Pears : will keep for a few weeks on a cool counter, but fine in a paper bag. To hasten the
ripening put an apple in with them.
Apple : Will keep for Two weeks on counter.
I don't thin apples and pears will last for 2 weeks if kept on cool counter outside the Fridge. They may get excessively ripe or get spoiled.
Does it depend upon when you bring home from store? For e.g. from the time they were picked up from the farm to the time you bring home is, anyone's guess. You don't know how long they have been in transit.
This may be true if you picked it some what fresh
Maybe it depends on climate too? I live in Southern CA and during the summer it's basically impossible for me to keep anything cool just sitting on a counter just because it's so hot here.
Either way this is pretty helpful. I'm always having celery go bad because I don't use it fast enough.