2020 CSAT, all questions

UPSC Prelims 2020 · CSAT

Question 76: Basic Numeracy

Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?

a2/3
b3/4
c4/5
d5/6

AnswerUPSC’s answer is (d).

Each fraction has the form n/(n + 1). Adding 5 to top and bottom gives (n + 5)/(n + 6). The change is (n + 5)/(n + 6) - n/(n + 1) = 5 / ((n + 1)(n + 6)), which shrinks as n grows. The largest n here is 5, in 5/6, so 5/6 changes least: from 0.833 to 0.909.

Why each option is right or wrong
  • (a) 2/3 changes by 5/24, the most.
  • (b) 3/4 changes by 5/36.
  • (c) 4/5 changes by 5/50 = 1/10.
  • (d) Right: 5/6 changes by only 5/66.

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.