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Placing Marbles Into Bags

Source: 2012 AMC 10B Problem #4

February 23, 2012
modular arithmeticAMC

Problem Statement

When Ringo places his marbles into bags with 66 marbles per bag, he has 44 marbles left over. When Paul does the same with his marbles, he has 33 marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with 66 marbles per bag. How many marbles will be left over?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 3<spanclass=latexbold>(D)</span> 4<spanclass=latexbold>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 3\qquad<span class='latex-bold'>(D)</span>\ 4\qquad<span class='latex-bold'>(E)</span>\ 5