for the product mpt to be even atleast one of the integers have to be even.

stmt 1 - t-p = p-m ==> p=(t+m)/2, also p is a positive integer. If p has to be integer then both t and m have to either even or odd. If we take an avg of an even and odd number then the avg will be a decimal. Now avg of any two even or two odd numbers wud be an even number...So p will be an even integer....Suff.

stmt 2 - t-m=16...means either both of them are even or both odd and also we dont know anything abt p.....So insuff........Ans is A

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

(1) t – p = p - m

i.e t + m= 2p now here both t& p can be odd or even hence
INSUFF

Jangojess p=(t+m)/2 if t +m = 18 (t=13,m=5)
then p =9 if t+m = 12 p =6

(2) t – m = 16

here also both can be odd or both can be even INSUFF

combine we have t= 16 + m & t+m =2p

so 16 +2m = 2p

sp 8 + m = p so if m is odd & t is odd then p is odd i.e all three odd

and all three can be even alos or atleast one can be even

henec INSUFF E

E

5 13 21

4 12 20

Both the above satisfies stmt1 and stmt2; both are in themselves insuff, too