MathDB
Boxes and Balls

Source: 2019 AMC 10A #4 / AMC 12A #3

February 8, 2019
AMCAMC 102019 AMC 12A2019 AMC 10Acounting

Problem Statement

A box contains 2828 red balls, 2020 green balls, 1919 yellow balls, 1313 blue balls, 1111 white balls, and 99 black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least 1515 balls of a single color will be drawn??
<spanclass=latexbold>(A)</span>75<spanclass=latexbold>(B)</span>76<spanclass=latexbold>(C)</span>79<spanclass=latexbold>(D)</span>84<spanclass=latexbold>(E)</span>91<span class='latex-bold'>(A) </span> 75 \qquad<span class='latex-bold'>(B) </span> 76 \qquad<span class='latex-bold'>(C) </span> 79 \qquad<span class='latex-bold'>(D) </span> 84 \qquad<span class='latex-bold'>(E) </span> 91