Two remainders at once — Number System Aptitude Question
Two remainders at once: What is the smallest number that leaves a remainder of 3 when divided by 5 and a remainder… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the smallest number that leaves a remainder of 3 when divided by 5 and a remainder of 5 when divided by 7?
Options
- 23
- 26
- 33
- 38
Show the answer and the worked solution
Correct answer: C. 33
Worked solution
- Numbers leaving remainder 3 with 5: 3, 8, 13, 18, 23, 28, 33, …
- Testing each against division by 7: 33 = 7 × 4 + 5. ✓
- The smallest such number is 33.
Answer: 33.
The idea
Write out the sequence for the larger modulus's condition, or the one with fewer candidates, and test against the other. Formal congruence machinery is rarely faster at exam scale.
Shortcut. Both remainders fall 2 short of the divisor (5 − 3 = 7 − 5 = 2), so N + 2 is a multiple of 35 and the smallest N is 35 − 2 = 33.
Common trap. 23 — the first option that leaves 3 on division by 5; 23 ÷ 7 leaves 2, not 5.