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Use digit sums only — no long division allowed. Exactly one of these four numbers is a multiple of 3. Which one?

Class 6Playing with NumbersPlaying with Numbers
  • A4,171
  • B5,204
  • C6,138
  • D7,225

Step-by-Step Solution

Use the digit-sum rule: 6 + 1 + 3 + 8 = 18 and 18 ÷ 3 = 6, so 6,138 is divisible by 3 (6,138 ÷ 3 = 2,046). The other digit sums are 13, 11 and 16, none of them multiples of 3. The trap is inspecting the last digit instead — that test belongs to 2, 5 and 10.
Answer: C) 6,138

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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