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To apply for the Blue card from American Express you need to have a good or excellent credit score. This means you need a credit score of at least 700. Although, some applicants have been approved with a credit score as low as 650. If you are a student, you can choose a credit card from those offered to students. Student credit cards usually have lower interest rates and fees. Some of them even come with rewards.
If you want a cash back credit card, you should consider the Discover it® Student Cash Back card. The card offers 1% cash back on all purchases. You can even get 5% cash back (up to the quarterly maximum) if you enroll in rotating categories every quarter.