**Core Concept**
The question is testing the knowledge of screening tests for diabetes, specifically focusing on sensitivity, which is the ability of a test to correctly identify those with the disease. In diabetes screening, sensitivity is crucial to avoid missing cases. Various tests are used to screen for diabetes, including fasting plasma glucose (FPG), oral glucose tolerance test (OGTT), and hemoglobin A1c (HbA1c).

**Why the Correct Answer is Right**
The correct answer is the OGTT because it has the highest sensitivity among the screening tests for diabetes. This is due to its ability to measure the body's ability to regulate blood sugar levels after consuming a glucose load. The OGTT is particularly useful in diagnosing gestational diabetes and in patients with symptoms of diabetes but normal FPG levels. The OGTT measures the body's insulin resistance and insulin secretion, providing a more comprehensive assessment of glucose metabolism.

**Why Each Wrong Option is Incorrect**
**Option A:** Fasting plasma glucose (FPG) has a high specificity but lower sensitivity compared to OGTT, especially in diagnosing gestational diabetes or in patients with impaired glucose tolerance.
**Option B:** Hemoglobin A1c (HbA1c) is a useful screening test but has a lower sensitivity than OGTT, particularly in patients with hemoglobinopathies or those with a short duration of hyperglycemia.
**Option C:** Random plasma glucose is not a suitable screening test for diabetes due to its low sensitivity and specificity.

**Clinical Pearl / High-Yield Fact**
The OGTT is a valuable screening tool for diabetes, especially in high-risk populations such as pregnant women, obese individuals, and those with a family history of diabetes.

**Correct Answer: C. Oral glucose tolerance test.**