Unsurprisingly, of course, they ultimately form a kind of unlikely friendship by both becoming attached to the newcomer in the building, a Japanese guy whom both fetishize as the ultimate in elegance and refinement, a worthy companion for their own lofty souls.
I'm being snarky, and actually, the text is somewhat more sympathetic than that, but that doesn't get around how obnoxious it is. The 12 year old, in particular, is irritating in her extreme narcissism. She has a great scheme to kill herself on her 13th birthday, and is thus keeping a notebook of "profound thoughts" to bequeath to the world in her absence. Her thoughts are not very profound. Her complaints about the people around her are somewhat understandable, but mostly elitist and tiresome. What is most annoying about her, though, is that she's not even remotely believable as a character - Burbery asks us to believe that she is as genius, and has read and understood, for instance, Lacan, but also that she mostly reads only manga. I think that what I find so annoying about it is that it actually masks a vague sort of anti-intellectualism - there's a sense that a 12 year old could have read all these texts and understood them, and yet, not be much better for that knowledge. Likewise with the concierge - it seems that all that their reading has given them is a few ideas to play with a sense of superiority.
Finally, there's the seemingly coincidental resonances in their thought that I find clunky and obnoxious. I suppose it's meant to be an elegant echo of different concepts across the pages, but it feels horribly contrived. And the ending - oh man. I won't spoil it for you, but it's the crowning jewel of obnoxiousness.
Alright, enough hateration from me. Time for dinner.
ps - Oh, I should add - some of the problem of the prose could be translation. I suspect it reads much better in the original French - in English, the attempt at combining refined vocabulary and slang comes across pretty poorly, which makes the characters seem even more pretentious.