From a remainder of 47 to a remainder mod 19 — Aptitude
From a remainder of 47 to a remainder mod 19: On dividing a number by 342, the remainder is 47. What will the… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
On dividing a number by 342, the remainder is 47. What will the remainder be when the same number is divided by 19?
Options
- 5
- 9
- 18
- Cannot be determined
Show the answer and the worked solution
Correct answer: B. 9
Worked solution
- The number is N = 342k + 47.
- 342 = 19 × 18, so 342k is divisible by 19 and contributes nothing to the remainder.
- 47 = 19 × 2 + 9, so the remainder is 9.
Answer: 9.
The idea
When the second divisor divides the first, the answer depends only on the given remainder. When it does not, the remainder genuinely cannot be determined — which is why that option is always offered.
Shortcut. Take the simplest such number, 47 itself (k = 0): 47 ÷ 19 leaves 9. Because 19 × 18 = 342, every other number of the form 342k + 47 leaves the same 9.
Common trap. Cannot be determined — assuming the unknown quotient k hides the answer, without checking that 19 divides 342 exactly.