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Ineq :furious:

Source: 2017 AMC 10B #3, 12B #2

February 16, 2017
AMCAMC 10AMC 10 Binequalities2017 AMC 10B

Problem Statement

Real numbers xx, yy, and zz satisfy the inequalities 0<x<1,−1<y<0,and1<z<2.0<x<1,\qquad-1<y<0,\qquad\text{and}\qquad1<z<2. Which of the following numbers is nessecarily positive?
<spanclass=′latex−bold′>(A)</span>y+x2<spanclass=′latex−bold′>(B)</span>y+xz<spanclass=′latex−bold′>(C)</span>y+y2<spanclass=′latex−bold′>(D)</span>y+2y2<spanclass=′latex−bold′>(E)</span>y+z<span class='latex-bold'>(A) </span> y+x^2 \qquad <span class='latex-bold'>(B) </span> y+xz \qquad <span class='latex-bold'>(C) </span>y+y^2 \qquad <span class='latex-bold'>(D) </span>y+2y^2 \qquad\\ <span class='latex-bold'>(E) </span> y+z
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