Q. P, Q, R and S appeared in a test.
Question: Has P scored more marks than Q?
Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
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 by using both the Statements together.
Correct answer: d) The Question cannot be answered even by using both the Statements together.
Question from UPSC Prelims 2024 CSAT
Explanation :
Analyzing Statement I Alone:
P + Q = R + S
This only shows sum of P and Q equals sum of R and S.
Examples:
P = 7, Q = 5, R = 4, S = 8 → P > Q
P = 6, Q = 6, R = 5, S = 7 → P = Q
P = 5, Q = 7, R = 4, S = 8 → P < Q
Statement I alone insufficient.
Analyzing Statement II Alone:
P + S > Q + R
Shows P and S together score more than Q and R.
Examples:
P = 7, S = 5, Q = 5, R = 4 → P > Q
P = 3, S = 6, Q = 4, R = 3 → P < Q
Statement II alone insufficient.
Combining Statements:
From I: P + Q = R + S → P = R + S – Q
From II: P + S > Q + R → S > Q
Substituting: P = R + (S – Q)
Examples:
If R = 35, S = 60, Q = 50 → P = 45 → P < Q
If R = 41, S = 60, Q = 50 → P = 51 → P > Q
Combined statements still insufficient.
Answer: d) The Question cannot be answered even by using both the Statements together.
