**Core Concept**
The question is testing the knowledge of pancreatic islet cell tumors, specifically their classification and frequency. Pancreatic islet cell tumors, also known as pancreatic neuroendocrine tumors (PNETs), arise from the islet cells of the pancreas and can be functioning or non-functioning. Functioning tumors produce excess hormones, leading to clinical symptoms.

**Why the Correct Answer is Right**
The most common functioning pancreatic islet cell tumor is the insulinoma. Insulinomas secrete excess insulin, causing hypoglycemia. They typically arise from the beta cells of the islet of Langerhans and can be benign or malignant. The pathophysiology involves the uncontrolled secretion of insulin, leading to low blood glucose levels.

**Why Each Wrong Option is Incorrect**
**Option A:** Gastrinoma is a type of PNET that secretes gastrin, causing peptic ulcers and acid hypersecretion. Although it is a functioning tumor, it is less common than insulinoma.
**Option B:** Glucagonoma is a rare PNET that secretes glucagon, causing hyperglycemia and a characteristic rash. It is even less common than gastrinoma.
**Option C:** Somatostatinoma is a rare PNET that secretes somatostatin, causing diabetes and gallstones. It is the least common of the functioning PNETs.

**Clinical Pearl / High-Yield Fact**
The Whipple procedure (pancreaticoduodenectomy) is often required for the surgical management of pancreatic islet cell tumors, especially if they are large or malignant.

**Correct Answer: A. Insulinoma.**