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Alice chose five positive integers and found that their product was even. What is the maximum number of odd integers she could have chosen?

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Answer:

In order for a product to be even, at least one factor must be even (so that the product is divisible by 2). The minimum number of even integers she could have chosen is 1, so the maximum number of odd integers she could have chosen is 4 :)

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Answer:

4

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