MathDB
Dividing Marbles

Source:

February 11, 2009

Problem Statement

Three boys agree to divide a bag of marbles in the following manner. The first boy takes one more than half the marbles. The second takes a third of the number remaining. The third boy finds that he is left with twice as many marbles as the second boy. The original number of marbles: <spanclass=latexbold>(A)</span> is none of the following<spanclass=latexbold>(B)</span> cannot be determined from the given data<spanclass=latexbold>(C)</span> is 20 or 26<spanclass=latexbold>(D)</span> is 14 or 32<spanclass=latexbold>(E)</span> is 8 or 38 <span class='latex-bold'>(A)</span>\ \text{is none of the following} \qquad <span class='latex-bold'>(B)</span>\ \text{cannot be determined from the given data}\\ <span class='latex-bold'>(C)</span>\ \text{is 20 or 26} \qquad <span class='latex-bold'>(D)</span>\ \text{is 14 or 32} \qquad <span class='latex-bold'>(E)</span>\ \text{is 8 or 38}