CAT Quant Practice Problems

Question: 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 expressions is necessarily equal to 1?

[f(x, y, z) – m(x, y, z)] / [g(x, y, z) – h(x, y, z)]
[m(x, y, z) – f(x, y, z)] / [g(x, y, z) – n(x, y, z)]
[j(x, y, z) – g(x, y, z)] / h(x, y, z)
[f(x, y, z) – h(x, y ,z)] / f(x, y, z)
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