Final answer:
The correct answer is a) Fault-block mountains, which are characterized by steep escarpments and gentle slopes, created by tensional stress and the movement of crustal blocks along faults.
Step-by-step explanation:
The geologic formation that fits the described characteristics, with rock layers breaking into sections with a gentle slope on one side and a steep escarpment on the other, leaving vertical rock faces between the breaks in the blocks, is a) Fault-block mountains.
These mountains are formed by the tensional stress that fractures the Earth's crust, creating blocks which then slide down along normal faults due to gravity. This process results in one side of the block having a steep, often cliff-like face known as an escarpment, and the other side a more gentle slope formed by the tilting of the block.