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?

The question asks whether (p + q - r) is greater than (p - q + r). Let's simplify this inequality: (p + q - r) > (p - q + r) Subtract p from both sides: q - r > -q + r Add q to both sides: 2q - r > r Add r to both sides: 2q > 2r Divide by 2: q > r So, the original question is equivalent to asking: Is q > r? Now let's evaluate the statements: Statement-1: (p - q) is positive. This means p - q > 0, which implies p > q. This statement gives us a relationship between p and q, but provides no information about r. We cannot determine if q > r from this alone. For example, if p=5, q=3 (so p>q), r could be 1 (then q>r is true) or r could be 4 (then q>r is false). So, Statement-1 alone is not sufficient. Statement-2: (p - r) is negative. This means p - r r from this alone. For example, if p=3, r=5 (so pr is true) or q could be 2 (then q>r is false). So, Statement-2 alone is not sufficient. Combining Statement-1 and Statement-2: From Statement-1: p > q From Statement-2: p r? Since we concluded that q < r, the answer to the question is definitively "No". Since we can provide a definite answer ("No"), both statements together are sufficient to answer the question. Therefore, the question can be answered by using both statements together, but cannot be answered using either statement alone. This corresponds to option C. The final answer is C.