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)
• Using two sticks, the lengths we can measure are whole-number combinations of 7·5 ft and 3·25 ft, so the smallest length is their HCF.
• In quarter-feet: 7·5 ft = 30 quarters and 3·25 ft = 13 quarters.
• HCF(30, 13) = 1 quarter = 0·25 ft. For example, 7 × 3·25 − 3 × 7·5 = 22·75 − 22·5 = 0·25 ft.
• Hence option (b).
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.