I wanted to use to charAt(0) on each element of the array list and loop through each choice until the asterisk was found, but I cannot use this method in my class since it is not defined.
I'm not sure I understand this - especially the "since it is not defined" bit.
You can put the code that determines the correct answer either in the Question class, or outside it. That really depends on how you are defining the Question class (ie what behaviour you intend it to have). Either way though every class you have will be defined!
Perhaps if you posted the code you have so far, and said where and what you are trying to do it would help.
There is nothing so far that suggests that inheritance is involved.