From statement A:-
if xyz is odd then , then all the three numbers are odd and difference of two odds result into an even number. So, it is enough to deduce that z- x is even.
From statement B :-
Since, it is given that xy + yz + zx is even.
Then, either each one of xy, yz and zx is odd or even. So , nothing can be deduce from statement B.
Option D is the Correct Answer.