**Core Concept**
The question is testing the student's understanding of the pathophysiology of familial hypercholesterolemia (FH), a genetic disorder characterized by elevated low-density lipoprotein (LDL) cholesterol levels due to impaired LDL receptor function.

**Why the Correct Answer is Right**
The correct answer is related to the LDL receptor, which plays a crucial role in removing LDL cholesterol from the bloodstream. A mutation in the LDL receptor gene (LDLR) leads to reduced or dysfunctional receptors, resulting in increased levels of LDL cholesterol in the blood. This is consistent with the patient's presentation of elevated cholesterol levels and a family history of premature cardiovascular disease.

**Why Each Wrong Option is Incorrect**
* **Option A:** Apolipoprotein B (ApoB) is a component of LDL particles, but a mutation in ApoB would primarily affect the secretion of very-low-density lipoproteins (VLDL) rather than LDL receptor function.
* **Option B:** HMG-CoA reductase is the rate-limiting enzyme in cholesterol synthesis, but mutations in this gene would lead to increased cholesterol levels due to overproduction, rather than impaired clearance.
* **Option C:** PCSK9 (proprotein convertase subtilisin/kexin type 9) is involved in the degradation of LDL receptors, but mutations in PCSK9 would lead to increased LDL receptor activity, not decreased activity.

**Clinical Pearl / High-Yield Fact**
Familial hypercholesterolemia is a heterozygous disorder, meaning that patients have one normal and one mutated allele of the LDLR gene. Homozygous patients with two mutated alleles have more severe elevation of LDL cholesterol and often present with cardiovascular disease in childhood.

**Correct Answer:** C.