Bunuel wrote:

Is x = y ?

(1) x^2 - y = 0

(2) x - 1 > 0

Is x=y?

(1) x^2 - y = 0; x=1 y=1, then condition is true. x=2 y=4, also true; x=-1 y=1, also true; not suf.

(2) x - 1 > 0; x must be > 1, what about y? not suf.

(Both) if (2) x > 1 then from (1) x is different than y, this is sufficient; answer is (C).