Divisibility Clue Hunt

The three-digit number A B C \overline{ABC} is divisible by 9 but not by 6. Must A + B + C A+B+C be odd?

No, it can be even Yes, it must be odd

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3 solutions

Jack Lam
Nov 21, 2016

Direct Counterexample: 189

another counterexample: 468

Sam Gilbert
Nov 21, 2016

909 is divisible by 9, but not divisible by 6. Since 9+0+9=18, which is even, the sum can be even.

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