Best way to part answers from solutions?

All of this can be achieved using the answers and hyperref package.

In the MWE below, I've linked the question number to the solution, and the solution number back to the question by using the hypertarget and hyperlink mechanism from the hyperref package.

The example I have shown is very simple, but you can get pretty sophisticated with it as I've shown in my answer to

Contest: Show Off Your Skillz in TeX & Friends [TeX.sx birthday]

The main thing to note is that I have renewenvironment for the solution file immediately before I have inputted it- you have to wait until this point to avoid messing up the process of writing to a file.

\documentclass{article}

\usepackage{answers}                            
\usepackage{enumitem}                       
\usepackage{hyperref}
\usepackage{multicol}

\setlength{\parindent}{0.0mm}

\hypersetup{colorlinks=true,
linkcolor=blue}

% very useful during de-bugging!
%\usepackage[left]{showlabels}
%\showlabels{hypertarget}
%\showlabels{hyperlink}

% solutions file
\Opensolutionfile{mysolutions}
\Newassociation{mysolution}{mySoln}{mysolutions}

% new environment that sets up hypertargets both in the question
% section, and in the answer section
\newlist{myenum}{enumerate}{3}
\newcounter{question}
\newenvironment{question}%
    {%
    \refstepcounter{question}%
    %  hyperlink to solution
         \hypertarget{question:{\thequestion}}{}%
         \Writetofile{mysolutions}{\protect\hypertarget{soln:\thequestion}{}}%
         \begin{myenum}[label=\bfseries\protect\hyperlink{soln:\thequestion}{\thequestion},ref=\thequestion]
         \item%
        }%
        {%
        \end{myenum}}

\begin{document}

\section{Questions}
\begin{multicols}{3}
    \begin{question}
        $\int\sqrt{4-x}\mathrm{d}x$
            \begin{mysolution}
                $-\frac{2}{3}(4-x)^{\frac{3}{2}}+C$
            \end{mysolution}
    \end{question}
    \begin{question}
        $\int(2x-1)^{50}\mathrm{d}x$
            \begin{mysolution}
                $\frac{1}{102}(2x-1)^{51}+C$
            \end{mysolution}
    \end{question}
    \begin{question}
        $\int\sqrt[n]{x}\mathrm{d}x$
            \begin{mysolution}
                $\frac{n}{n+1}x^{\frac{1+n}{n}}+C$
            \end{mysolution}
    \end{question}
\end{multicols}

% close solution file
\Closesolutionfile{mysolutions}

% renew the solution environment so that it hyperlinks back to 
% the question
\renewenvironment{mySoln}[1]{%
         % add some glue
         \vskip .5cm plus 2cm minus 0.1cm%
         {\bfseries \hyperlink{question:#1}{#1.}}%
}%
{%
}%

\clearpage
\section{Answers!}
% input the file if it exists
\IfFileExists{mysolutions.tex}{\input{mysolutions.tex}}{}
\end{document}

You can define a new environment to write the answer verbatim into a seperate file, and then you can \input the answer file when necessary.

Here is a private package for my own book:

\ProvidesPackage{latexexercise}[2011/08/03 by Leo]

\RequirePackage{verbatim}

\newwrite\ltxex@ansfile

\def\ltxex@ansfilename{\jobname.ans}

\newcounter{exercise}
\ifdefined\c@chapter
  \@addtoreset{exercise}{chapter}
  \def\theexercise{\arabic{chapter}.\arabic{exercise}}
\else\ifdefined\c@section
  \@addtoreset{exercise}{section}
  \def\theexercise{\arabic{section}.\arabic{exercise}}
\else
  \def\theexercise{\arabic{exercise}}
\fi\fi

\def\exercisename{Exercise}

\newcommand\startexercise{%
  \immediate\openout\ltxex@ansfile=\ltxex@ansfilename
  \immediate\write\ltxex@ansfile{\noexpand\begin{answerlist}}}
\newcommand\stopexercise{%
  \immediate\write\ltxex@ansfile{\noexpand\end{answerlist}}%
  \immediate\closeout\ltxex@ansfile}
\newcommand\printanswer{%
  \InputIfFileExists{\ltxex@ansfilename}%
    {\PackageInfo{latexexercise}{answer file `\ltxex@ansfilename' inputed.}}%
    {\PackageWarning{latexexercise}%
      {answer file `\ltxex@ansfilename' does not exsist.}}}

\newenvironment{exercise}%
  {\list{\ltxex@labelstyle\theexercise}%
     {\ltxex@listargs\normalfont\normalsize}%
   \ltxex@pre}%
  {\endlist}
\newenvironment{answer}%
  {\immediate\write\ltxex@ansfile{\noexpand\item[\theexercise]}%
   \ltxex@startwrite}%
  {\ltxex@endwrite}
\newenvironment{answerlist}%
  {\list{}{\ltxex@anslistargs\normalfont\normalsize}}%
  {\endlist}
%

\def\ltxex@pre{\item[]\hskip-\labelsep {\large\bfseries \exercisename}}
\def\ltxex@listargs{%
  \@nmbrlisttrue\def\@listctr{exercise}%
  %\topsep=0pt
  \partopsep=0pt
  \itemsep=0pt
  \leftmargin=0pt
  \rightmargin=0pt
  \parsep=\parskip
  \listparindent=\parindent
  \itemindent=\parindent
  \labelwidth=0pt
  \labelsep=0.5em}
\def\ltxex@labelstyle{\bfseries}

\def\ltxex@anslistargs{%
  \def\makelabel##1{\ltxex@anslabelstyle ##1}
  \topsep=0pt
  \partopsep=0pt
  \itemsep=0pt
  \leftmargin=0pt
  \rightmargin=0pt
  \parsep=\parskip
  \listparindent=\parindent
  \itemindent=\parindent
  \labelwidth=0pt
  \labelsep=0.5em}
\def\ltxex@anslabelstyle{\bfseries}

\def\ltxex@startwrite{%
  \begingroup
  \@bsphack
  \let\do\@makeother \dospecials
  \catcode`\^^M\active
  \def\verbatim@processline{%
    \immediate\write\ltxex@ansfile{\the\verbatim@line}}%
  \verbatim@start}

\def\ltxex@endwrite{\@esphack\endgroup}

\endinput

Test code:

\documentclass{article}
\usepackage{latexexercise}
\begin{document}

\startexercise

\section{Foo}

\begin{exercise}
\item $1+1=?$
\begin{answer}
$1+1=2$.
\end{answer}

\item $2\times 2 = ?$
\begin{answer}
That's 4.
\end{answer}
\end{exercise}

\section{Bar}

\begin{exercise}
\item Foo
\begin{answer}
Bar
\end{answer}
\end{exercise}

\stopexercise

\section{Solutions}
\printanswer
\end{document}