OP said he had 6GB of RAM. It is safe to assume that it's a 64 bit OS. Especially if it came from an OEM.
You're probably correct, however, I never "assume" anything.
I learned a long time ago, that word assume, will often make an "ass" out of "u" and "me".
I've seen a number of Best Buy variety HP, and Compaq computers about 2 years ago, that came with 4 & 6GB of memory and a 32 bit Win7 OS. That's why I asked. They no longer do that. If his machine is a year old or less, it's certainly 64bit, but I don't know that either. That's why I made those comments.