I'm not sure if there's really a good reason to inherit from AppStates here -- you're not actually using any of the functionality and it's complicating your life because it has a bunch of unnecessary states and such on it. I would rework it a bit to make a simpler class that has:

* a prefix for all its state names (which it adds automatically when state creators are added)
* explicitly keeps a reference to the begin state
* explicitly keeps a reference to the continue state
* explicitly keeps a separate list of question states

You can keep the random question selector method and use it the same way you do currently.