Q. 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.
Correct Answer : d)
UPSC Prelims 2025 CSAT
Explanation :
Let
Gq₀ = goals scored by Q up to the 80th minute,
Gp₀ = goals scored by P up to the 80th minute.
We know at 80′ Q was ahead by 3 goals:
Gq₀ − Gp₀ = 3 …(1)
Call in the last 10 minutes:
P scores 4 goals (Statement I),
Q scores B goals (unknown).
Thus final tallies are
Gp_f = Gp₀ + 4,
Gq_f = Gq₀ + B.
Statement II says total goals by Q in whole match is 4, so
Gq_f = 4 ⇒ Gq₀ + B = 4. …(2)
From (1): Gp₀ = Gq₀ − 3, so
Gp_f = (Gq₀ − 3) + 4 = Gq₀ + 1.
Then the final goal‐difference is
Gp_f − Gq_f = (Gq₀ + 1) − 4 = Gq₀ − 3.
But from (2) and non‐negativity of B, we get Gq₀ is either 3 or 4 (since Gq₀ + B = 4 and B ≥ 0).
Case 1: Gq₀ = 4, B = 0 ⇒ Gp_f − Gq_f = 1 ⇒ P wins.
Case 2: Gq₀ = 3, B = 1 ⇒ Gp_f − Gq_f = 0 ⇒ It’s a draw.
Since with both statements together P may win or may only draw, we cannot be sure.
Neither statement alone gives a unique answer, and even together they leave two possibilities. Hence (d).
