Rahul, i think the mistake you may be making is that you are consider something like 1,3,5 to be consecutive integers when they are not... silly mistake, which I have made on occassion. If not, then here is the explanation to help you out:
are integers x, y and z consecutive?
1) y equals the arithmetic mean of x and z
2,4,6 -> 4=(2+6)/2 --> not consecutive
1,2,3 -> 2(1+3)/2 --> consecutive
Therefore, since we both yes & no, the statement by itself is insufficient -> Choices A & D are eliminated
2) x = -z
we have nothing about y, so by itself the statement is insufficient -> B is eliminated
combining 1 & 2 ->
-1,0,1 -> 0= (-1+1)/2 && -1 = -(1) -->consecutive
-2,0,2 -> 0= (-2+2)/2 && -2=(-2) --> not consecutive
Therefore the two statements combined are also insufficient, and thus E is the correct answer.