MathDB
1987 AMC 12 #17 - Mathematics Competition

Source:

December 31, 2011
AMC

Problem Statement

In a mathematics competition, the sum of the scores of Bill and Dick equalled the sum of the scores of Ann and Carol. If the scores of Bill and Carol had been interchanged, then the sum of the scores of Ann and Carol would have exceeded the sum of the scores of the other two. Also, Dick's score exceeded the sum of the scores of Bill and Carol. Determine the order in which the four contestants finished, from highest to lowest. Assume all scores were nonnegative.
<spanclass=latexbold>(A)</span> Dick, Ann, Carol, Bill<spanclass=latexbold>(B)</span> Dick, Ann, Bill, Carol<spanclass=latexbold>(C)</span> Dick, Carol, Bill, Ann<spanclass=latexbold>(D)</span> Ann, Dick, Carol, Bill<spanclass=latexbold>(E)</span> Ann, Dick, Bill, Carol <span class='latex-bold'>(A)</span>\ \text{Dick, Ann, Carol, Bill} \qquad<span class='latex-bold'>(B)</span>\ \text{Dick, Ann, Bill, Carol} \qquad<span class='latex-bold'>(C)</span>\ \text{Dick, Carol, Bill, Ann} \\ \qquad<span class='latex-bold'>(D)</span>\ \text{Ann, Dick, Carol, Bill} \qquad<span class='latex-bold'>(E)</span>\ \text{Ann, Dick, Bill, Carol}