Well, you could make each option add a certain amount to a single variable. In other words, set one variable up.
Variable = 0
Then for the questions, as a result of the answer, add to that variable a special amount representative of what class that option best represents.
To show this, let's take a simple case.
Say, there are three classes (thief, fighter, mage), and three questions (answers yes or no).
Let's say that if the final variable result is low, say below 5, then the player is a thief, if it is between 5 and 10, he is a fighter, and if it is above 10 then mage
Then for the questions:
Are you sneaky?
Yes: Add 1 to the variable
No: Add 4 to the variable
Are you virtuous?
Yes: Add 1 to the variable
No: Add 4 to the variable
Are you smart?
Yes: Add 4 to the variable
No: Add 1 to the variable
Thus, if you answer [yes, yes, no] the variabale is 3, and so you are a thief. If you answer [no, no, yes] you are a mage, and if you answer any other combo you are a fighter.
Obviously, you'll need to select what is added to the variables dependent on answer more discriminately