Question

If $m=max\{||x-5|-|x-3||\}$ and $n=min\{|x-2|+|x-4|\},$
then the value of $m+n$ is

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is B $4$

We know that the maximum value of $||x-a|-|x-b||=|a-b|$
$\therefore m=max\{||x-5|-|x-3||\}=|5-3|=2$

And minimum value of $|x-a|+|x-b|=|a-b|$
$\therefore n=min\{|x-2|+|x-4|\}=|2-4|=2$

$\Rightarrow m+n=2+2=4$