Btukfyl

I am creating an answer key booklet using exam.cls for a question sheet that I made for some students.

Along with that, I've used the multicol package to create 2 columns within a question that is composed of multiple parts. However, I am faced with the issue of the part letters being in the wrong places:

As you can see, part (c) and (e) are placed at the positions of (d) and (f) respectively, causing quite a mess. I would like to avoid to repeating the question's text after question.
Here is my code:

documentclass[11pt]{exam}

usepackage{multicol}

begin{document}

    begin{questions}

        question

            begin{parts}

                begin{multicols}{2}

                    part answer

                    part answer

                end{multicols}

                begin{multicols}{2}

                    part answer

                    part answer

                end{multicols}

                begin{multicols}{2}

                    part answer

                    part answer

                end{multicols}

            end{parts}

    end{questions}

end{document}

I understand that the parts environment is used as the text for question, but I can't understand why the output appears like that. How can I modify my code to fix this problem? And is using exam.cls inappropriate for this purpose?