heres a little trick I figured out for hard starting atvs that seem to run but shut down and sputter out. If your having Backfiring through the carb, spitting gas out through the carb it maybe a bad intake valve not seating properly. To test this Pull spark plug out, move piston to TDC on compression stroke, Take some compressed air with a air nozzle in spark plug hole, make sure you can seal it to the hole so no air can escape. apply the air and listen for air escaping through the carb or the exhaust valves. that will determine if you have a bad valve. Best way to check for bad valves.