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 ✓ UPSC's answer
Why the answer is (d)
• Let the marks of P, Q, R and S be p, q, r and s.
• Statement I gives p + q = r + s, so r = p + q - s.
• Statement II gives p + s > q + r; substituting r gives p + s > q + p + q - s, i.e. 2s > 2q, so s > q.
• The combined statements therefore only establish that S scored more than Q; they do not establish whether P scored more than Q.
• For example, P=10, Q=5, R=5, S=10 satisfies both statements with P>Q, while P=6, Q=10, R=1, S=15 satisfies both statements with P<Q.
• Hence the question cannot be answered even by using both the Statements together, so option (d) follows.
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- Option (a) is wrong because neither Statement I alone nor Statement II alone determines whether P scored more than Q.
- (b) The Question can be answered by using either Statement alone
- Option (b) is wrong because neither Statement alone is sufficient to answer the question.
- (c) The Question can be answered by using both the Statements together, but cannot be…
- Option (c) is wrong because even together the statements only imply S scored more than Q, not that P scored more than Q.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2024, held on 16 June 2024. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.