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, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does 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 either Statement 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 using any of the Statements. ✓ UPSC's answer

Why the answer is (d)

• With 10 minutes left, let Q have g goals, so P has g − 3.

• Statement I alone: P scores 4 more and ends with g + 1, but Q may also score in the last 10 minutes, so the result is not known.

• Statement II alone: Q's final total is 4, but nothing is said about P's goals in the last 10 minutes, so the result is not known.

• Both together: if Q scored k goals in the last 10 minutes, Q ends with 4 and P with (4 − k − 3) + 4 = 5 − k. P wins only if k = 0; k = 1 gives a draw and k ≥ 2 a win for Q.

• k is not given, so the question cannot be answered even with both statements — option (d).

Why the other options are wrong

(a) The Question can be answered by using one of the Statements alone, but cannot be answered…: Statement I alone is insufficient because it does not account for potential goals scored by Team Q in the final 10 minutes.
(b) The Question can be answered by using either Statement alone.: Neither statement alone provides enough information to determine the final score, as Q's activity in the last 10 minutes is unknown.
(c) The Question can be answered by using both the Statements together, but cannot be…: Even using both statements together, we do not know if Team Q scored any goals in the last 10 minutes, so the final result remains indeterminate.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2025, held on 25 May 2025. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.