MathDB
2021 Individual #21

Source:

April 28, 2022
2021 Individual

Problem Statement

You have a collection of $20.21\$20.21, consisting of pennies, nickels, and quarters. To reduce the collection’s worth to kk cents, you simultaneously replace all pennies with quarters and all quarters with pennies (all coins are replaced one time). What is the minimum possible kk?
<spanclass=latexbold>(A)</span>105<spanclass=latexbold>(B)</span>120<spanclass=latexbold>(C)</span>125<spanclass=latexbold>(D)</span>505<spanclass=latexbold>(E)</span>101<span class='latex-bold'>(A) </span>105\qquad<span class='latex-bold'>(B) </span>120\qquad<span class='latex-bold'>(C) </span>125\qquad<span class='latex-bold'>(D) </span>505\qquad<span class='latex-bold'>(E) </span>101