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2017 AMC 12B Question 2

AMC12 · 2017 AMC 12B

Question 2

Real numbers $x,$ $y,$ and $z$ satisfy the inequalities

$$
0 \lt x \lt 1, \quad -1 \lt y \lt 0,
$$ and $$
1 \lt z \lt 2.
$$

Which of the following numbers is necessarily positive?
  1. $y + x^2$
  2. $y + xz$
  3. $y + y^2$
  4. $y + 2y^2$
  5. $y + z$