How long do bananas keep?

Bananas advance very quickly from green-yellow to yellow to brown- or black-yellow, sometimes within just a few days. A black-yellow banana may not taste the same as a yellow one--it's likely to taste sweeter--but the difference doesn't make it inedible. Far from it. You'll know an inedible banana when you see it-- plenty of shriveling, oozing, and a sharp odor reminiscent of nail polish. If refrigerated after ripening, bananas may keep up to  a week.  If not refrigerated, they may get mushy and brown within a few days after ripening. 
 
Source(s):
GourmetSleuth.com "Food Storage Guidelines"