How do I find out of my OS X 10.9.4 is 32 bit or 64 bit?
I do not believe that Mavericks shipped with a 32-bit version. You are probably running 64-bit OS X.

All of the Core i3, i5, and i7 Mac computers have 64-bit processors.

Apple Support document

To determine if you are running a 32-bit or 64-bit version of OS X, open a Terminal and type:

uname -a

On a 64-bit OS, the output will end with RELEASE_X86_64 x86_64. On a 32-bit OS, the output will end with RELEASE_I386 i386.

OSXDaily article