If x, y, and z represent consecutive integers, and x < y < z, then we can write:

x = x
y = x + 1 (since y must be 1 greater than x)
z = x + 2 (since z must be 1 greater than y)

Now check the 3 statements....

I. x + 1
Perfect! We can be certain that y = x + 1
Statement I works

II. (x + z)/2
Take: (x + z)/2
Replace z with x + 2 to get: (x + x + 2)/2
Simplify numerator to get: (2x + 2)/2
Divide numerator and denominator by 2 to get: (x + 1)/1, which equals x + 1
Perfect!
Statement II works


III. (x + y + z)/3
Take: (x + y + z)/3
Replace y with x+1 and replace z with x+2 to get: (x + x+1 + x+2)/3
Simplify numerator to get: (3x + 3)/3
Divide numerator and denominator by 3 to get: (x + 1)/1, which equals x + 1
Perfect!
Statement III works

Answer: E

Cheers,
Brent