Question : Is p greater than q ?
Statement-1 : p × 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 ?

Correct Option: The Question cannot be answered even by using both the Statements together.

We need to determine if p > q. Statement-1 gives p × q > 0. This means either both p and q are positive, or both are negative. If both are positive (e.g., p = 3, q = 2, then p > q), but if both are negative (e.g., p = -2, q = -3, then p > q, but what if p = -3, q = -2, then p < q). Thus, Statement-1 alone is insufficient. Statement-2 gives p^2 > q^2, which implies p^2 - q^2 > 0 => (p - q)(p + q) > 0. This can happen if both factors are positive or both are negative, which again allows multiple scenarios (e.g., p = 3, q = 2 gives p > q; but p = -3, q = -2 gives p^2 = 9 > q^2 = 4, yet p = -3 is less than q = -2). Combining both statements: Statement-1 says p and q have the same sign. Statement-2 says p^2 > q^2. If both are positive (e.g., p=3, q=2), p > q. If both are negative (e.g., p=-3, q=-2), then p^2 = 9 > q^2 = 4, but p (-3) < q (-2). Thus, even with both statements together, we get conflicting outcomes (-3 and -2 satisfy both statements, but -3 < -2; while 3 and 2 also satisfy both, and 3 > 2). Therefore, the question cannot be answered even by using both statements together.