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PYQ Question

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

Questions: Is p greater than q?
Statement-1: p × q is greater than zero.
Statement-2: p^2 is greater than q^2.
  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
  2. B. The Question can be answered by using either Statement alone.
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. D. The Question cannot be answered even by using both the Statements together.

Answer: D

Explanation

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^2. This implies |p| > |q|. If p=3, q=2, then p>q. If p=-3, q=2, then pq. If p=-3, q=-2, then 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. Therefore, the question cannot be answered even by using both statements together.