The Sapphire Preferred requires good credit (i.e. a credit score of 700+), but the Citi Prestige and the Altitude Reserve only accept applicants with excellent credit (i.e. a credit score of 750+).
The minimum credit limit of $5,000 is guaranteed for these cards, but as with most cards, the credit limit you ultimately get will depend on your creditworthiness, with an emphasis on your credit scores and income. In general, the better your credit and the higher your income, the higher your credit limits will be.
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