Something like this:
\documentclass{article}
\begin{document}
Page \pageref{pg:one} of the exam\label{pg:one}.
There are \pageref{pg:examend} pages in this examination.
\clearpage
Page \pageref{pg:two} of the exam\label{pg:two}.
\clearpage
Page \pageref{pg:three} of the exam\label{pg:three}.
\clearpage
Page \pageref{pg:four} of the exam\label{pg:four}.
\clearpage
Page \pageref{pg:five} of the exam\label{pg:five}.
\clearpage
Page \pageref{pg:six} of the exam\label{pg:six}.
\label{pg:examend}
\clearpage
Page \pageref{pg:seven} contains answers\label{pg:seven}.
\end{document}

Please note that I cannot check these images have uploaded correctly as I am unable to view images on the site at the present time.
EDIT: Since you are using the exam class and want to use \numpages, you could adapt the example from the manual of headers and footers to use this as follows:
\documentclass{exam}
\pagestyle{headandfoot}
\runningheadrule
\firstpageheader{Math 115}{First Exam}{July 4, 1776}
\runningheader{Math 115}
{First Exam, Page \thepage\ of \numpages}
{July 4, 1776}
\firstpagefooter{}{}{}
\runningfooter{}{}{}
\def\numpages{%
\pageref{pg:examend}
}% numpages
\begin{document}
Put your exam questions here.
\clearpage
Some more questions here.
\label{pg:examend}
\clearpage
Put the answers here.
\end{document}
The only oddity is that this will give e.g. "Page 3 of 2" on the final page which has the answers. You could avoid that if you liked by redefining the header command at the end of the exam.
lastpageor the more advancedpageslts? – Speravir Jan 09 '14 at 03:31pagesltsthere’s a section “Alternatives”, that you should read. Some of the packages look promising. – Speravir Jan 09 '14 at 03:40