How can you distinguish between these two minerals by using a piece of paper, a steel knife and a glass bottle?
Quartz, it is found in felsic igneous rocks(even after years of geology courses I sometimes confuse mafic and felsic, I think I have it right because my memory tool is felSIc, si for silicate minerals. The clay minerals weather away leaving the quartz which is then eroded, as it is transported it weathers and eventually becomes small grains of sand. It is not completely weathered away because it has a pretty high hardness(7, 10 is the max with diamonds at 9) and it is not broken down by rain etc like your micas, feldspars and the other clay minerals which make up felsic rocks.
The bright white sands found in tropical and subtropical coastal settings are eroded limestone and may contain coral and shell fragments in addition to other organic or organically derived fragmental material.
Quartz - it's everywhere. I would say it is not so much the toughness of the mineral that determines what makes a beach, but rather the quantity of it. Pretty much anything that forms in great quantities next to a large body of water will become sand. Most sand grains in the Bahamas, for instance, are made of calcite. Not really a tough mineral as it dissolves in acid, but there is so much that the beaches are made of it. In Hawaii basalt is everywhere, so that is what the beach is made of. Sand in Florida is mostly quartz, because that is what lasts the longest when it gets deposited here.
