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No, you will not be approved for any of the Sam's Club credit cards if you have bad credit. Your credit score must be decent to receive any of these credit offers. Similar to many other store cards you cannot choose whether you apply for the basic Sam’s Club credit card or the one branded with the MasterCard logo. Your only choice is whether you are applying for a business or personal account. However, you can choose to apply for a general credit card for bad credit.
The card you are given will be based on your credit score. A better score will be given the card branded with the MasterCard logo. The APR on the store card is standard, but the MasterCard has a varying interest rate. The better your credit the better rate you will be given.