So, quick:
Question bank...
Category 1: Subcategory 1a (10 questions); Subcategory 1b (10 questions)
Category 2: Subcategory 2a (10 questions); Subcategory 2b (10 questions)...and so on to 10 categories with 2 subs each.
Quiz...
random question from Category 1. There may be something you have to poke at to get it to select from sub categories.
I'm not saying I recommend this. I recommend Rick's solution. But if you have to have this structure, this should work.