Imagine a student got the wifi password of the school.
Can you specifically ask about the age of the student like this:
"A what age student stole the school's wi-fi password?"
OR
"What age student stole the school's wifi password?"
Although they do not sound idiomatic, I am not quite sure, maybe they can be used.
If yes, should it be "A what age student...." OR "What age student ...."