Clearly E since we have 3 variables and only 2 equations
moreover
1) x-y=y-z
y= (x+z) /2 we dont know x,y,z A,D gone
2) x^2-y^2 = z
(x-y) (x+y) =z. we dont know x,y,z B gone
put y = x+z /2 in 2nd equation
which will give quadratic but mean of x and z will be impossible to obtain... Insufficient C GONE
Remaining E is answer
moreover
1) x-y=y-z
y= (x+z) /2 we dont know x,y,z A,D gone
2) x^2-y^2 = z
(x-y) (x+y) =z. we dont know x,y,z B gone
put y = x+z /2 in 2nd equation
which will give quadratic but mean of x and z will be impossible to obtain... Insufficient C GONE
Remaining E is answer
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