UPSC Prelims 2020 · CSAT

Question 58: Basic Numeracy

For what value of n, the sum of digits in the number (10^n + 1) is 2?

aFor n = 0 only

bFor any whole number n

cFor any positive integer n only

dFor any real number n

AnswerUPSC’s answer is (b).

For n = 0, 10^0 + 1 = 2, whose digits sum to 2. For any positive integer n, 10^n + 1 is a 1, then zeros, then a 1 (for example 11, 101, 1001), so its digit sum is 2 as well. So the digit sum is 2 for every whole number n, which includes 0. For a non-integer such as n = 0.5, the value is not a whole number.

Why each option is right or wrong

(a) n = 0 is not the only case; n = 1 gives 11, whose digits also sum to 2.
(b) Right: n = 0 gives 2, and any positive integer n gives a 1, zeros, then a 1.
(c) Misses n = 0, which also works.
(d) A non-integer n gives a non-integer value, and a negative n gives a decimal, so the digit sum is not 2.

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.