MathDB
Squares and Cubes

Source:

November 26, 2009
geometry3D geometry

Problem Statement

The positive integers x x and y y are the two smallest positive integers for which the product of 360 360 and x x is a square and the product of 360 360 and y y is a cube. What is the sum of x x and y y? <spanclass=′latex−bold′>(A)</span> 80<spanclass=′latex−bold′>(B)</span> 85<spanclass=′latex−bold′>(C)</span> 115<spanclass=′latex−bold′>(D)</span> 165<spanclass=′latex−bold′>(E)</span> 610 <span class='latex-bold'>(A)</span>\ 80 \qquad <span class='latex-bold'>(B)</span>\ 85 \qquad <span class='latex-bold'>(C)</span>\ 115 \qquad <span class='latex-bold'>(D)</span>\ 165 \qquad <span class='latex-bold'>(E)</span>\ 610
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