Avast Antivirus Free will use around 20 MB of RAM
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Avast Internet Security will use around 40 MB of RAM
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Avast Internet Security comes with more layers of protection (eg: Avast Firewall, Avast Safe Zone) so it's to be expected to use a little more RAM and CPU than the Free version which is more basic. With that said, the Internet Security version of Avast should offer a better protection..
Now, here are the results from the latest Performance Test (May 2014) from Av-Comparatives:
http://www.av-comparatives.org/wp-content/uploads/2014/06/avc_per_201405_en.pdf just to give you an idea on how Avast will stack up against the competition.
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