UPSC CSE Prelims 2025

Correct Option (4)

The question asks whether Team P wins the match. To determine this, the final scores of both teams are required. Let P₁₀ and Q₁₀ represent the scores of Team P and Team Q, respectively, with 10 minutes remaining in the match. From the question, Team P was behind by 3 goals, implying Q₁₀ = P₁₀ + 3.

• Analysis of Statement I:

  • Statement I states: Team P scored 4 goals in the last 10 minutes.
  • Team P's final score = P₁₀ + 4.
  • The number of goals scored by Team Q in the last 10 minutes (let's call it G) is unknown.
  • Team Q's final score = Q₁₀ + G = (P₁₀ + 3) + G.
  • For Team P to win, P₁₀ + 4 > (P₁₀ + 3) + G, which simplifies to 1 > G.
  • If G = 0 (Team Q scored no goals in the last 10 minutes), Team P wins.
  • If G ≥ 1 (Team Q scored 1 or more goals in the last 10 minutes), Team P does not win (either draws or loses).
  • Since the value of G is not provided, Statement I alone is insufficient to determine if Team P wins.

• Analysis of Statement II:

  • Statement II states: Team Q scored a total of 4 goals in the match.
  • Team Q's final score = 4.
  • This statement provides no information about Team P's score at any point in the match.
  • Therefore, Statement II alone is insufficient to determine if Team P wins.

• Analysis using Both Statements Together:

  • From Statement I: Team P scored 4 goals in the last 10 minutes.
  • From Statement II: Team Q's final score = 4.
  • We know Q₁₀ = P₁₀ + 3.
  • Also, Team Q's final score = Q₁₀ + G = 4.
  • Substituting Q₁₀ = P₁₀ + 3 into the final score equation: (P₁₀ + 3) + G = 4.
  • Team P's final score = P₁₀ + 4.

  Consider two possible scenarios for G (goals scored by Team Q in the last 10 minutes):

  • Case 1: Assume Team Q scored 0 goals in the last 10 minutes (G=0).
    • Then (P₁₀ + 3) + 0 = 4, which implies P₁₀ = 1.
    • If P₁₀ = 1, then Q₁₀ = 1 + 3 = 4.
    • Team P's final score = P₁₀ + 4 = 1 + 4 = 5.
    • Team Q's final score = 4 (consistent with Statement II).
    • In this case, Team P (5) > Team Q (4), so Team P wins.
  • Case 2: Assume Team Q scored 1 goal in the last 10 minutes (G=1).
    • Then (P₁₀ + 3) + 1 = 4, which implies P₁₀ = 0.
    • If P₁₀ = 0, then Q₁₀ = 0 + 3 = 3.
    • Team P's final score = P₁₀ + 4 = 0 + 4 = 4.
    • Team Q's final score = Q₁₀ + G = 3 + 1 = 4 (consistent with Statement II).
    • In this case, Team P (4) = Team Q (4), so the match is a draw, and Team P does not win.

  Since different scenarios yield different outcomes (win vs. draw), even both statements combined are insufficient to definitively answer whether Team P wins the match.

Therefore, the question cannot be answered even using both statements together.

Incorrect Options:

• Option 1: "The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone." This is incorrect because neither Statement I nor Statement II alone provides sufficient information to answer the question, as demonstrated in their individual analyses.

• Option 2: "The Question can be answered by using either Statement alone." This is incorrect because both Statement I and Statement II individually provide insufficient information to determine the match outcome, as shown above.

• Option 3: "The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone." This is incorrect because, as established in the combined analysis, even both statements together do not provide enough information to definitively answer the question due to the ambiguity regarding the timing of Team Q's goals.