UPSC Prelims 2017 · CSAT
Question 12: Basic Numeracy
If there is a policy that 1/3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period?
AnswerUPSC’s answer is (d).
Each year one third of the community leaves, so two thirds of whoever is there stay. After six years the fraction left is (2/3)^6 = 64/729 of the original. Year by year: 2/3, 4/9, 8/27, 16/81, 32/243, 64/729. The trap is to subtract one third of the original population each year, which would remove more than everyone; always apply the fraction to what remains.
Why each option is right or wrong
- (a) 16/243 does not appear in the yearly sequence of fractions left.
- (b) 32/243 is the fraction left after five years, not six.
- (c) 32/729 mixes the five-year numerator with the six-year denominator.
- (d) Correct: (2/3)^6 = 64/729.
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.