Problem 4 · 2022 Math Kangaroo
Medium
Number Theory
digit-sumdivisibility
Which one of the following numbers is not divisible by its own digit sum?
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Answer: E — 2027
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Hint 1 of 2
Add the digits of each number, then test divisibility by that sum.
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Hint 2 of 2
Four of them divide evenly; find the one that leaves a leftover.
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Approach: digit-sum divisibility test
- 2022: digit sum 6, and 2022 = 6 × 337 (divisible).
- 2023: sum 7, 2023 = 7 × 289; 2024: sum 8, 2024 = 8 × 253; 2025: sum 9, 2025 = 9 × 225.
- 2027: sum 11, but 2027 = 11 × 184 + 3, not divisible.
- So the answer is 2027.
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