Problem 19 · 2024 Math Kangaroo
Hard
Number Theory
divisibilitycasework
We know of a positive integer n that exactly one of the following statements is true. Which is the true statement?
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Answer: C — n is odd.
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Hint 1 of 2
Divisible by 6 would force divisible by 3 too, so that statement cannot be the lone true one.
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Hint 2 of 2
Look for an n that makes exactly one statement true — an odd composite not divisible by 3 does it.
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Approach: eliminate statements that force others
- If n were divisible by 6 it would also be divisible by 3, giving two true statements — so that is out.
- Take n = 25: it is odd (true), but not divisible by 3, not prime, and not 2.
- Exactly one statement holds, and it is n is odd.
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