Finding all possible values of $\frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}$

Question

Given that $a$, $b$, and $c$ are nonzero real numbers, find all possible values of the expression
$\frac{a}{|a|} + \frac{b}{|b|} + \frac{c}{|c|} + \frac{abc}{|abc|}.$Enter all possible values, separated by commas.

I'm not sure what this problem wants. Aren't there infinite possible values to the expression?

Answer 1

Let's make cases

Case1 a,b,c>0 hence abc>0 therefore output is 4

Case2 a,b>0 c<0 hence abc<0 therefore output is 0

Case3 a>0 b,c<0 hence abc>0 therefore output is 0

Case4 a,b,c<0 hence abc<0 therefore output is -4

Hence the outputs of the given expression are {4,0,-4} and that's the answer.