A missing digit and divisibility by 3 — Aptitude Question
A missing digit and divisibility by 3: If the number 517324 is completely divisible by 3, what is the smallest… Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
If the number **517*324 is completely divisible by 3, what is the smallest digit that can replace *?
Options
- 0
- 1
- 2
- 4
Show the answer and the worked solution
Correct answer: C. 2
Worked solution
- Digit sum = 5 + 1 + 7 + x + 3 + 2 + 4 = 22 + x.
- The smallest x making this a multiple of 3 is x = 2 (giving 24).
- So the digit is 2.
Answer: 2.
The idea
Sum the known digits once, then ask what the unknown must add to reach the next multiple. Divisibility by 9 works the same way; divisibility by 11 uses the alternating sum instead.
Shortcut. Cast out threes: 5 + 1, 3 and 2 + 4 vanish, leaving 7, which is 1 more than a multiple of 3. The digit must add 2 more, and 2 is the smallest that does.
Common trap. 0 — picked on reflex as the smallest digit; it leaves the digit sum at 22, not a multiple of 3.