UPSC Prelims 2020 · CSAT

Question 8: Basic Numeracy

Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

c37

d(X + Y + Z)

AnswerUPSC’s answer is (b).

XYZ + YZX + ZXY puts each digit once in every place, so the sum is 111 × (X + Y + Z) = 3 × 37 × (X + Y + Z). It is therefore divisible by 3, by 37 and by (X + Y + Z). Divisibility by 9 would need an extra factor of 3, which could only come from (X + Y + Z); the condition rules that out.

Why each option is right or wrong

(a) Divisible: 111 contains a factor of 3.
(b) Right: 9 needs another factor of 3 from the digit sum, which the condition rules out.
(c) Divisible: 111 = 3 × 37.
(d) Divisible: the sum is (X + Y + Z) times 111.

Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.

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Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.