TuneUp provides Mac OS X versions for 64-bit capable systems as well as those only capable of running 32-bit applications.  Whether or not your computer can run 64-bit applications is a bit complicated, but essentially, it depends on which processor your computer uses, and, to some extent, which version of Mac OS X you have installed.  As a rule of thumb, in order for you to run 64-bit applications, the following must be true:

1. Your Mac is 6 years old or newer, you probably have an Intel Core 2 Duo processor or and Intel Xenon processor, which can run 64-bit applications.
2. You must be running OS X 10.6.x, Snow Leopard, or newer as well.

Why do you care? For more on that, read Why is 64 bit better? To know for sure where you stand, below is a chart, courtesy of Apple's support documentation that describes which processor supports 32 and/or 64 bit.  

To figure out which processor (and OS) you are running, do the following:

1. Go to the Apple Menu in the upper left corner of your screen and select "About This Mac" from the menu.

2. Look for the processor name and description of your processor