2019 CSAT, all questions

UPSC Prelims 2019 · CSAT

Question 33: Basic Numeracy

The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. The number of such pairs is

a5
b4
c3
d2

AnswerUPSC’s answer is (b).

Let the number be 10a + b. The ratio gives 7(10a + b) = 4(10b + a), so 66a = 33b and b = 2a. With digits from 1 to 9, a can be 1, 2, 3 or 4, giving 12 : 21, 24 : 42, 36 : 63 and 48 : 84, each of which reduces to 4 : 7. A value a = 5 would need b = 10, which is not a digit. So there are 4 pairs.

Why each option is right or wrong
  • (a) Wrong: a = 5 would need b = 10, which is not a digit.
  • (b) Right: a = 1, 2, 3 and 4 work.
  • (c) Wrong: undercounts; four values of a work.
  • (d) Wrong: undercounts; four values of a work.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.