## **Core Concept**
The question describes a child with mental retardation and a history of self-mutilation, which are characteristic features of **Lesch-Nyhan syndrome**. This syndrome is a genetic disorder caused by a deficiency of the enzyme **hypoxanthine-guanine phosphoribosyltransferase (HGPRT)**. The condition primarily affects males due to its X-linked recessive inheritance pattern.

## **Why the Correct Answer is Right**
The correct answer, **HGPRT enzyme assay**, is the diagnostic test for Lesch-Nyhan syndrome. This assay measures the activity of the HGPRT enzyme in red blood cells or other tissues. A deficiency in HGPRT enzyme activity confirms the diagnosis of Lesch-Nyhan syndrome. The syndrome is characterized by severe mental retardation, spasticity, and self-mutilating behaviors, such as biting of the fingers or lips.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option is incorrect because it does not specify a test relevant to the diagnosis of Lesch-Nyhan syndrome or similar genetic disorders.
- **Option B:** This option is incorrect as it also does not correspond to a specific diagnostic test for the condition described.
- **Option D:** This option is incorrect because, like options A and B, it does not accurately represent a diagnostic test for Lesch-Nyhan syndrome.

## **Clinical Pearl / High-Yield Fact**
A key clinical pearl is that Lesch-Nyhan syndrome is often associated with **urate overproduction**, leading to **kidney stones** and **gouty arthritis**, in addition to neurological symptoms. Early diagnosis through HGPRT enzyme assay can help in managing the condition and preventing some of its complications.

## **Correct Answer:** . **HGPRT enzyme assay**