UPSC CSE 2025 · PYQ · Data Sufficiency / Logical Reasoning · hard
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option.
Question: In a football match, when 10 minutes were left; team P playing against team Q was trailing by 3 goals. Did team P win the match?
Statement I: Team P scored 4 goals in the last 10 minutes.
Statement II: Team Q scored a total of 4 goals in the match.
Which one of the following is correct in respect of the above Question and the Statements?
A.The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
B.The Question can be answered by using both the Statements together but not by either alone.
C.The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
D.The Question cannot be answered even by using both the Statements together.✓ Correct
Explanation
Let P's score before last 10 minutes = x, then Q's score at that point = x+3. Using both statements: P's final score = x + 4, Q's final score = 4. We don't know x or how many goals Q scored in the last 10 minutes (only the total). If x+3 ≤ 4, then Q scored some in last 10 minutes. P final = x+4, Q final = 4. For P to win, x+4 > 4, i.e., x > 0. But we don't know x. If x=0, P's final = 4, Q's final = 4, match drawn. If x=1, P=5, Q=4, P wins. If x ≥ 2, then Q ≥ 5 before last 10 min, but Q's total is 4, impossible. So x ∈ {0,1}. Cannot uniquely determine if P won. Option (d) is correct — cannot be answered even with both statements.
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