Same remainder from three numbers — Aptitude Question
Same remainder from three numbers: Find the greatest number that will divide 62, 132 and 237 leaving the same… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
Find the greatest number that will divide 62, 132 and 237 leaving the same remainder in each case.
Options
- 25
- 30
- 35
- 70
Show the answer and the worked solution
Correct answer: C. 35
Worked solution
- Differences: 132 − 62 = 70, 237 − 132 = 105, 237 − 62 = 175.
- HCF(70, 105, 175) = 35.
- Check: 62 = 35 × 1 + 27, 132 = 35 × 3 + 27, 237 = 35 × 6 + 27 — remainder 27 each time. ✓
Answer: 35.
The idea
For an unknown but equal remainder, take the HCF of the pairwise differences: subtracting two numbers of the form dq + r removes r entirely. When the remainder is given instead, subtract it from each number first.
Shortcut. Two differences are enough: HCF(70, 105) = 35. Trying the largest option first also settles it — 70 leaves 62 from both 62 and 132 but 27 from 237, while 35 leaves 27 every time.
Common trap. 70 — the first difference, 132 − 62; it gives both of those the remainder 62 but leaves 27 from 237.