My 2010 15 in. 2.66 Ghz i7 dual core macbook pro randomly shuts off and reboots

Question

I am a student at a college, and I recently bought a used MacBook Pro from the computer store which is part of a 4 year turnaround program when Faculty get new machines. It is a 2010 15 in. 2.66 GHz i7 dual core MacBook Pro, and I have had it for almost 1 week. After I got it, I installed Office 365 and Microsoft Document Connection. Almost immediately after doing this, and when I opened a Office application, it shut down. So I thought that installing Office 365 was somehow causing the computer to shut down. But over the past week, I've had maybe 3 more random shut downs including when all Office applications were quit and thus inactive. They were pretty rare, so I actually thought it wasn't such a problem because they didn't interrupt my work too badly. The screen suddenly goes black with no warning, and then immediately without me doing anything the computer reboots to grey screen, apple logo with languages / licensing stuff, tells me I shut down my computer due to a problem do I want to return to the screen I was on with all my stuff on it?, I say yes and it quickly goes to the desktop with everything I was working on pulled up.
So I didn't mind too much until last night, when it shut down twice within rapid succession of one another. Shut down, reboot, within seconds of me clicking on mail or whatever, boom, shuts down, reboots again. That was annoying. Then this morning, I wake up, open my computer to do work, BOOM shut down 1, open again, try to work, this time I'm using Safari when boom shuts down again time #2 within 1 minute of last shut down, then BOOM shuts down A THIRD TIME this time within 5 minutes of the last shut down. But still 3 SHUT DOWN/ REBOOTS in 10 minutes. Needless to say this is extremely annoying. Also, these last three times it has been on Battery power, but last night it was plugged in, so I don't think it's a battery issue. Also, my computer was fully charged (or almost) this morning, so it's not like it's on really low battery or anything like that.
I checked this thread: https://discussions.apple.com/thread/5044196?start=30&tstart=0, and it seems like I may be having kernel panics due to a defective NVIDIA graphics card. How do I tell what is causing these shut down cycles? How do I get it fixed? Also, needless to say, this MacBook is 4 years old, and I am not the original owner / purchaser, so I'm sure it's out of warranty. Does anyone know how much this will cost me at the Apple Store?

Answer 1

ggp057,
it could be due to the NVIDIA GPU defect in the 15-inch Mid 2010 models. It might also be due to faulty RAM. Do you know whether it has its factory-installed RAM, or if the RAM had been replaced? The GPU defect can be confirmed by making an appointment at your nearest Apple store to have them run their Video System Test on your MacBook Pro. Yes, it’s long out of warranty; the diagnostic test should be gratis, but if the defect is present, it typically costs a few hundred dollars to remedy (it involves a logic board replacement).
Did you also receive the two grey installation DVDs which originally came in the box with your MacBook Pro? Among other things, it has your model’s Apple Hardware Test. If you didn’t receive them, and the computer store is unable to provide them to you, then you can purchase a replacement pair from Apple. The Apple Hardware Test includes a RAM test, although it isn’t able to detect all possible RAM problems.