If you have two straight sticks of length 7·5 feet and 3·25 feet, what is the minimum length can you measure?

(a) 0·05 foot
(b) 0·25 foot ✓ UPSC's answer
(c) 1 foot
(d) 3·25 feet

Why the answer is (b)

• Convert the stick lengths to a common unit to facilitate calculation: 7.5 feet is equivalent to 30 quarters (0.25 feet), and 3.25 feet is equivalent to 13 quarters.", "- The problem reduces to finding the greatest common divisor (GCD) of the integer values 30 and 13, as the minimum measurable length is the largest unit that divides both lengths exactly.", "- Since 13 is a prime number and does not divide 30, the GCD of 30 and 13 is 1.", "- This GCD of 1 corresponds to 1 quarter, which is 0.25 feet.", "- Therefore, the minimum length that can be measured using these two sticks is 0.25 feet, which matches option (b).", "- The key option follows because 0.25 feet is the fundamental unit derived from the lengths 7.5 and 3.25 feet.

Why the other options are wrong

(a) 0·05 foot: 0.05 feet is not a divisor of either 7.5 or 3.25 feet, so it cannot be the minimum measurable unit derived from these specific lengths.
(c) 1 foot: 1 foot is a multiple of the minimum unit (0.25 feet) but is not the smallest possible length that can be measured.
(d) 3·25 feet: 3.25 feet is the length of the shorter stick itself, not the minimum measurable unit which is 0.25 feet.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.