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Yes... It supports up to 16GB (4x4GB), so a 8GB (4x2GB) setup will work. Gateway DX4840-37 Specifications
I have the same chipset and i recently replaced my Kingston 1333Mhz 2x2GB DDR3 10666 with Corsair 1333Mhz 2x4GB DDR3 10666. Will i be able to use all four sticks because they have the same specs or is it best to have the same ones leading to 4x4?