IAS 2024 — CSAT Reasoning

2024mcqmedium

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?

Official previous-year question

Verified 2 Aug 2026.

Options

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
BThe Question can be answered by using either Statement alone
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
DThe Question cannot be answered even by using both the Statements together.

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Solution

Correct Option

The question asks to determine if P has scored more marks than Q (i.e., P > Q?).

Statement I: P + Q = R + S. This statement alone is insufficient.
- Consider Case 1: P=10, Q=5, R=8, S=7. Here, P + Q = 15 and R + S = 15. In this case, P > Q.
- Consider Case 2: P=5, Q=10, R=7, S=8. Here, P + Q = 15 and R + S = 15. In this case, P < Q.
- Since both P > Q and P < Q are possible while satisfying Statement I, it cannot definitively answer the question.
Statement II: P + S > Q + R. This statement alone is also insufficient.
- Consider Case 1: P=10, Q=5, S=3, R=2. Here, P + S = 13 and Q + R = 7. P + S > Q + R is satisfied. In this case, P > Q.
- Consider Case 2: P=5, Q=10, S=12, R=6. Here, P + S = 17 and Q + R = 16. P + S > Q + R is satisfied. In this case, P < Q.
- Since both P > Q and P < Q are possible while satisfying Statement II, it cannot definitively answer the question.
Combining Statement I and Statement II:
From Statement I: P + Q = R + S ...(i)

From Statement II: P + S > Q + R ...(ii)

Adding (i) and (ii):

(P + Q) + (P + S) > (R + S) + (Q + R)

$\Rightarrow$ 2P + Q + S > Q + S + 2R

$\Rightarrow$ 2P > 2R

This implies P > R.

Even with both statements combined, we can only conclude that P scored more marks than R. This information does not allow us to determine the relationship between P and Q. Therefore, the question cannot be answered even by using both statements together.

Incorrect Options:

Options 1, 2, and 3 are incorrect because, as demonstrated, neither Statement I alone nor Statement II alone is sufficient to answer the question. Furthermore, even when both statements are used together, the relationship between P and Q cannot be definitively established.

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Options

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

BThe Question can be answered by using either Statement alone

CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone

DThe Question cannot be answered even by using both the Statements together.

Solution

Correct Option

The question asks to determine if P has scored more marks than Q (i.e., P > Q?).

Statement I: P + Q = R + S. This statement alone is insufficient.
- Consider Case 1: P=10, Q=5, R=8, S=7. Here, P + Q = 15 and R + S = 15. In this case, P > Q.
- Consider Case 2: P=5, Q=10, R=7, S=8. Here, P + Q = 15 and R + S = 15. In this case, P < Q.
- Since both P > Q and P < Q are possible while satisfying Statement I, it cannot definitively answer the question.
Statement II: P + S > Q + R. This statement alone is also insufficient.
- Consider Case 1: P=10, Q=5, S=3, R=2. Here, P + S = 13 and Q + R = 7. P + S > Q + R is satisfied. In this case, P > Q.
- Consider Case 2: P=5, Q=10, S=12, R=6. Here, P + S = 17 and Q + R = 16. P + S > Q + R is satisfied. In this case, P < Q.
- Since both P > Q and P < Q are possible while satisfying Statement II, it cannot definitively answer the question.
Combining Statement I and Statement II:
From Statement I: P + Q = R + S ...(i)

From Statement II: P + S > Q + R ...(ii)

Adding (i) and (ii):

(P + Q) + (P + S) > (R + S) + (Q + R)

$\Rightarrow$ 2P + Q + S > Q + S + 2R

$\Rightarrow$ 2P > 2R

This implies P > R.

Even with both statements combined, we can only conclude that P scored more marks than R. This information does not allow us to determine the relationship between P and Q. Therefore, the question cannot be answered even by using both statements together.

Incorrect Options:

Options 1, 2, and 3 are incorrect because, as demonstrated, neither Statement I alone nor Statement II alone is sufficient to answer the question. Furthermore, even when both statements are used together, the relationship between P and Q cannot be definitively established.

IAS 2024 — CSAT Reasoning

Options

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Solution

Correct Option

Incorrect Options:

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IAS 2024 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option

Incorrect Options:

Your note

IAS Reasoning in other years

More IAS Reasoning questions

Other CSAT topics for IAS

Comprehension

Maths

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