For every triple (a,b,c) of nonzero real numbers, form the number a|a|+ b|b|+ c|c|+(abc)/(|abc|). The set of all numbers formed is

1977 AMC 12 Problem 8

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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

\{0\}

\{-4,0,4\}

\{-4,-2,0,2,4\}

\{-4,-2,2,4\}

none of these

Each of the first three fractions is either

1

-1

The sign of the final fraction is the product of the first three signs

Let

r,

s,

t\in\{-1,1\}

be the signs of

a,

b,

c.

The expression is

r+s+t+rst.

If all three signs are positive it is

4,

and if all are negative it is

-4.

If the signs are mixed, direct cancellation gives

0.

Hence the set is

\{-4,0,4\}.

Therefore, the correct answer is B.