CAT 1997QA Question 28

Basics (Functions)Easy
Passage / Data

Direction: Answer the questions based on the following information.

For these questions the following functions have been defined.

la(x, y, z) = min(x + y, y + z)

le(x, y, z) = max (x − y, y − z)

ma(x, y, z) = 12 [le(x, y, z) + la(x, y, z)]

Given that x > y > z > 0. Which of the following is necessarily true?

Answer & solution

  • A

    la(x, y, z) < le(x, y, z)

  • B

    ma(x, y, z) < la(x, y, z)

  • C

    ma(x, y, z) < le(x, y, z)

  • None of these

Solution

This question can be done by assuming some values for x, y and z, e.g. 

Let x = 4, y = 3 and z = 1.
la(4, 3, 1) = min(7, 4) = 4;
le(4, 3, 1) = max(1, 2) = 2; 
ma(x, y, z) = 12 (4 + 2) = 3. 

Hence, we can reject options (a) & (c).

Let x = 10, y = 3 and z = 1.
la(10, 3, 1) = min(13, 4) = 4;
le(10, 3, 1) = max(7, 2) = 7; 
ma(x, y, z) = 12 (4 + 7) = 5.5. 

Hence, we can reject option (b) also.

Hence, option (d).

CAT 1997 QA Q28: Given that x > y > z > 0. Which of the following is necessarily true? — Solution | TheCATExam