A missing digit and divisibility by 9 — Aptitude Question
A missing digit and divisibility by 9: For which digit x is the four-digit number 45x3 divisible by 9? Answer and worked solution on CodeKairo.
- Topic: Number System
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
For which digit x is the four-digit number 45x3 divisible by 9?
Options
- 3
- 5
- 6
- 9
Show the answer and the worked solution
Correct answer: C. 6
Worked solution
- Digit sum = 4 + 5 + x + 3 = 12 + x.
- For divisibility by 9 the sum must be 18 (the next multiple of 9 above 12 that a single digit can reach): 12 + x = 18 gives x = 6.
- Check: 4563 ÷ 9 = 507. ✓
Answer: 6.
The idea
Divisibility by 3 and by 9 depend only on the digit sum; by 11 on the alternating digit sum; by 4 and 8 on the last two and three digits. Memorise these and a missing-digit question is arithmetic on one line.
Shortcut. Cast out nines: 4 + 5 vanishes, leaving 3, so x must bring the total to a multiple of 9: x = 6.
Common trap. 3 — it makes the digit sum 15, which passes the test for 3 but not for 9.