UPSC Prelims 2017 · CSAT
Question 14: Logical Reasoning and Mental Ability
The sum of income of A and B is more than that of C and D taken together. The sum of income of A and C is the same as that of B and D taken together. Moreover, A earns half as much as the sum of the income of B and D. Whose income is the highest?
AnswerUPSC’s answer is (b).
Write the conditions: A + B > C + D, A + C = B + D, and A = (B + D)/2. From the last two, A + C = 2A, so C = A. Put C = A in the first: A + B > A + D, so B > D. Since A is the average of B and D, B > A = C > D. So B earns the most. Remember: when one person is the average of two others, they sit between them.
Why each option is right or wrong
- (a) A is only the average of B and D, so it is below B.
- (b) Correct: B > D, and A = C = (B + D)/2 lies between them.
- (c) C equals A, which is below B.
- (d) D is the lowest of the four.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.