So after taxes and such you would have $1,800 a month of $25K/year. $100K in student loan debt is around another $800. So that leaves you with about a grand for everything else (rent, food, transportation, etc.). Yes, that's doable but that's not much of a life, is it?
I meant the 25K per year for people not having any/much debt. It may be difficult starting out, but I know plenty of folks who moved up here after college and did just that.
Also, someone making $25K a year will not take home $1,800 a month after taxes and benefits and whatnot. It will be less than that by a considerable amount (especially if there is a state income tax). I'd count on monthly take-home being closer to $1,600.