Equation numbering and solutions exam class

Question

I use the exam class for exams. When I use equations in the solution environment, the counter for equation numbering is updated, even when the solutions are not printed. Is it possible not to consider the counter inside the solution environment when solutions are not printed?

Below is a MWE. It produces a wrong equation numbering. The numbering is correct for the case in which the solutions are printed.

%\documentclass[11pt,answers]{exam}
\documentclass[11pt]{exam}
\usepackage{parskip}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{lmodern}
\usepackage{microtype}

\usepackage{mathtools}
\usepackage{amsmath}

\usepackage{hyperref}

\begin{document}

\centerline{\bf Exam Class: Numbering Equations, MWE}

\begin{questions}

\question Answer the following questions.

\begin{parts}

\part Let $ a=3 $ and $ b=4 $. Consider the equation

\begin{equation}
a^{2} + b^{2} = c^{2},
\end{equation}
where all values are positive. Calculate the value of $ c $.

\begin{solution}
    We have, given that $ c>0 $,
    \begin{equation}
        c^{2} = 3^{2} + 4^{2} \Rightarrow c = 5.
    \end{equation}
\end{solution}

\part Let $ a=5 $. The variable $ b $ is given by
\begin{equation}
b = a^{2}.
\end{equation}
Calculate the value of $ b $.

\begin{solution}
    We have
    \begin{equation}
        b = 5^{2} \Rightarrow b = 25.
    \end{equation}
\end{solution}

\end{parts}

\end{questions}

\end{document}

Answer 1

A quick fix would to use \begin{equation*} and \end{equation*} or the normal equation environment based on the answers option. So we define a new environment equationsolution:

\newenvironment{equationsolution}{%
\ifprintanswers\begin{equation}\else\begin{equation*}\fi
}{%
\ifprintanswers\end{equation}\else\end{equation*}\fi
}

MWE:

%\documentclass[11pt,answers]{exam}
\documentclass[11pt]{exam}
\usepackage{parskip}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{lmodern}
\usepackage{microtype}

\usepackage{mathtools}
\usepackage{amsmath}

\usepackage{hyperref}

\newenvironment{equationsolution}{%
\ifprintanswers\begin{equation}\else\begin{equation*}\fi
}{%
\ifprintanswers\end{equation}\else\end{equation*}\fi
}

\begin{document}

\centerline{\bf Exam Class: Numbering Equations, MWE}

\begin{questions}

\question Answer the following questions.

\begin{parts}

\part Let $ a=3 $ and $ b=4 $. Consider the equation

\begin{equation}
a^{2} + b^{2} = c^{2},
\end{equation}
where all values are positive. Calculate the value of $ c $.

\begin{solution}
    We have, given that $ c>0 $,
    \begin{equationsolution}
        c^{2} = 3^{2} + 4^{2} \Rightarrow c = 5.
    \end{equationsolution}
\end{solution}

\part Let $ a=5 $. The variable $ b $ is given by
\begin{equation}
b = a^{2}.
\end{equation}
Calculate the value of $ b $.

\begin{solution}
    We have
    \begin{equationsolution}
        b = 5^{2} \Rightarrow b = 25.
    \end{equationsolution}
\end{solution}

\end{parts}

\end{questions}

\begin{equation}
c = \sqrt{a^2+b^2}
\end{equation}
\end{document}

Mind you that there will be inconsistencies between the exam the student sees and the exam with the solutions. That's why I always put the solutions after the exam questions.

Answer 2

I found a solution that uses a new counter and ifprintanswers. The new counter stores the value of the equation counter, and it is used later if the answers are printed. The solution of the counter is based on the solution to this question.

Here is the new MWE:

%\documentclass[11pt,answers]{exam}
\documentclass[11pt]{exam}
\usepackage{parskip}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{lmodern}
\usepackage{microtype}

\usepackage{mathtools}
\usepackage{amsmath}

\usepackage{hyperref}

\newcounter{eqBeforeSolution} % New counter

\begin{document}

\centerline{\bf Exam Class: Numbering Equations, MWE}

\begin{questions}

\question Answer the following questions.

\begin{parts}

\part Let $ a=3 $ and $ b=4 $. Consider the equation

\begin{equation}
a^{2} + b^{2} = c^{2},
\end{equation}
where all values are positive. Calculate the value of $ c $.

\setcounter{eqBeforeSolution}{\value{equation}} % Store current equation counter value 
\begin{solution}
    We have, given that $ c>0 $,
    \begin{equation}\label{eq10}
        c^{2} = 3^{2} + 4^{2} \Rightarrow c = 5.
    \end{equation}
    Equation \eqref{eq10} shows the solution.
\end{solution}

\ifprintanswers 
\else
    % Uses the value of the new counter to reset the equation counter
    \setcounter{equation}{\value{eqBeforeSolution}}
\fi

\part Let $ a=5 $. The variable $ b $ is given by
\begin{equation}
b = a^{2}.
\end{equation}
Calculate the value of $ b $.

\begin{solution}
    We have
    \begin{equation}
        b = 5^{2} \Rightarrow b = 25.
    \end{equation}
\end{solution}

\end{parts}

\end{questions}

\end{document}