Hi Abhinav,
First off, a 680/Q45 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. Depending on the Schools that you plan to apply to, you would likely find it beneficial to speak with an Admissions Expert about your overall profile. There's a Forum full of those Experts here:
https://gmatclub.com/forum/ask-admissio ... tants-124/GMAC has publicly stated that the Official Score that you earn on Test Day is within +/- 30 points of actual ability. Assuming a similar 'swing' in how your CATs function, most of your CAT score results - along with your Official Score - show that you essentially performed the same each time (about 680 +/- a few points); the 750 is an 'outlier', so we cannot assume that that is a completely accurate assessment of your current skill level. You handle certain aspects of the GMAT consistently well, but you also make certain consistent mistakes.
Before I can offer you the specific advice that you’re looking for, it would help if you could provide a bit more information on how you've been studying and your goals:
Studies:
1) How many hours did you typically study each week?
2) What study materials have you used so far?
3) What were the Quant and Verbal Scaled Scores on EACH of your CATs?
Goals:
4) What is your overall goal score?
5) When are you planning to apply to Business School?
From your post, it sounds as if you have purchased the Enhanced Score Report. 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). You will need to post at least 5 times in the GMATClub Forums before you are allowed to include attachments with your posts and PMs. If you would rather not go through those extra steps, then you can feel free to email me your ESR and I'll be happy to analyze it for you.
GMAT assassins aren't born, they're made,
Rich