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Yeah, you will probably approve as long as that one 30 days late is not recent.
I didn't have any prequals on the site either. I applied for the Delta Gold and was approved only $1000 sl but then applied for the green card and was approved for that one as well. My scores are hovering around 650 with one baddie over 4 years old. If you can afford the HP then I would say go for it. I was just looking for a foot in the door.