**Core Concept**
The sensory supply to the posterior one-third of the tongue is provided by the glossopharyngeal nerve (cranial nerve IX), which carries taste fibers from the circumvallate papillae and general sensory fibers from the posterior one-third of the tongue.

**Why the Correct Answer is Right**
The glossopharyngeal nerve is responsible for transmitting sensory information from the posterior one-third of the tongue, including taste from the circumvallate papillae and general sensation such as touch, pressure, and temperature. This is mediated by the nerve's general sensory fibers, which terminate in the nucleus of the solitary tract in the medulla oblongata. The glossopharyngeal nerve also provides parasympathetic innervation to the parotid gland, but this is not relevant to the sensory supply of the tongue.

**Why Each Wrong Option is Incorrect**
* **Option A:** The lingual nerve, a branch of the mandibular division of the trigeminal nerve (cranial nerve V), provides general sensory innervation to the anterior two-thirds of the tongue, making it an incorrect choice.
* **Option B:** The vagus nerve (cranial nerve X) provides general sensory innervation to the epiglottis and the larynx, but not to the tongue, making it an incorrect choice.
* **Option C:** The hypoglossal nerve (cranial nerve XII) is a motor nerve that supplies the intrinsic and extrinsic muscles of the tongue, but it does not provide sensory innervation to the tongue, making it an incorrect choice.

**Clinical Pearl / High-Yield Fact**
The glossopharyngeal nerve is also responsible for the gag reflex, which is mediated by the afferent fibers from the posterior one-third of the tongue and the efferent fibers to the pharyngeal muscles. This reflex is an important clinical sign that can be used to assess the integrity of the glossopharyngeal nerve.

**Correct Answer:** C.