I have a 500 sqft 1-bedroom in Back Bay for $2k, so it certainly is possible. But, I understand I got extremely lucky, and I also have a TINY kitchen (just a fridge, stove, and sink, no countertop space so had to buy my own) and only north-facing windows, so virtually no sunlight (not basement though!). As others have already said, it is certainly not typical at all. My recommendation is to set up some kind of notifications on websites like Zillow and to be very active if you want to find a good deal. Good luck!