what happens if i entered into a written contract with rpm but the contract was based on a lie that the salesman told ? would it be nullified?

The short answer is that if the salesman made a material misrepresentation of fact on which you relied in entering into the contract, it could be nullified based on fraudulent inducement (although it is likely that the contract you signed says something like that the writing constitutes the entire agreement between the parties, and you acknowledge that you didn't rely on any oral representations in entering into the contract.)  However, I don't see any fraud in what you described.  Buying the car in your name made you responsible for paying for it - that's the only reason the dealership sold the car, since apparently the dealership was not satisfied with your friend's signature.  It's your friend who has damaged you by not making the payments she agreed to make, not the dealership.  You can sue her for any amount you have to pay the dealership. However, you are correct that the dealership should not be able to recover the full price of the car from you.  The amount the dealership received for the car on resale (less expenses connected with the sale such as the expense of repossessing it) should be deducted from the amount you owe.