A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. Question: Has P scored more marks than Q? Statement-I: The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II: The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. 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
Explanation
Statement-I alone (P + Q = R + S) gives no direct comparison between P and Q. Statement-II alone (P + S > Q + R) also does not directly compare P and Q. Combining both: from I, P − R = S − Q, i.e., P − Q = R − S (rearranging). From II, P − Q > R − S. But from I we got P − Q = R − S, which contradicts II unless we treat them as independent. Actually, from I: P + Q = R + S → P − S = R − Q. From II: P + S > Q + R → P − Q > R − S. These together do not allow us to determine whether P > Q because P − Q can be positive, negative, or zero depending on specific values consistent with both. Counterexamples can be constructed in either direction, so even both statements together are insufficient.
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