There are two other major variables..the length of time the title search takes and the length of time the loan takes..Also, with titile in most areas is a letter from the town called the municipal search..It is basically a letter form the town saying there are no outstanding certificated of occupancy or propert violations..if there are, this will extend the transaction time..
I practice in New York..here the qucikest transactions take 60 days and the average transaction takes 90 days..Also keep in mind a cash transaction is the shortest duration followed by a conventional loan, the FHA and finally veteran's adminiatration Loans
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Understand that the seller might not agree to it. But if you and the seller can reach agreement, then you're set. Your Realtor can give you more specific advice.
Hope that helps.