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I have no scholarship offer at GW but I was offered a $38,000 per year, no tips scholarship to GMU... bringing tuition down to a tolerable $2700 per year. Meanwhile, I have no scholarship at GW and tuition is ridiculous. I didn't apply to either school until late April when I got feeler emails encouraging me to apply, and I was accepted to both this month. My LSAT is at their 25th but my GPA is around 75th for both. Do I have any kind of leverage?

Not really. Best course of action would be to retake the LSAT and reapply next cycle.

With a ~3.8/159, you really owe it to yourself to retake the LSAT. A 165+ would likely net you >$100k from GW.