X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number?
- (a) XY ✓ UPSC's answer
- (b) X/Y
- (c) Y/X
- (d) (X + Y)/XY
Why the answer is (a)
• X and Y are natural numbers greater than 1 with Y > X, so X ≥ 2 and Y ≥ 3.
• X/Y is less than 1, and (X + Y)/XY = 1/X + 1/Y is also less than 1.
• Y/X is greater than 1, but XY is larger still: XY ÷ (Y/X) = X², which is at least 4.
• So XY is the largest, option (a).
Why the other options are wrong
- (b) X/Y
- X/Y is less than 1 because Y > X.
- (c) Y/X
- Y/X is smaller than XY, since XY ÷ (Y/X) = X² ≥ 4.
- (d) (X + Y)/XY
- (X + Y)/XY = 1/X + 1/Y is less than 1.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.