Equal Space in the exam enviroment or other alternative

I am trying to write a multiple choice exam with the exam package. For each questions I have 6 possible answers (3 in each line). Here is a minimal work example.

\documentclass[addpoints]{exam}
\begin{document}

\begin{center}
\end{center}

\begin{questions}

\titledquestion{\textbf{Multiple Choice}}[10]

What is the capital of the United states?

\begin{oneparchoices}
\choice NY
\choice Texas
\choice LA \\\\
\choice San Antonio
\choice Chicago
\CorrectChoice Washington D.C.

\end{oneparchoices}

\end{questions}

\end{document}


I want to have every three answer distributed evenly in one line with equal spaces between them and to have answer a above d and b above e and c above f directly.

Thanks

I rely on egreg's code (as most of the times) which he gave me on one of the occasions when I was a victim of similar requirement. Here is a slight modification of his code and I have defined a new environment myoneparchoices so that you will have the original oneparchoices intact.

\documentclass[addpoints]{exam}

\usepackage{environ,xparse}

%% ------------------egreg's code begins---------------------------
\ExplSyntaxOn
\cs_undefine:N \choices
\cs_undefine:N \endchoices
\NewEnviron{myoneparchoices}{%
\par\nopagebreak
\abd_dochoices:V \BODY
\par
}
\tl_new:N \l_abd_choices_tl
\seq_new:N \l_abd_choices_seq
\seq_new:N \l_abd_choices_final_seq

\cs_new_protected:Npn \abd_dochoices:n #1
{
\setcounter{choice}{0}
\tl_set:Nn \l_abd_choices_tl { #1 }
\tl_replace_once:Nnn \l_abd_choices_tl { \CorrectChoice } { \choice* }
\seq_set_split:NnV \l_abd_choices_seq { \choice } \l_abd_choices_tl
\seq_pop_left:NN \l_abd_choices_seq \l_tmpa_tl
\seq_set_map:NNn \l_abd_choices_final_seq \l_abd_choices_seq
{ \exp_not:n { \makechoice ##1 } }
\seq_map_inline:Nn \l_abd_choices_final_seq
{
\makebox[.3333333333333333333\linewidth][l]{
\parbox[t]{.3\linewidth}{\raggedright \hangindent1.5em ##1\strut}
}\hspace{0pt plus .1\linewidth}
}
}
\cs_generate_variant:Nn \abd_dochoices:n { V }
\ExplSyntaxOff
\makeatletter
\NewDocumentCommand{\makechoice}{s}
{
\stepcounter{choice}
}
\makeatother

\begin{document}

\begin{center}
\end{center}

\begin{questions}

\titledquestion{\textbf{Multiple Choice}}[10]

What is the capital of the United states?

\begin{myoneparchoices}
\choice NY
\choice Texas
\choice LA
\choice San Antonio
\choice Chicago
\CorrectChoice Washington D.C.
\end{myoneparchoices}

\end{questions}

\end{document}