MathDB
2020 Individual #20

Source:

May 1, 2022
2020 Individual

Problem Statement

John can purchase pieces of gum in packs of 44, 1414, and 2020 pieces. Given that he purchases at least one of each kind of pack, what is the positive difference between the greatest and least number of packs he can purchase to end up with exactly 8686 pieces of gum?
<spanclass=latexbold>(A)</span>5<spanclass=latexbold>(B)</span>6<spanclass=latexbold>(C)</span>7<spanclass=latexbold>(D)</span>8<spanclass=latexbold>(E)</span>9<span class='latex-bold'>(A) </span>5\qquad<span class='latex-bold'>(B) </span>6\qquad<span class='latex-bold'>(C) </span>7\qquad<span class='latex-bold'>(D) </span>8\qquad<span class='latex-bold'>(E) </span>9