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2017 AMC 10B Question 3

AMC10 · 2017 AMC 10B

Question 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?
  1. $y+x^2 $
  2. $y+xz $
  3. $y+y^2 $
  4. $y+2y^2 $
  5. $y+z $