MathDB
Sum Products!

Source: 2017 AMC 10A #5, 2017 AMC 12A #2

February 8, 2017
AMCAMC 10AMC 10 AAMC 12 A2017 AMC 10A2017 AMC 12AAMC 12

Problem Statement

The sum of two nonzero real numbers is 44 times their product. What is the sum of the reciprocals of the two numbers?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 2<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 8<spanclass=latexbold>(E)</span> 12<span class='latex-bold'>(A)</span>\ 1\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 8\qquad<span class='latex-bold'>(E)</span>\ 12