Should I retake the SAT?

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I don't think you should retake it, unless youre absolutely sure you can get a higher score. You didn't do bad, so I also don't think that a course would be of much use to you.
 
Those are very good SAT scores. Your writing could use a teeeeny, tiny bit more on your writing, but to be honest; with your EC's, you really shouldn't have any trouble getting into NYU. I don't think you'd get a MUCH higher score on your SAT's, so it's really up to you. But for NYU, you seem to right in the middle of their general applicants, maybe even the upper half.