"So, if we want to increase the size of our applicant pool, we need to raise our tuition and fees." In other words, raising tuition and fees (RTF) is necessary for an increase in the applicant pool (IAP).
IAP - - > RTF
How would we diagram answer choice C? RTF - -> IAP Do you see how the sufficient and necessary conditions have been reversed? This is too strong. We do not need higher tuition to guarantee a bigger applicant pool. Higher tuition is the necessary condition, not the sufficient.
I'll try the negation test on C to demonstrate: "An increase in tuition and fees at the university would NOT guarantee a larger applicant pool." Does this destroy the argument? No, because the university president never said it was a guarantee. She was saying that, without a tuition increase, the applicant pool will not increase.
This is a pretty common type of wrong answer on strengthen with sufficient premise questions. They will often try to trick you into choosing an answer choice that is too strong for what the argument actually says. Also, pay attention to sufficient and necessary indicators like "need" and "guarantee."