If the question is: If m,p, and t are positive integers and m<p<t, is the product mpt an even integer?

(1) t-p = p-m

(2) t-m= 16.

(1) t-p = p-m implies t = 2p - m
2p will always be even whether p is even or odd since 2(even) = even and 2(odd) = even
m can be even or odd.
If m is even then t = even - even = even
If m is odd then t = even - odd = odd
So, (1) is NOT SUFFICIENT.

(2) t-m= 16 implies t = 16 + m
m can be even or odd.
If m is even then t = 16 + even = even
If m is odd then t = 16 + odd = odd
So, (2) is NOT SUFFICIENT.

Combining (1) and (2), 2p - m = 16 + m or 2p = 16 + 2m or p = 8 + m. This also doesn't imply if p and m are even or odd.

The correct answer is (E).