**Core Concept**
The question tests the student's knowledge of the anatomy of the brachial plexus, a complex network of nerves that supply the arm. The brachial plexus is formed by the ventral rami of C5 to T1 spinal nerves and has five main branches: the superior, middle, inferior, medial, and lateral cords.

**Why the Correct Answer is Right**
The largest branch of the brachial plexus is the posterior cord, which is formed by the union of the upper, middle, and lower parts of the lateral cord and the posterior cord itself. The posterior cord gives rise to the axillary and radial nerves, which are responsible for innervating the muscles of the shoulder and arm. The posterior cord is the largest and most posterior branch of the brachial plexus due to its extensive contribution to the innervation of the arm.

**Why Each Wrong Option is Incorrect**
**Option A:** The superior trunk is not the largest branch of the brachial plexus, although it is a significant contributor to the innervation of the arm.
**Option B:** The middle trunk is smaller than the posterior cord and is primarily responsible for innervating the biceps and brachialis muscles.
**Option C:** The inferior trunk is the smallest of the three trunks and is responsible for innervating the muscles of the forearm and hand.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that the brachial plexus is formed by the ventral rami of C5 to T1 spinal nerves, and its branches are responsible for innervating the muscles of the arm, shoulder, and forearm.

**Correct Answer:** D. Posterior cord