You could mention Avast to them and let them decide. It is free, after all.
RAM doesn't work that way. Nothing does, really. If your CPU is now 2X the rating as before, it doesn't equate to an exact 2x speed-up. Also, if you have more RAM, you may be less likely to turn off background apps since you (think you) have RAM to spare.
Basically, if your computer runs out of RAM, it starts moving stuff from memory to the hard drive and back. Even the fastest modern drives are slower than the slowest modern RAM, so you will feel the impact. More RAM means more stuff in memory before this happens.
So, to simplify an example, if you had 256MB of RAM, and the program neeed 257MB, even a tiny increase in RAM would give an increase in performance. However, you only saved yourself from that 1MB of data swapping, and you might not even notice the performance boost.
If instead, the program needed 513MB, then doubling your RAM to 512MB still leaves a little bit that must get swapped in and out. Now, however, you have almost doubled what can get kept in memory, so that 1MB left over becomes trivial and you will probably feel a huge boost in performance. In fact, since you are measuring RAM vs. hard drive speed, you could even see well over 2x speed up!
There is no hard and fast rule for RAM vs. speed. Many factors are involved. About the only rule there is simply says: get the most RAM you can afford.
p.s. There is also fast RAM vs. normal RAM, etc. But if you are going to get into all that, and want the ultimate 3D gaming PC, you owe it to yourself to do the research yourself and start learning these terms.
p.p.s. Computer experts: yes, my examples are inaccurate, but I think they serve the explanation.