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CAT 1995 — QA Question 38

Basics (Functions)Easy
Passage / Data

Directions for next 4 questions: Answer the questions based on the following information.

le(x, y) = Least of (x, y)
mo(x) = |x|
me(x, y) = Maximum of (x, y)

Which of the following must always be correct for a, b > 0?

Answer & solution

  • A

    mo(le(a, b)) ≥ (me(mo(a), mo(b))

  • B

    mo(le(a, b)) > (me(mo(a), mo(b))

  • C

    mo(le(a, b)) < (le(mo(a), mo(b))

  • mo(le(a,b)) = le(mo(a), mo(b))

Solution

Please note that the fastest way to solve these sums is the method of simulation, i.e., select any arbitrary values in the range given and verify whether the option holds good. E.g. a = 2, b = 3.
In this case, option (a) LHS = mo(le(2, 3)) = mo(2) = 2.
RHS = (me(mo(2), mo(3)) = (me(2, 3)) = 3. Hence, LHS < RHS.
(b) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (me(mo(2), mo(3)) = (me(2, 3)) = 3. Hence, LHS < RHS.
(c) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (le(mo(2), mo(3)) = le(2, 3) = 2. Hence, LHS = RHS.
(d) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (le(mo(2), mo(3)) = le(2, 3) = 2. Hence, LHS = RHS.

CAT 1995 QA Q38: Which of the following must always be correct for a, b > 0? — Solution | TheCATExam