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\multipartquestion
\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}
\rowsep{3pt}
\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}
%\ifwithdesign\promoteNewPageHere[6\baselineskip]\fi
\rowsep{3pt}
\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}
%\promoteNewPageHere{4\baselineskip}
\rowsep{3pt}
\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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