Q: Shuts off when tank has less than qtr. of a tank and sputters when I "step on it on 2008 Chevrolet Tahoe

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Rpm are not steady when stopped at a light.
(1) Answer
replace the fuel filter. If this doesn't cure it, then the fuel pump is going out. With less than a 1/4 tank, the weight of the fuel isn't enough to keep the pump running at the proper pressure. Have the fuel system pressure checked.