Question 712268: If m and p are positive integers and (m+p) x m is even, which of the following must be true. A)if m is odd, then p is odd B)if m is odd, then p is even C)if m is even, then p is even D)if m is even, then p is odd.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! (m+p) x m is even
so either m is even or m+p is even
If m is even, then m+p is odd only if p is odd.
If m+p is even, then
a) both m and p are even (since even + even = even)
or
b) both m and p are odd (since odd + odd = even)
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So let's go through the choices
A)if m is odd, then p is odd
This is true because m+p is even if both m and p are odd and m+p must be even for (m+p) x m to be even (since m is odd)
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B)if m is odd, then p is even
This is false because it's the complete opposite of choice A which was true.
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C)if m is even, then p is even
If m is even, then (m+p) x m is even (since even x odd = odd x even = even x even = even)
So because p could be even or odd (it wouldn't change the outcome), we can't say for sure if p is even
So this is false
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D)if m is even, then p is odd.
Using the same logic above, we can't determine if p is odd when m is even. So there's no way of knowing.
So this is false too.
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