**Core Concept**
The complaint of numbness and weakness in the left leg and foot in a hypertensive patient suggests a vascular issue affecting the lower limb. The most likely cause is atherosclerotic disease affecting the arteries supplying blood to the lower limb.

**Why the Correct Answer is Right**
The correct answer is related to the occlusion of the **Infrarenal Aorta** or its major branches, specifically the **Common Iliac Artery** or **Superficial Femoral Artery**. These arteries supply blood to the lower limb. Occlusion of these arteries can lead to decreased blood flow to the limb, resulting in numbness, weakness, and pain due to ischemia. In a hypertensive patient, atherosclerosis is a common cause of vascular disease.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **Vertebral Artery** supplies blood to the brain and is not directly related to symptoms in the lower limb.
* **Option B:** The **Renal Artery** supplies blood to the kidneys and is not directly related to symptoms in the lower limb.
* **Option C:** The **Carotid Artery** supplies blood to the brain and is not directly related to symptoms in the lower limb.

**Clinical Pearl / High-Yield Fact**
In patients with lower limb ischemia, a thorough vascular examination is crucial to identify the level and extent of arterial occlusion. This includes assessing the pulses in the lower limb, checking for capillary refill, and evaluating the ankle-brachial index (ABI).

**Correct Answer:** C.