Hi energetics,
To start, a 660 is a strong score, so it could be enough to get you into your first-choice School. As such, a retest might not be necessary. The Q43 won't "impress" anyone though, so there's a certain logic to retesting (and you certainly have the opportunity to pick up some serious points in the Quant section). Since you're interested in some highly-competitive Schoos, beyond having a strong GMAT Score, you need to have a strong OVERALL profile AND you need to properly "market yourself" to each individual Program that you apply to. As such, you would likely find it beneficial to speak with an Admissions Expert about your overall profile and plans. While you probably already know this, there's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/From what you describe, there are areas that you clearly have not been working on. You're probably trying to do too much work "in your head" (which is the WORST way to approach a GMAT question). Based on your Quant Scaled Scores from your CATs, your general "math skills" are likely fine. Getting in some extra Algebra practice would probably be a good idea, but you seem dead-set on not taking advantage of how the GMAT is written - and that mindset is keeping you from scoring higher. The GMAT is a big 'critical thinking test' - and as such, it rewards Test Takers who know how to think about questions in critical and strategic ways (the same ways that Business Schools want you to be thinking). Quant and Verbal Tactics are absolutely essential to scoring at the highest levels (and Tactics work on questions of all difficulty levels, so if you want a Q49+, then you're going to have to hone your Tactical skills).
While the ESR doesn’t provide a lot of information, there are usually a few data points that we can use to define what went wrong on Test Day (and what you should work on to score higher). Since you have purchased the ESR, I'll be happy to analyze it for you. If you would rather not post that information publicly, then you can feel free to PM or email it to me directly.
GMAT assassins aren't born, they're made,
Rich