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Rectangular box side ratios

Source: Problem #5 2016 AMC 10A

February 3, 2016
AMCAMC 10AMC 10 A2016 AMC 10Ageometryratio

Problem Statement

A rectangular box has integer side lengths in the ratio 1:3:41: 3: 4. Which of the following could be the volume of the box?
<spanclass=′latex−bold′>(A)</span> 48<spanclass=′latex−bold′>(B)</span> 56<spanclass=′latex−bold′>(C)</span> 64<spanclass=′latex−bold′>(D)</span> 96<spanclass=′latex−bold′>(E)</span> 144<span class='latex-bold'>(A)</span>\ 48\qquad<span class='latex-bold'>(B)</span>\ 56\qquad<span class='latex-bold'>(C)</span>\ 64\qquad<span class='latex-bold'>(D)</span>\ 96\qquad<span class='latex-bold'>(E)</span>\ 144
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