2018 CSAT, all questions

UPSC Prelims 2018 · CSAT

Question 24: Basic Numeracy

X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?

aXY
bX/Y
cY/X
d(X+Y)/XY

AnswerUPSC’s answer is (a).

Take X = 2 and Y = 3: XY = 6, X/Y = 0.67, Y/X = 1.5, (X+Y)/XY = 0.83. In general X/Y is below 1 because Y is larger; Y/X is at most Y/2 because X is at least 2; (X+Y)/XY = 1/X + 1/Y is below 1. But XY is at least 2Y, which is larger than Y/2. So XY is always the largest.

Why each option is right or wrong
  • (a) Correct: XY is at least 2Y, bigger than every other expression.
  • (b) X/Y is below 1 because Y > X.
  • (c) Y/X is at most Y/2 because X is at least 2, so smaller than XY.
  • (d) (X+Y)/XY = 1/X + 1/Y, which is below 1.

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

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Source: UPSC, Civil Services (Preliminary) Examination 2018, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.