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Anyone have a hankering for a slice of piping hot algebra?

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Suppose x = 2m and y = 5n, where m and n are positive integers.

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Which of the following conclusions can be drawn based on the above information on m and n?

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Here are the potential answers...

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Okay, this question wants us to use... reason.

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Not the chocolate kind.

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What can we deduct from the stuff that's given to us?

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Well, let's see. X is equal to 2 times m, which is a positive integer...

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...which means that x must be an even number. Because if we're multiplying ANY positive

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integer by 2, we're going to wind up with something that's even.

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Similar deal with y... except we're multiplying n by 5, so we know y must be a multiple of 5.

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Let's look at our answer choices.

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X is divisible by 3? Um, no... we know it's divisible by 2, and it MIGHT be divisible

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by 3, but we can't be sure.

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X is odd? Definitely not. We just decided it had to be even. Next.

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Y is a negative number? No way. Not if n is positive and being multiplied by 5.

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So it seems like D is going to be the answer to all our prayers, but let's make sure.

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Is x times y a multiple of 10?

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Well, if one is a multiple of 2 and the other is a multiple of 5...

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...then yeah, it makes sense that the two multiplied together would be a multiple of 10.

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Our answer is D. As in, "Disney got it wrong."

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