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UPSC Prelims 2023CSATLogical Reasoning & Analytical AbilityData Sufficiency - Inequalities

Q66. Questions: Is p greater than q?
Statement-1: p × q is greater than zero.
Statement-2: p^2 is greater than q^2.

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

Detailed Solution

✓ Correct Answer: Option D

The question asks if p > q. Statement 1: p × q > 0. This implies p and q have the same sign (both positive or both negative). If p=3, q=2, then p>q. If p=-2, q=-3, then p>q.

But if p=2, q=3, then p<q. If p=-3, q=-2, then p<q. Thus, Statement 1 alone is not sufficient. Statement 2: p^2 > q^2. This implies |p| > |q|. If p=3, q=2, then p>q. If p=-3, q=2, then p<q.

If p=3, q=-2, then p>q. If p=-3, q=-2, then p<q. Thus, Statement 2 alone is not sufficient. Combining both statements: p and q have the same sign, and |p| > |q|. If p and q are both positive, then p > q (e.g., p=3, q=2).

If p and q are both negative, then p < q (e.g., p=-3, q=-2). Since both scenarios are possible, even with both statements combined, we cannot definitively answer if p > q. Therefore, the question cannot be answered even by using both statements together.

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