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I recently applied for the Green card and got NPSL pretty easily, I have a thin file but have been building my scores up. My CS is 749 according to TU, wasn't approved instantly however; they verified some information and then gave me an approval over the phone. I further applied for the Amex Skymiles Blue Card, after some Recon; I came out of it with a $10k credit limit. Hope this gives you some insight into Amex's approval practices.
I got approved for the Amex green card with a fico score of 638