**Core Concept**
Pulmonary embolism (PE) is a life-threatening condition characterized by the blockage of a pulmonary artery by a blood clot, leading to impaired gas exchange and potentially fatal outcomes. The clinical presentation of PE can vary depending on the size and location of the clot, as well as the patient's overall health status.

**Why the Correct Answer is Right**
The most common symptom of pulmonary embolism is **cough**, which occurs in approximately 50-70% of patients. This symptom is thought to be due to the release of chemical mediators and inflammatory cytokines from the damaged lung tissue, leading to an increase in bronchial secretions and subsequent coughing. Additionally, cough may be exacerbated by the increased pressure within the pulmonary capillaries, causing irritation of the bronchial nerves.

**Why Each Wrong Option is Incorrect**
* **Option A:** **Sudden onset of chest pain** is a common symptom of pulmonary embolism, but it is not the most common. Chest pain in PE is typically sharp and pleuritic, meaning it worsens with deep breathing or coughing.
* **Option B:** **Shortness of breath** is a frequent symptom of PE, but it is not the most common. Dyspnea in PE is often described as a feeling of impending doom or suffocation.
* **Option D:** **Syncope** (fainting) is a less common symptom of pulmonary embolism, occurring in approximately 10-20% of patients. While syncope can occur due to the sudden drop in blood pressure, it is not the most common presenting symptom.

**Clinical Pearl / High-Yield Fact**
The Wells score is a clinical prediction rule for pulmonary embolism, which includes symptoms such as cough, dyspnea, and chest pain, as well as risk factors like recent surgery or trauma. A score of ≥4 suggests a high likelihood of PE.

**Correct Answer: C. Cough**