P = (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A is greater than B. In this context, which of the following statements is correct?
- (a) P is greater than Q.
- (b) Q is greater than P.
- (c) P is equal to Q.
- (d) None of the above can be concluded with certainty. ✓ UPSC's answer
Why the answer is (d)
• Let A = 100 and B = 0 (satisfying A > B). Then P = 40 + 0 = 40 and Q = 50 + 0 = 50, so Q > P.
• Let A = 100 and B = 99 (satisfying A > B). Then P = 40 + 64.35 = 104.35 and Q = 50 + 49.5 = 99.5, so P > Q.
• Since the relationship between P and Q changes depending on the specific values of A and B, no single inequality holds universally.
• Therefore, it is impossible to determine with certainty whether P is greater than, less than, or equal to Q based solely on the condition A > B.
• This leads to the conclusion that none of the definitive comparisons can be made.
Why the other options are wrong
- (a) P is greater than Q.
- P is not always greater than Q, as shown by the case where A=100 and B=0, resulting in Q > P.
- (b) Q is greater than P.
- Q is not always greater than P, as shown by the case where A=100 and B=99, resulting in P > Q.
- (c) P is equal to Q.
- P is not necessarily equal to Q, as the values differ in both test cases provided.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2017, held on 18 June 2017. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.