If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure?
Answer & explanation
Answer: (b) 0.25 foot
Laying the sticks end to end, forwards or backwards, measures any whole-number combination of 7·5 and 3·25 feet. The smallest positive length such combinations can give is their HCF, 0·25 foot.
- Convert to hundredths of a foot: 7·5 = 750/100 and 3·25 = 325/100.
- HCF(750, 325) = 25 (750 = 2 × 3 × 5³ and 325 = 5² × 13), so HCF of the lengths = 0·25 foot.
- Any length made by laying the sticks forwards and backwards is a multiple of 0·25 foot, and 0·25 itself can be made.
- Check: 7 × 3·25 = 22·75 and 3 × 7·5 = 22·5; 22·75 − 22·5 = 0·25 foot.
Remember · The smallest length measurable with two rods (by adding and subtracting whole lengths) is the HCF of their lengths.
Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·