does the wattage requirement stack?

Solution
Don't confuse the "recommended power supply" wattage for a GPU with the power the GPU actually consumes. That recommended wattage is the manufacturer's guess at what you ought to get without know what other components you have, or the quality of the PSU.
Don't confuse the "recommended power supply" wattage for a GPU with the power the GPU actually consumes. That recommended wattage is the manufacturer's guess at what you ought to get without know what other components you have, or the quality of the PSU.
 
Solution