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1977 AMC 12 Question 8

AMC12 · 1977 AMC 12

Question 8

For every triple $(a,b,c)$ of nonzero real numbers, form the number $$
\frac a{|a|}+\frac b{|b|}+\frac c{|c|}+\frac{abc}{|abc|}.
$$ The set of all numbers formed is
  1. $\{0\}$
  2. $\{-4,0,4\}$
  3. $\{-4,-2,0,2,4\}$
  4. $\{-4,-2,2,4\}$
  5. none of these