2017 CSAT, all questions
UPSC Prelims 2017 · CSAT
Question 30: Basic Numeracy
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?
aP is greater than Q.
bQ is greater than P.
cP is equal to Q.
dNone of the above can be concluded with certainty.
AnswerUPSC’s answer is (d).
P - Q = (0.4A + 0.65B) - (0.5A + 0.5B) = 0.15B - 0.1A. This is positive when 1.5B > A and negative when 1.5B < A. Knowing only that A > B does not decide which: for A = 2, B = 1, P < Q; for A = 1.2, B = 1, P > Q. The signs of A and B are not given either. So nothing can be concluded with certainty.
Why each option is right or wrong
- (a) P > Q only if 1.5B > A, which is not guaranteed.
- (b) Q > P only if A > 1.5B, which is not guaranteed.
- (c) P = Q only if A = 1.5B, a special case.
- (d) Correct: the sign of 0.15B - 0.1A depends on values not given.
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.