I am thinking you have an old cracked line somewhere from the tank to the carb, try replacing this first since it is the cheapest. Also try and clean or replace any full tank filter. Look at the
Arctic Cat Parts, Snowmobiles, Atv, Generator Sales at Alpha Sports Center Arctic Cat Arctic Cat Four Wheelers Artic Cat ATV Arctic Cat Portable Generators home page website concerning your model of ski and it will have a diagram of the tank and the lines. This will give you a birds eye view of the lines and where they lie/connect and there path.
Good Luck!