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Answer the following question based on the information given below.
For three distinct real numbers $x, y$ and $z,$ let

  • $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$
  • $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$
  • $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$
  • $j(x, y, z) = \min(\min(x, y), \min(y, z), \min(z, x))$
  • $m(x, y, z) = \max(x, y, z)$
  • $n(x, y, z) = \min(x, y, z)$

Which of the following is necessarily greater than $1?$

  1. $(h(x, y, z) – f(x, y, z))/j(x, y, z)$
  2. $j(x, y, z)/h(x, y, z)$
  3. $f(x, y, z)/g(x, y, z)$
  4. $(f(x, y, z) + h(x, y, z) – g(x, y, z))/j(x, y, z)$
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