MathDB
Sum of Fractions

Source:

February 27, 2008

Problem Statement

Let n n be a positive integer such that \tfrac{1}{2}\plus{}\tfrac{1}{3}\plus{}\tfrac{1}{7}\plus{}\tfrac{1}{n} is an integer. Which of the following statements is not true?
<spanclass=latexbold>(A)</span> 2 divides n<spanclass=latexbold>(B)</span> 3 divides n<spanclass=latexbold>(C)</span> 6 divides n<spanclass=latexbold>(D)</span> 7 divides n<spanclass=latexbold>(E)</span> n>84 <span class='latex-bold'>(A)</span>\ 2\text{ divides }n \qquad <span class='latex-bold'>(B)</span>\ 3\text{ divides }n \qquad <span class='latex-bold'>(C)</span>\ 6\text{ divides }n \qquad <span class='latex-bold'>(D)</span>\ 7\text{ divides }n \\ <span class='latex-bold'>(E)</span>\ n>84