Any statement taken by itself is obviously insufficient. Let's see if you get anything by combining their powers... If x = -z, that means that the arithmetic mean of x and z is zero, giving you y = 0. That is not sufficient however, since you don't know anything about the nature of x and z. They could be -3 and 3, 12345 and -12345 and so forth.

So E would be correct.

I do not understand why (1) is INSUFF

let x y z be consecutive
x, x+1, x+2
(x+x+2)/2 = x+1
this is actually stem (1)

(1) y equals to the arithmetic mean of x and z
Can you prove that it is INSUFF?

May be it is easy but I am stuck (((

Let me just give you an example:
x = 2
y = 4
z = 6.

x+z = 8, so y is the arithmetic mean of x and z.
It is obvious that the three numbers are not consecutive, but still they respect rule 1.

The mistake you are making here is that you're seeing things the other way around. You do not start by knowing that x, y and z are consecutive, you need to get there. You should know that y being the mean of x and z does not necessarily mean that they're consecutive. They just have to be in an arithmetic progression.
Any numbers like these have y = mean of x and z:

a, a+b and a+2b, no matter what the values of a and b are.

- 1 0 1

-5 0 5

-1200 0 1200

Thank you
I made silly mistake