Question: Is p greater than q? Statement- 1: p x q is greater than zero. Statement- 2: p² is greater than q². Which one of the following is correct in respect of the above Question and the Statements?

The question asks whether p is greater than q (p > q). We need to determine if the given statements, individually or together, can definitively answer this.

Analyze Statement 1: p x q is greater than zero (p * q > 0). This statement implies that p and q must have the same sign. Case 1: p and q are both positive. Example: p=3, q=2. Here p > q. Example: p=2, q=3. Here p q. Example: p=-3, q=-2. Here p q in some cases, p q²). This statement implies that the absolute value of p is greater than the absolute value of q (|p| > |q|). Case 1: p and q are both positive. If |p| > |q|, then p > q. (e.g., p=3, q=2. Here p > q). Case 2: p is positive, q is negative. If |p| > |q|, then p > q. (e.g., p=3, q=-2. Here p > q). Case 3: p is negative, q is positive. If |p| > |q|, then p |q|, then p 2 is true, but -3 is not greater than -2). Since we get different answers (p > q in some cases, p |q|.

Let's combine these conditions: Scenario A: p and q are both positive. If p > 0 and q > 0, and |p| > |q|, then it must be that p > q. Example: p=3, q=2. (p*q=6 > 0, p^2=9 > q^2=4). In this case, p > q.

Scenario B: p and q are both negative. If p |q|, then it must be that p 0, p^2=9 > q^2=4). In this case, p q, and another scenario (p=-3, q=-2) where p < q, even using both statements together, we cannot definitively answer whether p is greater than q.

Therefore, the question cannot be answered even by using both statements together.

The final answer is D