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While I'm a bit confused about your education, but the two #s you've thrown out there (3.1 and 2.7) aren't terribly low. Yes, you have some explanations to do, but it's not insurmountable. Schools that you should look into can definitely be in the top 20's, and if you're willing to inch out a few more spots past the 20, you should have a good plan. Without knowing too much about you, I'd pick just one school in the top 7 (H/S/W, Kellogg, Sloan, Booth, Columbia), this is to satisfy your own desire and to leave you with no regret. Then in the top 8 to 15, I'd pick 2 or 3 more, schools such as Darden, Fuqua, Ross, Haas, Tuck, Anderson, Stern, and Yale). Then schools in the 16 to 24 can get you the last 3 or 4 schools, such as Tepper, UNC, USC, Cornell, and UT.
A 3.1 is not bad, just an fyi. You will still have to explain some, but since it's also upward-trending (from a 2.7 to a 3.1 only means that you've been getting higher than 3.1 thus far), it's also a positive sign. In terms of GMAT, if you think you can get over 740, then yes, I'd recommend it. But if you don't think you can and that your practice CATs have been topping out at 700 and 710, I would focus more on the application and your stories than another month of GMAT.
I had very nearly identical stats - 3.1 undergrad but with a downward trend and a 710 gmat. Currently a manager at a healthcare company. Applied to Wharton, Vanderbilt, Duke and Kellogg. Got into all but Wharton and am attending Kellogg in the Fall. After a couple years of applications and considerable reflection, it really seems like a lot of it is how you frame your story. The more compelling the rest of your application, the more willing the adcoms seem to be to overlook a stat like a 3.1 GPA. Honestly, for most applicants it was quite a few years ago and if you have a great track record since then and are able to VERY clearly articulate why an MBA and your passion for the school you should be fine.
More important than targeting a set number of schools in different subsets (i.e. 1 in M7, etc.) I would spend a lot of time thinking about why you want to get an MBA and what skillsets you want to develop. Then target those programs that will most enable you to reach your goals. I was targeting a school with a strong healthcare program that would allow me to gain some knowledge on the product side. Recruiting was another huge consideration. Once I got to my list more intuitively it made it easier to articulate why I wanted to go to school and why the schools on my list.
I think yellowjacket made a really good point. Instead of focusing on the tier of schools, think about which schools are strong in the field that you want to be in. Make your compelling story and really stand out among the crowd. A 3.1 really isn't that bad (I graduated with a 3.1 as well) and as long as you have a good story to tell, good knowledge to bring to the table, you have all the tools you'll need to gain admission. Good luck!