# Q. Question: Is (p+q-r) greater than (p-q+r), where p, q and r are integers ?

Statement-1: (p-q) is positive.

Statement-2: (p-r) is negative.

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: (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.

#### Question from UPSC Prelims 2023 CSAT

**Explanation : **

From the given question, we need to find whether (p+q-r) is greater than (p-q+r) or not.

## Is (p+q-r) greater than (p-q+r), where p, q and r are integers ?

If we simplify this, we get 2q > 2r or q > r. So, we need to determine whether q is greater than r or not.

Statement-1: (p-q) is positive. This means p > q. But this statement doesn’t give any information about r. So, we cannot answer the question using this statement alone.

Statement-2: (p-r) is negative. This means p < r. But this statement doesn’t give any information about q. So, we cannot answer the question using this statement alone.

Using both the statements together, we know that p > q and p < r. This implies that r > p > q or r > q. So, q is not greater than r. Therefore, (p+q-r) is not greater than (p-q+r).

So, the correct answer is (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.