Problem 1 · 2009 Math Kangaroo
Medium
Number Theory
divisibilitydigit-sum
Which of the following numbers is divisible by 3?
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Answer: E — (2 + 0)·(0 + 9)
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Hint 1 of 2
A number is a multiple of 3 exactly when its digit sum is.
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Hint 2 of 2
Just evaluate each option and check for a factor of 3 — a product is easiest.
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Approach: evaluate each option and test divisibility by 3
- Option E is the product (2+0)·(0+9) = 2·9 = 18.
- 18 is a multiple of 3, so option E works.
- The others give 2009, 11, 191, and 512, none divisible by 3.
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