CAT 2000 — QA Question 22
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 is necessarily greater than 1?
Answer & solution
- 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)
(f(x, y, z) + h(x, y, z) – g(x, y, z))/j(x, y, z)
x, y and z are distinct real numbers.
∴ Without loss of generality, let x < y < z
Then,
f(x, y, z) = y; g(x, y, z) = y; h(x, y, z) = z
j(x, y, z) = x; m(x, y, z) = z; n(x, y, z) = x
Substituting these values in the given options,
Option 1 = (z – y)/x may or may not be greater than 1.
Option 2 = x/z < 1
Option 3 = y/y = 1
Option 4 = (y + z − y)/x > 1
Hence, option (d).