Is x^2 < x – |y|?

(1): y > x. This means that x |y| is negative. In contrast, x^2 cannot be negativeit can equal zero, but any value of x other than zero yields a positive value of x^2. Since a negative number will always be less than any positive number (or zero), answer to question is definitely "no."
Sufficient
(2): x < 0. x^2 >0. Since an absolute value such as |y| is always either a positive number or zero, then x |y| equals either a negative minus a positive or a negative minus zero. In either case, result is negative.
Since a positive number is always greater than a negative number, x^2 > x |y|, and answer to question is definitely "no."
Sufficient