AMC 12 2017b Problem 2

Real numbers $x$, $y$, and $z$ satify the inequalities $0<x<1$, $-1<y<0$, and $1<z<2$. Which of the following numbers is necessarily positive?

\textbf{(A)}\ y+x^2 \textbf{(B)}\ y+xz \textbf{(C)}\ y+y^2 \textbf{(D)}\ y+2y^2 \textbf{(E)}\ y+z