2022 CSAT, all questions

UPSC Prelims 2022 · CSAT

Question 66: Basic Numeracy

Let p be a two-digit number and q be the number consisting of same digits written in reverse order. If p×q = 2430, then what is the difference between p and q?

a45
b27
c18
d9

AnswerUPSC’s answer is (d).

We need p × q = 2430 where q is p with its digits reversed. Factor 2430 = 2 × 3⁵ × 5 and look for two-digit factors that are reverses of each other: 45 × 54 = 2430. The difference is 54 − 45 = 9. In general, with p = 10a + b and q = 10b + a, the difference is 9 times (a − b), a multiple of 9; here the digits differ by 1.

Why each option is right or wrong
  • (a) 45 is one of the two numbers, not their difference.
  • (b) 27 would need the digits to differ by 3.
  • (c) 18 would need the digits to differ by 2.
  • (d) Correct: 54 − 45 = 9.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.