MathDB
Dividing Halloween Candy

Source:

February 17, 2008
ratioAMC 12

Problem Statement

Al, Bert, and Carl are the winners of a school drawing for a pile of Halloween candy, which they are to divide in a ratio of 3:2:1 3 : 2 : 1, respectively. Due to some confusion they come at different times to claim their prizes, and each assumes he is the first to arrive. If each takes what he believes to be his correct share of candy, what fraction of the candy goes unclaimed?
<spanclass=latexbold>(A)</span> 118<spanclass=latexbold>(B)</span> 16<spanclass=latexbold>(C)</span> 29<spanclass=latexbold>(D)</span> 518<spanclass=latexbold>(E)</span> 512 <span class='latex-bold'>(A)</span>\ \frac {1}{18} \qquad <span class='latex-bold'>(B)</span>\ \frac {1}{6} \qquad <span class='latex-bold'>(C)</span>\ \frac {2}{9} \qquad <span class='latex-bold'>(D)</span>\ \frac {5}{18} \qquad <span class='latex-bold'>(E)</span>\ \frac {5}{12}