43. 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?

1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
2. B. The Question can be answered by using either Statement alone.
3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
4. D. The Question cannot be answered even using any of the Statements.

Answer: D

Explanation

Initial Information: With 10 minutes remaining, Team Q was leading Team P by 3 goals. Let the scores be Q_initial and P_initial. So, Q_initial – P_initial = 3.

Statement I: Team P scored 4 goals in the last 10 minutes.
Final score of P = P_initial + 4. We don’t know how many goals Q scored in the last 10 minutes, nor do we know Q_initial or P_initial. For example, if Q_initial=3, P_initial=0, then P_final=4. If Q scores 0 more goals, Q_final=3, P wins. If Q scores 2 more goals, Q_final=5, P loses. So, Statement I alone is not sufficient.

Statement II: Team Q scored a total of 4 goals in the match.
Final score of Q = 4. We know Q_initial – P_initial = 3. We don’t know how many goals P scored in the last 10 minutes, nor how many Q scored in the last 10 minutes. For example, if Q_initial=3, P_initial=0, and Q scores 1 more goal (total 4), P scores 0 more goals (total 0), P loses. If Q_initial=4, P_initial=1, and Q scores 0 more goals (total 4), P scores 4 more goals (total 5), P wins. So, Statement II alone is not sufficient.

Combining Statement I and Statement II:
Final score of P = P_initial + 4.
Final score of Q = 4.
We know Q_initial – P_initial = 3.
Case 1: Assume Q_initial = 3, P_initial = 0. From Statement II, Q scored 1 more goal (3+1=4). From Statement I, P scored 4 more goals (0+4=4). Final scores: Q=4, P=4. Match is a draw. P does not win.
Case 2: Assume Q_initial = 4, P_initial = 1. From Statement II, Q scored 0 more goals (4+0=4). From Statement I, P scored 4 more goals (1+4=5). Final scores: Q=4, P=5. P wins.
Since we get different answers (draw or P wins) depending on valid initial scores, even combining both statements is not sufficient to definitively answer if Team P won the match. This is a classic data sufficiency problem.