**Core Concept:** Type 2 Diabetes Mellitus (T2DM) is a chronic disorder characterized by insulin resistance, impaired insulin secretion, and a combination of both. Genetic factors play a significant role in the development of T2DM, with family history being a strong indicator.

**Why the Correct Answer is Right:** In this question, the patient has a positive family history of diabetes mellitus, specifically his grandfather and father both having the disease. Additionally, the patient is not overweight (having a BMI of 20.5), which is a common feature in type 1 diabetes (T1DM) patients. However, the absence of ketonuria is most consistent with T2DM, as T1DM is characterized by the presence of ketonuria in the absence of insulin production.

**Why Each Wrong Option is Incorrect:**

A. Type 1 Diabetes Mellitus (T1DM) is an autoimmune disorder where insulin production is absent. Ketonuria is typically present in T1DM.
B. Ketonuria is also absent in gestational diabetes (GDM), a temporary condition during pregnancy.
C. Type 3 Diabetes Mellitus is not a recognized type of diabetes.
D. Type 4 Diabetes Mellitus is not a recognized type of diabetes.

**Why the Correct Answer is Right:** The presence of a positive family history and absence of ketonuria make T2DM the most likely diagnosis in this scenario.

**Clinical Pearl:** In patients with a positive family history of diabetes, particularly in those with normal weights, T2DM should be considered in the differential diagnosis, as T1DM is more likely in overweight patients with no family history. It is essential for a proper diagnosis and appropriate management of the patient.