MathDB
Turkey NMO 2007 1st Round - P15 (Algebra)

Source:

October 4, 2012

Problem Statement

What is the minimum value of ab+cdab+cd, if ab+cd=ef+ghab+cd = ef+gh where a,b,c,d,e,f,g,ha,b,c,d,e,f,g,h are distinct positive integers?
<spanclass=latexbold>(A)</span> 34<spanclass=latexbold>(B)</span> 33<spanclass=latexbold>(C)</span> 32<spanclass=latexbold>(D)</span> 31<spanclass=latexbold>(E)</span> 30 <span class='latex-bold'>(A)</span>\ 34 \qquad<span class='latex-bold'>(B)</span>\ 33 \qquad<span class='latex-bold'>(C)</span>\ 32 \qquad<span class='latex-bold'>(D)</span>\ 31 \qquad<span class='latex-bold'>(E)</span>\ 30