How does one remain focused while studying for the GRE?
A few things that helped me
Pomodoro Technique - Study for 25 minutes with a 5-minute break in-between.  After 4 Pomodoros, give yourself a longer break.
Timeboxing - Limit your study time to specific times of the day, like 9-4 with a lunch break.  This will train your brain to expect to focus during the time-window, then do other things after.  Combine this with the Pomodoro Technique to best utilize your time.
Retake a practice test at the end of each week - This will both get you as familiar with the test as possible, and let you take a snapshot of your progress.  This snapshot should happen during your timebox.  Arrange to take the test during this timebox as well.
Take at least 1 day off a week - Be sure to give yourself at least 1 day off a week where you do not study or do work.
See a therapist - Studying for the GRE and applying to grad schools is stressful.  It may help to deal with your ruminations so they won't be as distracting.  They may also be able to teach you how to manage stress and time better.
It sounds like you may have burned out studying in one week.  Take a day off.  Tomorrow regroup and try at least some of these suggestions.  You'll likely need to play with the times suggested, but they are a good place to start.
Finally, remember that a few hours of focused, uninterrupted time is better than a day filled with interruptions and poor planning.  Make sure you're getting quality study time, then look at increasing the quantity.