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    \item\PTs{20} Answer each of the following multiple
        selection problems. Each correct answer is worth $3$
        points, and each incorrect answer is worth $-2$ points.
    \begin{questions}


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        \item\PTs{9} Select which people who served as a President
                     of the United States. (Select all correct choices.)

        \begin{manswers}{2}%
            \bChoices
                \Ans[-2]{0} Henry Clay\eAns
                \Ans[-2]{0} Ben Franklin\eAns
                \Ans[3]{1}\label{aj} Andrew Jackson\eAns
                \Ans[3]{1}\label{rr} Ronald Reagan\eAns
                \Ans[-2]{0} George Meade\eAns
                \Ans[3]{1}\label{gc} Grover Cleveland\eAns
                \Ans[-2]{0} John Jay\eAns
                \Ans[-2]{0} Paul Revere\eAns
            \eChoices
        \end{manswers}

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        \item\PTs{9} Select which people who served as a Chancellor of the
            German Republic. (Select all correct choices.)
        \begin{manswers}{2}%
            \bChoices[2]
                \Ans[-2]{0} Gustav Heinemann\eAns
                \Ans[-2]{0} Theodor Heu{\ss}\eAns
                \Ans[3]{1} Konrad Adenauer\eAns
                \Ans[-2]{0} Richard von Weizs\"{a}cker\eAns
                \Ans[3]{1} Willy Brandt\eAns
                \Ans[-2]{0} Heinrich L\"{u}bke\eAns
                \Ans[-2]{0} Roman Herzog\eAns
                \Ans[3]{1} Ludwig Erhard\eAns
            \eChoices
        \end{manswers}

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      \item\PTs{2} If you select all choices in part~(a), you will
          receive $-1$ points as a penalty for bad guessing. \textbf{Question:}
          Determine the \emph{number of correct choices} in part~(a)?
          \begin{answers}*{4}
          \bChoices
            \Ans0 1\eAns
            \Ans0 2\eAns
            \Ans1 3\eAns
            \Ans0 4\eAns
            \Ans0 5\eAns
            \Ans0 6\eAns
            \Ans0 7\eAns
            \Ans0 8\eAns
          \eChoices
          \end{answers}
\begin{solution}
Let $x$ be the number of correct answers, then $ 3x - 2(8-x) = -1 $. Solving this simple
equation we get $ x = 3 $.
\end{solution}
    \end{questions}
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