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UPSC Prelims 2023CSATLogical Reasoning & Analytical AbilityData Sufficiency - Inequalities

Q67. Questions: 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.

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.✓ Correct
D. The Question cannot be answered even by using both the Statements together.

Detailed Solution

✓ Correct Answer: Option C

The question asks: Is (p + q - r) > (p - q + r)? Simplifying this inequality: p + q - r > p - q + r => 2q > 2r => q > r. So, the question is equivalent to asking: Is q > r? Statement 1: (p - q) is positive, which means p > q.

This statement gives no information about the relationship between q and r. Thus, Statement 1 alone is not sufficient. Statement 2: (p - r) is negative, which means p < r. This statement also gives no information about the relationship between q and r.

Thus, Statement 2 alone is not sufficient. Combining both statements: From Statement 1, p > q. From Statement 2, p < r. Together, these imply q < p < r. From this combined information, we can definitively conclude that q < r.

Since the question is 'Is q > r?', and we found q < r, the answer is a definitive 'No'. Therefore, both statements together are necessary and sufficient to answer the question.

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