CAT 2022 Slot 2 QA Question 20: If $a$ and $b$ are non-negative real numbers such that $a + 2b = 6$, then the average of the maximum and minimum possible values of $a+b$ is

Question

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

Accepted Answer

From the given equation:

$a + 2b = 6$
$a + b = 6 - b$

Since $a$ and $b$ are non-negative, $b$ can range from 0 to 3.

The expression $a + b = 6 - b$ is maximum when $b$ is minimum and minimum when $b$ is maximum.

$	ext{Maximum value of }a + b = 6	ext{, when }b = 0$
$	ext{Minimum value of }a +

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