Question 712268
(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.