The specification of my system is HP Pavilion p2-1256il Desktop PC

 Processor : Intel Core i3 2120T
 Motherboard : IPXSB-DM (Cork2)

 Memory

 •Amount: 2 GB
 •Speed: PC3-12800 MB/sec (runs as PC3-10600 in this system)
 •Type: DDR3-1600
Memory upgrade information As Given in the Support Page:  
 • Dual channel memory architecture
 •Two 240-pin DDR3 UDIMM sockets
 •Supports DDR3 UDIMMs
 •PC3-8500 (DDR3-1066)
 •PC3-10600 (DDR3-1333)
 •PC3-12800 (DDR3-1600 with Ivy Bridge processors)
 •Non-ECC memory only, unbuffered
 •Supports up to 16 GB on 64-bit systems (with 8 GB UDIMMs)
 Will it support Any of the following RAM:
 G.SKILL 4GB X 1 DDR3 1600MHZ CL9 RIPJAWS X
 Link : http://goo.gl/1Q2Ruk
 Corsair CMZ4GX3M1A1600C9 Vengeance 4GB Single Module DDR3 Memory Kit
 Link : http://goo.gl/IfSK5q
 And if possible say which is better .
 PLEASE HELP ME
 P E A C E I'd check out your other RAM stick the 2GB stick to see if its a 1600, it might just be a 1333mhz fsb stick. I like to match the FSB on RAM especially when mixing memory. You will not get dual-channel memory with a size pairing mismatch, but you will get the 6GB. I prefer Corsair over G-Skill.

You mentioned its a 1600 running at 1333. I'd double check on this by inspecting the memory stick itself.He would be better off using 2 matched stiks and taking it to 8G ...instead of mis-matched 6G...I agree that a mismatch of size is not the best, however PERFORMANCE impact is very small in single channel vs dual channel. Its like only a 5% loss of performance hit last I read to run single channel. If money is tight and they dont mind a 5% performance hit to the memory it will probably work out just fine as long as both RAM sticks play well TOGETHER. The performance benefit of more memory would likely far outweigh the 5% performance hit as for 2GB of RAM is really tight for OS Windows 7 or newer and especially if any modern gaming or heavy multitasking is to be involved. There should be a great reduction in paging to hard drive which will make the system feel more responsive and less laggy.

If they can afford a matched pair of 4GB sticks to get 8GB in dual channel that would be best, however is the extra 2GB memory and 5% memory performance gain worth the extra money...  I'm cheap and would probably run on 6GB myself and eventually get another 4GB stick down the road from a free dead computer or something if it was my system.   

My wifes system has 3GB RAM all mismatched brands from other dead computers i gutted for good parts, 2 x 1GB and 2 x 512MB DDR2 667Mhz sticks and no problems, other than her system a Core 2 Duo E6600 with Geforce 9800GT 1GB Video Card with a ATA100 160GB HDD running Windows 7 32-bit is starting to show its age with games she plays to where I have had to lower GRAPHIC settings in games to get the frame rate back up and make her happy and stretch the systems LIFE another year or so for a 2007 model computer. Its fortunate that the most complex game is World of Warcraft which performance settings can be reduced greatly in graphics and not look too horrible to maintain 30 fps.