2020 CSAT, all questions
UPSC Prelims 2020 · CSAT
Question 12: Basic Numeracy
If you have two straight sticks of length 7·5 feet and 3·25 feet, what is the minimum length can you measure?
a0·05 foot
b0·25 foot
c1 foot
d3·25 feet
AnswerUPSC’s answer is (b).
With two sticks you can only produce lengths that are multiples of their highest common factor, so the shortest measurable length is that HCF. In hundredths of a foot the sticks are 750 and 325. Since 750 = 2 × 3 × 5 × 5 × 5 and 325 = 5 × 5 × 13, the HCF is 25 hundredths, which is 0.25 foot. Check: 3.25 - 3 × 1 = 0.25, and 1 = 7.5 - 2 × 3.25.
Why each option is right or wrong
- (a) 0.05 foot divides both lengths, but the sticks can only produce multiples of their HCF, so it cannot be measured.
- (b) Right: the HCF of 7.5 and 3.25 is 0.25 foot.
- (c) 1 foot can be made (7.5 minus two 3.25s) but it is not the smallest length.
- (d) 3.25 feet is one stick itself; shorter lengths such as 1 foot can be made.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2020, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.