Hi
nihilisticanalystCongrats on mentioning Jim Simons, not many people would know him and yet he is the best money manager in the world, based on rate of return, contrary to the popular belief that would not be Warren Buffett.
And you would be right in connecting the dots about my username and research/career interest.
Just based on that observation I can see we are alike and we should connect, I will pm you regarding that.
About being blunt, it is not uncommon to have lower undergraduate GPA and then have higher on master studies, after all people are immature on bachelor studies, don't have ambitious goals, don't really know themselves or what they want to do in life.
Therefore, your situation is somewhat desirable in sense that there is clear progress, once you got serious about pursuing PhD you knew that master GPA would be important and you acted accordingly.
Offering explanation that you were not interested in subject area of your bachelor studies is not only true but perfect explanation and believe me something they encounter many times in evaluation of candidates.
In same way, that you are not fan of rote learning, that you find GMAT dull and boring and that you are not good at standardized testing, which is only one size fits all attempt for comparison is okay and understandable, you just need to find how to spin your story in SOP, how to sell it.
I would go with approach that where you are motivated and genuinely interested you excel like on MBA studies vs. bachelor/GMAT where you just did what was expected from you, to complete the task.
Since PhD is all about research, that approach would be okay in my book.
My intention was within reach, however I based that mostly on your target of green schools, assuming you knew why you picked them overall, not only on test score category.
Regarding your quant score...on MBA studies how many exams were quant based ?
What is your MBA specialization ?
Of course your research background will remedy quant score, moreover that is your strongest characteristic in application and card "we" play on.
Regarding Olin and other schools, what you are referring is average score across all disciplines...which is not what is your prime interest... yeah it is some guidance...but you need average score of admitted students in your area of specialization where you want to pursue PhD, aka Business Analytics/ Operations Research / Management Information Systems /Data Mining.
If you want to play more safe, then add to the list Rutgers, U of Miami, Price Oklahoma....instead of first above mentioned dream category.
I can see you did gather info from Professors and PhD program coordinators, that is the way to go, if it is not already stated on website.
Beware Professors will always offer you higher score as average

in their reply, which is rather something they would like to see, than real accurate data, that's little trick that should not afraid you....but at the end of the day you will compete with other applicants for spot, so past data are just guidance and ballpark, any given year those figures may fluctuate more or less.
I can see what is your intention, you want to base your list on 670 score +- 20-30 points, where + would be dream, approximately exact score would be fit and - would be safety ones.
It is pretty easy for me to tell you which ones that fall in those categories are good schools, what I am trying to say to you, is that you should pick them, I cannot know your preference toward location, geography, climate, big city vs. more quite environment, professors you would like to work with (although I do happen to know somewhat about strength of relevant departments) and million other things that can influence your decision...you should look for hidden gems that are strong in your area of expertise and research, but may not be known as top business school overall necessarily.
I will attach your research.
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