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Values of Absolute Values

Source: 2017 AMC 8 #21

November 22, 2017
absolute valueAMC 8

Problem Statement

Suppose aa, bb, and cc are nonzero real numbers, and a+b+c=0a+b+c=0. What are the possible value(s) for a∣a∣+b∣b∣+c∣c∣+abc∣abc∣\frac{a}{|a|}+\frac{b}{|b|}+\frac{c}{|c|}+\frac{abc}{|abc|}?
<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1 and −1<spanclass=′latex−bold′>(C)</span>2 and −2<spanclass=′latex−bold′>(D)</span>0,2, and −2<spanclass=′latex−bold′>(E)</span>0,1, and −1<span class='latex-bold'>(A) </span>0\qquad<span class='latex-bold'>(B) </span>1\text{ and }-1\qquad<span class='latex-bold'>(C) </span>2\text{ and }-2\qquad<span class='latex-bold'>(D) </span>0,2,\text{ and }-2\qquad<span class='latex-bold'>(E) </span>0,1,\text{ and }-1
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