CAT 1997 — QA Question 28
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) = [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
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) = (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) = (4 + 7) = 5.5.
Hence, we can reject option (b) also.
Hence, option (d).