1979 AHSME Problem 13

The inequality y-x<\sqrt{x^2} is satisfied if and only if

\textbf{(A) }y<0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(B) }y>0\text{ or }y<2x\text{ (or both inequalities hold)}\qquad \textbf{(C) }y^2<2xy\qquad \textbf{(D) }y<0\qquad \textbf{(E) }x>0\text{ and }y<2x

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.