[Tex/LaTex] Encoding with the tasks package

Question

How do I encode problems 3.) and 5.) that is consistent with the remaining code? The display is what I want.

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\newlength\labelwd
\settowidth\labelwd{\bfseries viii.)}
\usepackage{tasks}
\settasks{counter-format =tsk[a].), label-format=\bfseries, label-offset=1em, label-align=right, label-width
=\labelwd, before-skip =\smallskipamount, after-item-skip=0pt}
\usepackage{enumitem}
\setlist[enumerate,1]{% (
leftmargin=*, itemsep=12pt, label={\textbf{\arabic*.)}}}


\begin{document}


\begin{center}\Large{\textbf{Elementary Number Theory}}\end{center}\vskip0.25in

\begin{enumerate}[itemsep=\baselineskip]
\item How many positive integers less than 100 have a remainder of 3 upon division by 7?
        \begin{tasks}(3)
          \task 10
          \task 11
          \task 12
          \task 13
          \task 14
        \end{tasks}
\end{enumerate}

\begin{enumerate}[start=2, itemsep=\baselineskip]
\item For every natural number $n$, $\tau(n)$ is the number of positive divisors of $n$. Evaluate $\tau^{3}(12)$.
        \begin{tasks}(3)
          \task 1
          \task 2
          \task 3
          \task 4
          \task 6
        \end{tasks}
\end{enumerate}



\noindent {\textbf{3.) }}$p$ and $q$ are prime numbers greater than 2. which of the following statements must be true? \\
\hspace*{3em} \hphantom{3.)\ }
\begin{tabular}{r l}
{\bf I}     &   \hspace*{-0.5em}$p + q$ is even. \\
{\bf II}    &   \hspace*{-0.5em}$pq$ is odd. \\
{\bf III}   &   \hspace*{-0.5em}$p^{2} - q^{2}$ is even
\end{tabular}
\begin{tabbing}
\hspace*{2em} \= \hspace{2.5in} \= \kill
\> {\textbf{a.) }}I only        \> {\textbf{b.) }}II only \\
\> {\textbf{c.) }}I and II only \> {\textbf{d.) }}I and III only \\
\> {\textbf{e.) }}I, II, and III
\end{tabbing}
\vskip0.25in


\begin{enumerate}[start=4, itemsep=\baselineskip]
\item How many integers less than 1000 are such that the remainder upon division by each of 2, 3, 4, 5, 6, and 7 is 1?
        \begin{tasks}(3)
          \task 0
          \task 1
          \task 2
          \task 3
          \task 4
        \end{tasks}
\end{enumerate}


\noindent {\textbf{5.) }}$n$ is a positive integer. Which of the following quantities is divisible by 3? \\
\hspace*{3em} \hphantom{3.)\ }
\begin{tabular}{r l}
{\bf I}     &   \hspace*{-0.5em}$n^{3} - 1$ \\
{\bf II}    &   \hspace*{-0.5em}$n^{3} + 1$ \\
{\bf III}   &   \hspace*{-0.5em}$n^{3} + 2n$
\end{tabular}
\begin{tabbing}
\hspace*{2em} \= \hspace{2.5in} \= \kill
\> {\textbf{a.) }}I only        \> {\textbf{b.) }}II only \\
\> {\textbf{c.) }}I and II only \> {\textbf{d.) }}II and III only \\
\> {\textbf{e.) }}I, II, and III
\end{tabbing}

\end{document}

Answer 1

I would do it this way:

\documentclass{amsart}
\usepackage[showframe]{geometry}
\usepackage{amsmath}
\usepackage{amsfonts}
\newlength\labelwd
\settowidth\labelwd{\bfseries viii.)}
\usepackage{tasks}
\settasks{counter-format =tsk[a].), label-format=\bfseries, label-offset=1em, label-align=right, label-width
=\labelwd, before-skip =\smallskipamount, after-item-skip=0pt}
\usepackage[inline]{enumitem}
\setlist[enumerate]{% (
labelindent = 0pt, leftmargin=*, itemsep=12pt, label={\textbf{\arabic*.)}}}


\begin{document}


\begin{center}\Large{\textbf{Elementary Number Theory}}\end{center}\vskip0.25in
%\setlist[enumerate, 1]{itemsep=\baselineskip}
\begin{enumerate}
  \item How many positive integers less than 100 have a remainder of 3 upon division by 7?
        \begin{tasks}(3)
          \task 10
          \task 11
          \task 12
          \task 13
          \task 14
        \end{tasks}

  \item For every natural number $n$, $\tau(n)$ is the number of positive divisors of $n$. Evaluate $\tau^{3}(12)$.
        \begin{tasks}(3)
          \task 1
          \task 2
          \task 3
          \task 4
          \task 6
        \end{tasks}

  \item $p$ and $q$ are prime numbers greater than 2. Consider the following statements:

        \begin{tasks}[counter-format = tsk[R], label-format=\normalfont, after-skip=1\medskipamount](3)
          \task $p + q$ is even.
          \task $pq$ is odd.
          \task $p^{2} - q^{2}$ is even
        \end{tasks}
        Which of the following must be true?
        \begin{tasks}(3)
          \task I only
          \task II only
          \task I and II only
          \task I and III only
          \task I, II, and III
        \end{tasks}

  \item How many integers less than 1000 are such that the remainder upon division by each of 2, 3, 4, 5, 6, and 7 is 1?
        \begin{tasks}(3)
          \task 0
          \task 1
          \task 2
          \task 3
          \task 4
        \end{tasks}

  \item $n$ is a positive integer. Consider the following quantities:
  \begin{tasks}[counter-format = tsk[R], label-format=\normalfont,  after-  skip=1\medskipamount](3)
        \task $n^{3} - 1$ \
        \task $n^{3} + 1$
        \task $n^{3} + 2n$
  \end{tasks}
  Which is divisible by 3?
  \begin{tasks}(3)
    \task I only
    \task II only
    \task I and II only
    \task II and III only
    \task I, II, and III
  \end{tasks}
\end{enumerate}

\end{document} 

A variant:

\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\newlength\labelwd
\settowidth\labelwd{\bfseries viii.)}
\usepackage{tasks}
\settasks{counter-format =tsk[a].), label-format=\bfseries, label-offset=1em, label-align=right, label-width
=\labelwd, item-indent=\dimexpr\labelwd+1em\relax, before-skip =\smallskipamount, after-item-skip=0pt}
\usepackage{enumitem}
\setlist[enumerate,1]{% (
leftmargin=*, itemsep=12pt, label={\textbf{\arabic*.)}}}

\begin{document}

\begin{center}\Large{\textbf{Elementary Number Theory}}\end{center}\vskip0.25in

\begin{enumerate}[itemsep=\baselineskip]
\item How many positive integers less than 100 have a remainder of 3 upon division by 7?
        \begin{tasks}(3)
          \task 10
          \task 11
          \task 12
          \task 13
          \task 14
        \end{tasks}
\end{enumerate}

\begin{enumerate}[start=2, itemsep=\baselineskip]
\item For every natural number $n$, $\tau(n)$ is the number of positive divisors of $n$. Evaluate $\tau^{3}(12)$.
        \begin{tasks}(3)
          \task 1
          \task 2
          \task 3
          \task 4
          \task 6
        \end{tasks}
\end{enumerate}

\noindent {\textbf{3.) }}$p$ and $q$ are prime numbers greater than 2. which of the following statements must be true?
\begin{tasks}[counter-format =tsk[R], item-indent=5.1em](1)
\task $p + q$ is even.
\task $pq$ is odd. 
\task $p^{2} - q^{2}$ is even
\end{tasks}
\begin{tasks}[ item-indent=\dimexpr\labelwd+2.85em](2)
\task I only
\task II only
\task I and II only
\task I and III only
\task I, II, and III
\end{tasks}

\begin{enumerate}[start=4, itemsep=\baselineskip]
\item How many integers less than 1000 are such that the remainder upon division by each of 2, 3, 4, 5, 6, and 7 is 1?
        \begin{tasks}(3)
          \task 0
          \task 1
          \task 2
          \task 3
          \task 4
        \end{tasks}
\end{enumerate}

\noindent {\textbf{5.) }}$n$ is a positive integer. Which of the following quantities is divisible by 3? 
    \begin{tasks}[counter-format =tsk[R], item-indent=5.1em](1)
   \task $n^{3} - 1$ 
    \task   $n^{3} + 1$ 
    \task $n^{3} + 2n$
    \end{tasks}
    \begin{tasks}[item-indent=\dimexpr\labelwd+2.85em](2)
    \task I only
    \task II only
    \task I and II only
    \task II and III only
    \task I, II, and III
    \end{tasks}

\end{document}