To find out whether the stone is quartzite or not, you should try using a sharp object like a knife etc. on the surface of the stone. If it is real quartzite, it will have a sharp surface but no marks, and if there are marks, they will be very light marks. Or you can leave lemon and vinegar on the surface of quartzite for some time, if it is real quartzite, then its surface will either not be smeared at all or if it will be negligible.