Tournament points & goals deduction
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.
The result of the match between P and Q is a draw with the score 0-0.
- 2.
The number of goals scored by R against Q is 1.
Options
I only
II only
Both I and II
Neither I nor II
Explanation
Analyze points first. 3 teams playing exactly once yields 3 total matches. P(3), Q(2), R(1) means total points awarded = 6. Since every match awards exactly 2 points (2+0 for win/loss, or 1+1 for draw), the points dictate the outcomes: P(3) = 1 Win, 1 Draw. Q(2) = 2 Draws. R(1) = 1 Draw, 1 Loss. Matches: P drew with Q. P beat R. Q drew with R. Now map the 3 goals (one scored by each team total): P beat R. Since P's total tournament goals = 1, P must have scored it here (1-0). R scored 0 against P. Since P scored 1 against R, P scored 0 against Q. Their draw must be 0-0. (Statement I is True). Since Q vs P was 0-0, Q's single tournament goal was scored against R. Since Q vs R was a draw, and Q scored 1, R must have scored 1 against Q to tie 1-1. (Statement II is True).
Answer: (c).
Question details
Year
2025
Paper
CSAT
Question
Q70
Section
Logical & Analytical Reasoning
Sub-topic
Logical Puzzles
Type
Inequality logic
Difficulty
Hard
Source hint
Logical deduction
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