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. ✓ UPSC's answer
- (d) The Question cannot be answered even by using both the Statements together.
Why the answer is (c)
• The question asks if (p + q - r) > (p - q + r), which simplifies to 2q > 2r, or q > r.
• Statement 1 states (p - q) > 0, implying p > q. This does not provide any information about the relationship between q and r, so it is insufficient alone.
• Statement 2 states (p - r) < 0, implying p < r. This does not provide any information about the relationship between q and r, so it is insufficient alone.
• Combining both statements: From Statement 1, p > q. From Statement 2, p < r. Therefore, q < p < r, which implies q < r.
• Since q < r, the inequality q > r is false. Thus, (p + q - r) is not greater than (p - q + r). The answer is 'No'.
• Since neither statement alone is sufficient but together they provide a definitive answer, option (c) is correct.
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- Statement 1 alone is insufficient because it only relates p and q, not q and r.
- (b) The Question can be answered by using either Statement alone.
- Neither statement alone is sufficient to determine the relationship between q and r.
- (d) The Question cannot be answered even by using both the Statements together.
- The question can be answered definitively as 'No' by using both statements together.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.