Example 1 · level 1
What is the smallest digit that can replace * so that 1*900 is divisible by 3?
Show solution
- Digit sum must be divisible by 3.
- Digits that work: 2, 5, 8.
- Smallest = 2: 12,900 ÷ 3 = 4,300.
Answer: 2
SSC & BANK EXAMS: QUANTITATIVE APTITUDE · NUMBER SYSTEM
Divisibility rules: find the missing digit
3/9: digit sum divisible by 3/9. 11: (sum of odd places − sum of even places) is 0 or a multiple of 11. 4: last two digits. 8: last three digits.
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Worked examples
Example 2 · level 2
What is the smallest digit that can replace * so that 18855* is divisible by 6?
Show solution
- Divisible by 6 = divisible by both 2 and 3.
- Digits that work: 0, 6.
- Smallest = 0: 1,88,550 ÷ 6 = 31,425.
Answer: 0
Example 3 · level 3
What is the smallest digit that can replace * so that 4074*64 is divisible by 88?
Show solution
- 88 = 8 × 11: the number must pass both tests.
- Digits that work: 6.
- Smallest = 6: 40,74,664 ÷ 88 = 46,303.
Answer: 6