TLDR; Is it rude to ask how much a new neighbour paid for their apartment? My view is that it isn't, because it's information that's probably their favourite topic of conversation right now, and also in the public domain.
Recently, some new people in my apartment building moved in. Unfortunately, they appear very friendly, and have already telegraphed a degree of interest in developing some form of non-transactional relationship with me.
Two days in a row now we have both given each other friendly hellos and acknowledged one another's existence but not actually stopped to introduce ourselves. The worst type of faux-relationship you can have with someone is the one that consists of hellos without ever stopping to talk. I have decided that I will not be that person.
So next time I bump into them I intend to actually make an effort. Not a huge one, but an earnest one nonetheless.
Presently, I am self-indulgently trying to come up with possible topics of conversation. For example, they were sanding the floor the other night which means they bought the place, which means I might pretend to not have already looked up the sale price and to casually ask if they bought it or are renting, then ask how much they paid.
I am aware of the typical sensitivities regarding questions that pry into matters relating to finances e.g. income, personal expenses, etc but I don't think that such graces apply if these things are publicly available
For example, I find the following unlikely:
"I hear that's very competitive to get accepted into. Tell me, how much does a year at this elite boarding school for toddlers cost?"
"We'll, that's none of your damn busine--"
"Actually never mind, they have a price list on their website"
Generally speaking, is my perspective on this reasonable? If it's of any relevance, I will not be deploying any offense-taking countermeasures such as the classic "if you don't mind me asking" gambit.