Final answer:
The most common mineral grain in mature clastic sediments is quartz due to its high stability and resistance to weathering.
Step-by-step explanation:
As clastic sediments mature, the mineral grain that becomes most common is quartz. This is because quartz is exceptionally stable and has a high resistance to mechanical and chemical weathering during erosion processes. As mentioned, most sand-size grains in mature sedimentary rocks are indeed quartz, given its durability as compared to other minerals like olivine, plagioclase, and biotite. These other minerals are less stable and tend to break down more quickly into clay minerals or be dissolved during the transportation and weathering process.