We can do this test using utility named MEMTEST.Various other utilities are also available for this purpose.Reputed memory makers like corsair,crucial etc reccoment MEMTEST to test their products
1.Download MEMTEST
Download MEMTEST and create the bootable media.Decide whether you want to download the ISO image file to create a CD/DVD or if you want to download auto installer for USB keys to create a USB flash drive.
2.Create a MEMTEST bootable media
If you want to create a MEMTEST CD/DVD,unzip the downloaded ISO and burn it to create a bootable CD/DVD.In windows 7 simply right click and select "Burn disc image" and follow directions.
If you want to create a bootable USB flash drive run the auto installer and follow the directions.Remember that the installation will delete all files in the drive
3.Run MEMTEST
Start your computer with the bootable media inserted and test will begin automatically.A successful test will complete with out any errors .Afailed test will report errors in the error column and you will see lot of red blocks.
If your RAM fails MEMTEST ,that should be enough to most companies to approva a replacement.Remember that a failed MEMTEST can also be indication of problems with your processor ,mother board or misconfigured RAM.
