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Which test correctly identifies a number divisible by 9?

Class 6Playing with NumbersPlaying with Numbers
  • ALast digit is 0 or 9.
  • BSum of digits is divisible by 9.
  • CLast two digits form a number divisible by 9.
  • DNumber is greater than 9.

Step-by-Step Solution

Divisibility by 9: sum the digits and check whether the sum is divisible by 9. (Same idea as the 3-test, but stricter.)
Answer: B) Sum of digits is divisible by 9.

Key idea: Quick divisibility tests

Some checks are so fast you can do them in your head:

- **By 2**: the last digit is even (0, 2, 4, 6, or 8).
- **By 3**: the sum of the digits is divisible by 3. (273 → 2 + 7 + 3 = 12 → 12 ÷ 3 = 4 ✓)
- **By 5**: the last digit is 0 or 5.
- **By 9**: the sum of the digits is divisible by 9.
- **By 10**: the last digit is 0.
- **By 4**: the last two digits form a number divisible by 4.

These let you spot factors without doing the full division.

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