 1 win + 1 draw.
• P draws with Q (1+1), P beats R (2). P=3✓.
• Q: drew with P (1), beat R (2)?
• Q=3≠2. Try: P beats Q (2), P draws R (1). P=3✓.
• Q beats R (2)=Q total 2✓.
• R: 1 from draw with P=1✓.
• Check Statement I: P vs Q → P wins, not a draw.
• Statement I says P-Q is a draw with 0-0 → FALSE.
• Statement II: Goals — each team scored exactly 1 goal total in tournament.
• R scored 1 goal; it was against Q (since R lost to P with P scoring, R scored 0 against P, so R's 1 goal was against Q). Statement II: TRUE. Only II is correct. Answer: II only.