Not bad premise but too many illogical issues and improbabilities. Specifically:
She is 16 when she enters college but coincidentally Charlie just happens to have done so as well so there is only a one year age difference. For some unexplained reason, she sees it as a problem when he turns 18 and she's only 17, but "they'll have been dating for a year by then." I don't know why it would be a problem for an 18 yo to date a 17 yo. It happens every day so I'm not sure what the issue would be.
Charlie also just happens to be the real nephew of the woman she pretended to be the neice of (somehow that never came up in all the Google searching she did). The sorority mathwork is totally implausible. Supposedly they have to get clearance from their National to take more than 2 pledges. This doesn't explain how the sorority can have enough members for there to be at least 26 sisters to generate the Alpha-Bet. Most colleges only have one sorority rush per year but even if they take 2 more pledges in the spring that gives them 4 each year. So they'd have to have 7 years worth of pledges to get the minimum number needed. No Greek organization could survive with those minimums (speaking as a former fraternity president).
The college is big enough to have 300 people in an organic chemistry class but there are only 2 sororities on campus and only 33 girls go through rush to try to join the social powerhouse Alphas? And Sloane is sneaky enough to pledge Alpha without anyone knowing that she's already a Zeta, yet she blows her cover by being in charge of a Zeta fundraiser and openly meeting with Charlie to plan it (and Charlie somehow doesn't pick up which sorority she's representing)? Grace lies to the Alphas and resigns but they then initiate her anyway because she saves them from the Zeta's.
The science contest is also a little incongruent. It's not clear why college students would be entering a contest that offers 4 years of college scholarship as the prize. Sounds like that should be for high school students. Given that she has already won the contest (and the full-ride to college) it isn't clear what she gains from entering again (or why she would be allowed to). And Charlie is a college sophmore and he's entered in the competition as well.
On the positive side, it showed Grace rethinking a lot of her attitudes about her family, particularly her mother, and having a lot of personal growth. The bet requirements were sometimes amusing and Jentry was amazingly tolerant of Grace's brother. Without the logical issues that I found distracting I could have rated this higher.