Exam paper in A3 booklet format

Question

I use the exam class for my tests. I usually give them in a booklet format which is the folded version of A3 paper. Here is a sample 4-page test:

\documentclass[addpoints, 10pt, a4paper]{exam}

%\usepackage[a3paper, landscape, twocolumn]{geometry}

\usepackage{lastpage}
\footer{}{Page \thepage / \pageref{LastPage}}{}

\usepackage{graphicx}

\begin{document}

\pagestyle{headandfoot}
\firstpageheader{\begin{center}
Sample Test
\end{center}}{}{}
\runningheader{\begin{center}
Sample Test
\end{center}}{}{}
\gradetable[h]

\begin{questions}
\question[25]
\begin{figure}[h]
    \includegraphics[width=0.5\textwidth]{figs/test.eps} 
\end{figure}
\newpage
\question[25]
\newpage
\question[25]
\newpage
\question[25]
\end{questions}
\end{document}

When the geometry line uncommented, what I expect is this:

.

But the page footer does not align and it looks like it's 2-page. More importantly, the page order is not in correct order (4,1,2,3) for booklet format.

How I prepared the A3 booklet by now is quite impractical. After I compiled the test pdf in A4, passed it to PDFLaTeX like:

\documentclass{article}
\usepackage[landscape,a3paper]{geometry}
\usepackage{pdfpages}
\begin{document}
\includepdf[pages={4,1},nup=2x1]{test.pdf}
\includepdf[pages={2,3},nup=2x1]{test.pdf}
\end{document}

Is there any way I can do this directly in my document?

Answer 1

This uses the booklet package. Removing the [print] option will format normally.

\documentclass[addpoints, 10pt, a4paper]{exam}
\usepackage[twouparticle,print]{booklet}
\source{\magstep0}{\paperwidth}{\paperheight}
\target{\magstep0}{2\paperwidth}{\paperheight}

\usepackage{graphicx}
%\AtBeginDocument{\setpdftargetpages}% pdflatex
\AtBeginDocument{\setdvipstargetpages}% otherwise

\usepackage{lipsum}
\usepackage{lastpage}
\footer{}{Page \thepage{} / \pageref{LastPage}}{}

\pagestyle{headandfoot}
\firstpageheader{}{Sample Test}{}
\runningheader{}{Sample Test}{}

\begin{document}
\gradetable[h]

\begin{questions}
\question[25]\lipsum[1]
\fullwidth{\includegraphics[width=\columnwidth]{example-image}}
\newpage
\question[25]
\newpage
\question[25]
\newpage
\question[25]
\end{questions}

\end{document}