CAT 2000 — QA Question 23
Answer the following question based on the information given below.
For three distinct positive 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?
Answer & solution
(f(x, y, z) – m(x, y, z))/(g(x, y, z) – h(x, y, z))
- B
(m(x, y, z) – f(x, y, z))/(g(x, y, z) – n(x, y, z))
- C
(j(x, y, z) – g(x, y, z))/h(x, y, z)
- D
(f(x, y, z) – h(x, y, z))/f(x, y, z)
Using the values from previous answer,
Option 1 = (y − z)/(y − z)
Option 2 = (z − y)/(y − x)
Option 3 = (x − y)/z
Option 4 = (y − z)/y
It can be easily concluded that the expression in option 1 is necessarily equal to 1.
Hence, option (a).