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Instructions

Directions for the next 3 questions: For three distinct real positive 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)

Question 116

Which of the following expressions is necessarily equal to 1?

Solution

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From the given functions we can make out that function h and m give max value , function n and j give min value , function f and g give middle  value. So according to equation (f(x, y, z)- m(x, y, z))/(g(x, y, z)-h(x,y, z)) , value of numerator and denominator is equal and hence ratio is equal to 1. 

Suppose x>y>z

f(x,y,z) = y

g(x,y,z) = y

h(x,y,z) = x

j(x,y,z) = z

Option a = (y-x)/(y-x) = 1

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