For every triple $(a,b,c)$ of non-zero real numbers, form the number $\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}$. 
The set of all numbers formed is
$\textbf{(A)}\ {0} \qquad \textbf{(B)}\ \{-4,0,4\} \qquad \textbf{(C)}\ \{-4,-2,0,2,4\} \qquad \textbf{(D)}\ \{-4,-2,2,4\}\qquad \textbf{(E)}\ \text{none of these}$
Solution by e_power_pi_times_i
$\dfrac{x}{|x|} = 1$ or $-1$ depending whether $x$ is positive or negative. If $a$, $b$, and $c$ are positive, then the entire thing amounts to $4$. If one of the three is negative and the other two positive, the answer is $0$. If two of the three is negative and one is positive, the answer is $0$. If all three are negative, the answer is $-4$. Therefore the set is $\boxed{\textbf{(B)}\ \{-4,0,4\}}$.
This is very similar to [https://artofproblemsolving.com/wiki/index.php/2017_AMC_8_Problems/Problem_21](https://artofproblemsolving.comhttps://artofproblemsolving.com/wiki/index.php/2017_AMC_8_Problems/Problem_21)