**Core Concept**
Obesity in association with mental retardation is a characteristic feature of certain genetic disorders that affect body weight regulation and cognitive function. These conditions often involve alterations in genes that regulate appetite, metabolism, and growth.

**Why the Correct Answer is Right**
The correct answer is Prader-Willi syndrome, which is a genetic disorder caused by the deletion of a portion of chromosome 15. This deletion leads to a deficiency of the hormone leptin, which regulates appetite and metabolism. As a result, individuals with Prader-Willi syndrome often experience excessive hunger and hyperphagia, leading to severe obesity. Additionally, they may also have intellectual disability, short stature, and other physical characteristics. The hypothalamus, a region in the brain that controls appetite and metabolism, is also affected in Prader-Willi syndrome.

**Why Each Wrong Option is Incorrect**
* **Option A:** Down syndrome is a genetic disorder that affects cognitive and physical development, but it is not typically associated with obesity.
* **Option B:** Fragile X syndrome is a genetic disorder that causes intellectual disability and behavioral problems, but it is not typically associated with obesity.
* **Option C:** Cretinism is a condition caused by a lack of thyroid hormone, which can lead to growth retardation and intellectual disability, but it is not typically associated with obesity.

**Clinical Pearl / High-Yield Fact**
Prader-Willi syndrome is a genetic disorder that affects approximately 1 in 15,000 to 1 in 30,000 people worldwide, and it is often associated with other medical conditions such as sleep apnea, type 2 diabetes, and osteoporosis.

**Correct Answer: C. Cretinism is a condition caused by a lack of thyroid hormone, which can lead to growth retardation and intellectual disability, but it is not typically associated with obesity.