Thanks to one minute of the Earth we know that beach sand mother rock, besides the quartz itself, is (or was?) made of olivine, amphibole and orthoclase. I wonder, what is the name of that rock and where do the 3 annihilated minerals go if only quartz is left?
In only one minute of presentation there isn't time for detailed discussion, so one has to make broad generalizations which, on closer inspection, aren't quite true. It is true that most sand is made of quartz, and that most of this quartz arises from weathered granitic rocks, of which the main minerals are quartz, orthoclase and plagioclase, usually with some mica, quite rarely some amphibole and almost never olivine. In the magma olivine and quartz react to make either amphiboles (if it is a very hydrous melt) or pyroxenes.
It is possible to find a sedimentary rock made of weathered out quartz and feldspar grains. Depending upon the original chemistry the feldspar could be potassium-rich (orthoclase) or sodium-calcium-rich (plagioclase). The resulting sedimentary rock is known as an arkose. Arkose is common in dry areas of eroding granite, such as the dryer parts of sub Saharan Africa. However, it is much more common for the weathering to involve wet erosion - thousands of cycles of rain and sun, hot and cold, in which case the feldspars mostly decompose to clay (many varieties and sub-species).
Olivine is much more characteristic of basic volcanic rocks, especially basalts, which do not weather to yield quartz grains. Another rock type in which olivine is a major component is peridotite. This weathers to yield goethite (a kind of ironstone) and serpentine. Occasionally, if the pyroxene to olivine ratio is sufficiently high, the weathering can yield quartz as a secondary by-product.
Another feature of quartz: Over long periods and especially at high temperatures and/or high pressures, it is very slightly soluble. Not that you would notice. The sand isn't going to dissolve beneath your feet, but every litre of surface water contains a few milligrams of dissolved quartz as silicic acid, which takes part in a whole catalogue of geological processes. In addition, there are many other rocks besides granite which yield quartz grains, including quartzite, weathered pre-existing sandstone, schist, gneiss, and some intermediate rocks (complex chemistry between granite and basalt. Even limestone - rocks that are generally thought of as 'pure' calcium carbonate, generally have a percent or two of insoluble residue, of which quartz is the dominant component.