When a positive integer $x$ is divided by a positive integer $y$, the quotient is $u$ and the remainder is $v$, where $u$ and $v$ are integers. 
What is the remainder when $x+2uy$ is divided by $y$?
$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 2u \qquad \textbf{(C)}\ 3u \qquad \textbf{(D)}\ v \qquad \textbf{(E)}\ 2v$
We can solve this problem by elemetary modular arthmetic,
$x \equiv v\ (\textrm{mod}\ y)$ $=>$ $x+2uy \equiv v\ (\textrm{mod}\ y)$
~GEOMETRY-WIZARD