2020 CSAT, all questions
UPSC Prelims 2020 · CSAT
Question 51: Basic Numeracy
What is the greatest length x such that 3 1/2 m and 8 3/4 m are integral multiples of x?
a1 1/2 m
b1 1/3 m
c1 1/4 m
d1 3/4 m
AnswerUPSC’s answer is (d).
Both lengths must be whole-number multiples of x, so x is their highest common factor. Write them as fractions with the same denominator: 3 1/2 = 7/2 = 14/4 and 8 3/4 = 35/4. The HCF of such fractions is the HCF of the numerators over the common denominator: HCF(14, 35) = 7, so x = 7/4 = 1 3/4 m. Check: 14/4 is 2 times 7/4 and 35/4 is 5 times.
Why each option is right or wrong
- (a) 1 1/2 m does not divide 3 1/2 m evenly.
- (b) 1 1/3 m does not divide 3 1/2 m evenly.
- (c) 1 1/4 m divides 8 3/4 m seven times but 3 1/2 m only 2.8 times.
- (d) Right: 1 3/4 m goes into the two lengths exactly 2 and 5 times.
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.