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Yes but you won't get max performance. When running Aperture it usually takes just under a GB on my machine. If you're not running a lot of other apps at the same time it should do ok.
 
Aperture is one of the most heavily demanding RAM programs there is. It eats up RAM like no tomorrow. You can technically "run" the program with 4GB of memory but the way aperture caches images it just loads them all up into RAM. Thus, scrolling through a photo roll of some event can all of the sudden drop your RAM down to 0. Take home point: you can NEVER have enough RAM to meet aperture's requirements.
 
Yep, It'll work. But it will eat all of it, regardless of how much you have.
I'm rocking an older '08 MacBook, it runs it just dandy, but it can easily eat up 6GB + of my 8GB just scrolling around with some RAW photos. But with the SSD and if Aperture is the only intensive app running, you should be fine. I've ran it on 2GB before and it was "OK". Just a little slow.
 
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