What does the rental application say?
I am not sure why you wonder if they can or can not.... they may just want to make sure that
you are talking about a child and not an adult child, as that may require an application etc.
Seldom requested but often willingly provided by the tenants like "let the landlord know who is moving into their property"
Landlords want to know your income, your employment, your references, your credit score and your background check.... the ages of children may just be asked to know who is moving into their home or did you think the question was asked for a different reason.
Feel free to get back to us...
Most Sincerely yours,
Edith YourRealtor4Life and Chicago and North Shore Expert
Working always in the very BEST interest of her clients with @Properties