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CAT 2000 — QA Question 24

Basics (Functions)Easy
Passage / Data

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 indeterminate?

Answer & solution

Correct answer: (f(x, y, z) + h(x, y, z) + g(x, y, z) + j(x, y, z))/(j(x, y, z) + h(x, y, z) – m(x, y, z) – n(x, y, z))

  • A

    (f(x, y, z) – h(x, y, z))/(g(x, y, z) – j(x, y, z))

  • (f(x, y, z) + h(x, y, z) + g(x, y, z) + j(x, y, z))/(j(x, y, z) + h(x, y, z) – m(x, y, z) – n(x, y, z))

  • C

    (g(x, y, z) – j(x, y, z))/(f(x, y, z) – h(x, y, z))

  • D

    (h(x, y, z) – f(x, y, z))/(n(x, y, z) – g(x, y, z))

Solution

Using the values found previously,

Option 1 = (y − z)/(y − x)

Option 2 = (y + z + y + x)/(x + z – z − x)

Option 3 = (y − x)/(y – z)

Option 4 = (z − y)/(x – y)

The denominator in the expression in option 2 is zero.

Hence, the expression in option 2 is indeterminate.

Hence, option (b).

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CAT 2000 QA Q24: Which of the following expressions is indeterminate? — Solution | TheCATExam