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If you have a 660 in the first attempt, I am sure you know what it takes to get that kind of a score. You just need to focus a little bit more on some of the weaker areas and get to that 7** magic number. I am sure you would have hit that number in your practice tests.
Good Luck and I am sure you will be there in no time.
In terms of whether or not you can hit 700+, I would look at your practice scores for the answer. If you have hit 700+ on at least 20-30% of your practice tests (including MGMAT, PR, and GMATPrep, but not Kaplan), then I would say you have a shot. But if you have not done this, I would say getting a 570, 660 and then pulling off a 700+ in just 3 weeks is a huge stretch and I would encourage you to take a bit more time (5-6 weeks) to ensure you really get the core concepts and timing down perfectly.