CAT 2022 Slot 2 QA Q4 Inequalities & Modulus

Question 4 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

If \(a\) and \(b\) are non-negative real numbers such that \(a+2 b=6\), then the average of the maximum and minimum possible values of \((a+b)\) is

A
4
B
4.5
C
3.5
D
3

Answer: (B) 4.5 Inequalities & Modulus MCQ

Solution

\(a=6-2b\ge0\) gives \(0\le b\le3\), and \(a+b=6-b\).
Maximum 6 (at \(b=0\)), minimum 3 (at \(b=3\)); their average is 4.5.