Q43. 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?

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.