2023 CSAT, all questions

UPSC Prelims 2023 · CSAT

Question 17: Basic Numeracy

For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :

a7 and 11 only
b11 and 13 only
c7 and 13 only
d7, 11 and 13

AnswerUPSC’s answer is (d).

XYZXYZ = XYZ x 1000 + XYZ = XYZ x 1001, whatever the digits X, Y, Z are. And 1001 = 7 x 11 x 13. So the number is always divisible by 7, 11 and 13. Remember this for any six-digit number made by repeating a three-digit block, such as 523523 or 861861.

Why each option is right or wrong
  • (a) Wrong: it is also divisible by 13.
  • (b) Wrong: it is also divisible by 7.
  • (c) Wrong: it is also divisible by 11.
  • (d) Right: 1001 = 7 x 11 x 13 is a factor.

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.