AMC 10 2017b Problem 3

Real numbers $x$, $y$, and $z$ satisfy the inequalities $0<x<1$, $-1<y<0$, and $1<z<2$. Which of the following numbers is necessarily positive? $\textbf{(A)}\ y+x^2 \textbf{(B)}\ y+xz \textbf{(C)}\ y+y^2 \textbf{(D)}\ y+2y^2 \textbf{(E)}\ y+z$