2023 CSAT, all questions

UPSC Prelims 2023 · CSAT

Question 27: Basic Numeracy

A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13 ?

a11
b9
c7
d1

AnswerUPSC’s answer is (a).

Since 999999 = 13 x 76923, 10^6 leaves remainder 1 when divided by 13. Write N = 10^99 - 1. Now 99 = 6 x 16 + 3, so 10^99 behaves like 10^3 = 1000, and 1000 = 13 x 76 + 12 leaves 12. So N leaves 12 - 1 = 11.

Why each option is right or wrong
  • (a) Right: N leaves 12 - 1 = 11.
  • (b) Wrong: the remainder is 11.
  • (c) Wrong: the remainder is 11.
  • (d) Wrong: the remainder is 11.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.