# Q. Question: Is p greater than q?

Statement-1: p x 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?

(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 Answer: (d) The Question cannot be answered even. by using both the Statements together.

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

## Question – Is p greater than q?

**Statement-1**: p x q is greater than zero. This statement implies that both p and q are either positive or negative. However, it does not provide information about whether p is greater than q.

**Statement-2**: p^2 is greater than q^2. This statement implies that the absolute value of p is greater than the absolute value of q. However, it does not provide information about whether p is greater than q, because both p and q could be negative.

Even if we use both statements together, we cannot definitively answer whether p is greater than q. For example, if p and q are both positive and p^2 is greater than q^2, then p is greater than q. But if p and q are both negative and p^2 is greater than q^2, then p is actually less than q.

Therefore, the correct answer is (d) The Question cannot be answered even by using both the Statements together.