GE Capital Retail Bank, Creditor review: Fraud/Scam 2

I recieved a letter that didnt look like an offical document from the bank, telling me that I recently applied for a credit card from paypal, from GE Capital Retail Bank. I never applied for any credit and I do not own a paypal account. I called the number that was written in the document, [protected], on Tuesday May 21, 2013 at 8:03 am and spoke with Alicia. I was told to give them my full social security number and my date of birth, which I declined, because I believe they should already have the information. I also made them aware that I did not apply for this credit card. They said that if i didnt give them my information that they will not be able to do anything with the account. I believe that this is a scam. The letter had no email, no letter heading from the company that issued the letter.