Air Purifiers

I have 3 bedrooms in my upstairs, combined about 600 sq. feet, I just bought an air cleaner good for 780 sq.feet, can I just put this on a wall in the hall and if the bedroom doors are open will to work in all the rooms? Thank you.

Hi. We just got a puppy and my allergies are really bad. We also have a cat and it's more than I can handle. Which air purifier do you recommend for smells/ dander/ dust and everything else? We have a 2300 square foot house but I'm mostly concerned w/ our bedrooms. Should I buy one big unit to cover the entire area or should I buy three smaller units to put in our bedrooms?