Final answer:
Potassium feldspar cleaves in two directions and can be scratched by olivine. For the group that contains only minerals, halite and olivine fit the criteria as both are pure minerals.
Step-by-step explanation:
To answer the question, What mineral cleaves in two directions and can be scratched by olivine?, it's crucial to understand the characteristics of minerals and how they can be identified. Cleavage is a property of minerals that reflects how they break along certain planes based on their crystal structure. Minerals may exhibit distinct cleavage in one, two, three, or more directions.
In terms of the options given, potassium feldspar (orthoclase) is the correct answer. Potassium feldspar cleaves in two directions at right angles, which is a characteristic feature that helps in its identification. On the other hand, olivine, which has a higher hardness, can scratch minerals with lower hardness. Indeed, potassium feldspar has a lower hardness than olivine, making it possible for olivine to scratch it.
For the second question, which group contains only minerals, the criteria are that all examples given within a group must be minerals. Considering this, the correct answer is group (4) halite and olivine. Both halite and olivine are pure minerals, unlike the other options which include rocks or non-mineral substances such as limestone, quartzite, and coal.