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Yes theoretically you could but its not advisable. I'll try to explain why:
First it depends a little on the type of RAM you have and your motherboard. Sometimes mixing RAM doesnt work out too well (especially in dual channel mode).
Then the thing is your current RAM has more than likely slower timings - could be CL2.5 (something like 2.5-4-4-8) or even CL3 (if it was very "affordable" value RAM.
Now when you'd mix the RAM the new fast CL2 modules would be forced to run at the slower timings of the old RAM. The difference between CL3 and CL2 is quite considerable (up to 30% performance difference). And seeing that performance gain by using more than 1GB of RAM is usually not that big (depending on the application) you will lose more if you make your new RAM really slow than you can gain by going from 1Gb to 1.5.
Of course you can always run some benchmarks and games after you have it so you see what i mean.
If i was you i'd test the old RAM stick by stick (or in pairs of 2) - and if one is bad then sell the other 3. (or 2 - however many turn out to be ok)
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