MathDB
Quotient Remainder

Source: 1964 AHSME Problem 3

September 12, 2012
AMC

Problem Statement

When a positive integer xx is divided by a positive integer yy, the quotient is uu and the remainder is vv, where uu and vv are integers. What is the remainder when x+2uyx+2uy is divided by yy?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 2u<spanclass=latexbold>(C)</span> 3u<spanclass=latexbold>(D)</span> v<spanclass=latexbold>(E)</span> 2v{{ <span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 2u \qquad<span class='latex-bold'>(C)</span>\ 3u \qquad<span class='latex-bold'>(D)</span>\ v }\qquad<span class='latex-bold'>(E)</span>\ 2v }