Q. A Question is given followed by two Statements I and II. Consider the Question and the Statements.

# 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 Paper

**Explanation:**

Let’s analyze this step-by-step:

1. The question asks if P scored more marks than Q.

2. Statement I:**P + Q = R + S**

This statement alone doesn’t tell us anything about the relative scores of P and Q.

3. Statement II:**P + S > Q + R**

This statement gives us some information about P and Q, but not enough to definitively answer the question.

4. Using both statements together:**From Statement I: P + Q = R + S****From Statement II: P + S > Q + R**

If we substitute R + S from Statement I into Statement II:

P + S > Q + (P + Q – S)

P + S > P + Q

S > Q

This tells us that S scored more than Q, but it still doesn’t tell us how P’s score compares to Q’s.

5. Conclusion:

Even with both statements together, we cannot determine if P scored more marks than Q. We only know that S scored more than Q, but P’s score relative to Q remains unknown.

Therefore, the correct answer is: d) The Question cannot be answered even by using both the Statements together.