UPSC Prelims 2017 · CSAT
Question 53: Basic Numeracy
The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again?
AnswerUPSC’s answer is (b).
Last year's age is a square and next year's is a cube, two years apart, so we need a square and a cube differing by 2: 25 and 27. His age now is 26. Next year he is 27, a cube; the next cube after that is 4³ = 64. Counting from his present age of 26, he waits 64 - 26 = 38 years for his age to be a cube again.
Why each option is right or wrong
- (a) After 42 years his age would be 68, not a cube.
- (b) Correct: 64 - 26 = 38.
- (c) After 25 years his age would be 51, not a cube.
- (d) After 16 years his age would be 42, not a cube.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.