MathDB
2018 Individual #25

Source:

January 13, 2023
2018 Individual

Problem Statement

The figure below contains two squares which share an edge, one with side length 200200 units and the other with side length 289289 units. The figure is divided into a whole number of regions, each with an equal whole number area but not necessarily of the same shape. Given that there is more than one region and each region has an area greater than 11, find the sum of the number of regions and the area of each region. [asy] size(4cm); draw((0,0)--(200,0)--(200,200)--(0,200)--cycle); label("200200",(0,0)--(200,0)); label("289289",(200,0)--(489,0)); draw((200,0)--(489,0)--(489,289)--(200,289)--cycle); [/asy] <spanclass=latexbold>(A)</span>704<spanclass=latexbold>(B)</span>874<spanclass=latexbold>(C)</span>924<spanclass=latexbold>(D)</span>978<spanclass=latexbold>(E)</span>1028<span class='latex-bold'>(A) </span> 704\qquad<span class='latex-bold'>(B) </span> 874\qquad<span class='latex-bold'>(C) </span> 924\qquad<span class='latex-bold'>(D) </span> 978\qquad<span class='latex-bold'>(E) </span> 1028