There aren't [ many / any / no ] young people in our apartment block. (It's 'many' but..... Why not 'any'?)

I have the above question in one of my classes but can't find a reason as to why the answer can't be 'There aren't any young people.... '

The only thing I can think of is if it something like you can't assume that there are no young people in a building - statistically unlikely - or something like that.

Is there a rule that I don't know?

Cheers.

Aren't many implies that the number of young people are few but not zero. Aren't any implies that the number of young people are zero. As Kate points out, Aren't no would need to be replaced by Are no to avoid the double negative.