CAT 2000 | Question: 77

Question

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 $1?$

• A. $(h(x, y, z) – f(x, y, z))/j(x, y, z)$
• B. $j(x, y, z)/h(x, y, z)$
• C. $f(x, y, z)/g(x, y, z)$
• D. $(f(x, y, z) + h(x, y, z) – g(x, y, z))/j(x, y, z)$