I have experienced the same problem. It worked ok at the shop after I fixed it at home for half an hour, it started making noise and at a sudden..it went quiet and dead!!!!
Used AC's are not measured by their ability of cooling..there is also the mechanics and electricity. Cooling is a part and they cheat by filling some gas and spraying WD40 to clear the rust.

My advise when buying a used AC, firstly look for the Brand that is on "High Demand" in the market..I noticed General is the best. Secondly ask for an inspection by a technician and don't trust the sellers. You can inspect yourself by checking the interior for welding signs which means that the compressor has been replaced!! Otherwise take off the doubts by saving some pennies and buy a new one!!!