IAS 2023 — CSAT Reasoning

2023mcqhard

Is p greater than q?

Statement-1: $p \times q$ is greater than zero.

Statement-2: $p^{2}$ is greater than $q^{2}$ .

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.

Did you get this right?

Solution

Correct Option: 4

The question seeks to determine if $p > q$ .

Consider Statement-1: $p \times q > 0$ . This condition implies that p and q must have the same sign (both positive or both negative).

If p=2 and q=1, then $p \times q = 2 > 0$ , and $p > q$ .
If p=-2 and q=-1, then $p \times q = 2 > 0$ , and $p < q$ .

Since both $p > q$ and $p < q$ are possible outcomes, Statement-1 alone is insufficient to answer the question.

Consider Statement-2: $p^{2} > q^{2}$ . This condition implies that $|p| > |q|$ .

If p=2 and q=1, then $p^{2} = 4 > q^{2} = 1$ , and $p > q$ .
If p=-2 and q=1, then $p^{2} = 4 > q^{2} = 1$ , and $p < q$ .

Since both $p > q$ and $p < q$ are possible outcomes, Statement-2 alone is insufficient to answer the question.

Consider both Statement-1 and Statement-2 together: From Statement-1, p and q have the same sign. From Statement-2, $|p| > |q|$ .

If p and q are both positive: Given $|p| > |q|$ , it follows that $p > q$ . (e.g., p=2, q=1).
If p and q are both negative: Given $|p| > |q|$ , it implies that p is numerically larger than q but negative. Consequently, $p < q$ . (e.g., p=-2, q=-1, where $|-2| > |-1|$ but $-2 < -1$ ).

As the combined statements allow for scenarios where $p > q$ and scenarios where $p < q$ , the question "Is p greater than q?" cannot be definitively answered even by using both statements together.

Incorrect Options:

Options 1, 2, and 3 are incorrect because, as demonstrated, neither statement alone nor both statements together provide a conclusive answer to whether $p > q$ .

Your note

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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: 4

The question seeks to determine if $p > q$ .

Consider Statement-1: $p \times q > 0$ . This condition implies that p and q must have the same sign (both positive or both negative).

If p=2 and q=1, then $p \times q = 2 > 0$ , and $p > q$ .
If p=-2 and q=-1, then $p \times q = 2 > 0$ , and $p < q$ .

Since both $p > q$ and $p < q$ are possible outcomes, Statement-1 alone is insufficient to answer the question.

Consider Statement-2: $p^{2} > q^{2}$ . This condition implies that $|p| > |q|$ .

If p=2 and q=1, then $p^{2} = 4 > q^{2} = 1$ , and $p > q$ .
If p=-2 and q=1, then $p^{2} = 4 > q^{2} = 1$ , and $p < q$ .

Since both $p > q$ and $p < q$ are possible outcomes, Statement-2 alone is insufficient to answer the question.

Consider both Statement-1 and Statement-2 together: From Statement-1, p and q have the same sign. From Statement-2, $|p| > |q|$ .

If p and q are both positive: Given $|p| > |q|$ , it follows that $p > q$ . (e.g., p=2, q=1).
If p and q are both negative: Given $|p| > |q|$ , it implies that p is numerically larger than q but negative. Consequently, $p < q$ . (e.g., p=-2, q=-1, where $|-2| > |-1|$ but $-2 < -1$ ).

Incorrect Options:

Options 1, 2, and 3 are incorrect because, as demonstrated, neither statement alone nor both statements together provide a conclusive answer to whether $p > q$ .

IAS 2023 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option: 4

Incorrect Options:

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IAS 2023 — CSAT Reasoning

Options

Did you get this right?

Solution

Correct Option: 4

Incorrect Options:

Your note

IAS Reasoning in other years

More IAS Reasoning questions

Other CSAT topics for IAS

Comprehension

Maths

Keep practicing Reasoning