2016 CSAT, all questions
UPSC Prelims 2016 · CSAT
Question 62: Basic Numeracy
If R and S are different integers both divisible by 5, then which of the following is not necessarily true ?
aR – S is divisible by 5
bR + S is divisible by 10
cR × S is divisible by 25
dR^2 + S^2 is divisible by 5
AnswerUPSC’s answer is (b).
Write R = 5a and S = 5b. Then R - S = 5(a - b), R x S = 25ab and R^2 + S^2 = 25(a^2 + b^2), so those are divisible by 5, 25 and 5 respectively. R + S = 5(a + b) is divisible by 10 only when a + b is even; for 5 and 10 the sum is 15, which is not. So (b) is not necessarily true.
Why each option is right or wrong
- (a) R - S = 5(a - b) is always divisible by 5.
- (b) Right: 5 + 10 = 15 is not divisible by 10.
- (c) R x S = 25ab is always divisible by 25.
- (d) R^2 + S^2 = 25(a^2 + b^2) is always divisible by 5.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.