## Core Concept
The child's symptoms, including aggressive behavior, poor concentration, joint pain, reduced urinary output, and self-mutilation, suggest a systemic disorder that affects multiple systems in the body. This combination of symptoms is characteristic of **Lesch-Nyhan syndrome**, a genetic disorder caused by a deficiency of a specific enzyme involved in purine metabolism.

## Why the Correct Answer is Right
The correct answer, **HGPRT (Hypoxanthine-Guanine Phosphoribosyltransferase)**, is an enzyme crucial for the recycling of purines. A deficiency in HGPRT leads to an overproduction of uric acid, which causes the renal symptoms (reduced urinary output), and to the accumulation of toxic substances that affect the central nervous system, leading to behavioral problems and self-mutilation. The joint pain could be related to uric acid crystals depositing in joints.

## Why Each Wrong Option is Incorrect
* **Option A:** This option is incorrect because it does not specify an enzyme related to the described symptoms. Without a clear relation to purine metabolism or the symptoms presented, it cannot be considered a viable option.
* **Option B:** Similarly, this option lacks specificity and does not directly relate to the known causes of Lesch-Nyhan syndrome or the symptoms described.
* **Option D:** This option is incorrect because it does not correspond to the enzyme deficiency associated with Lesch-Nyhan syndrome.

## Clinical Pearl / High-Yield Fact
A key clinical pearl is that **Lesch-Nyhan syndrome** is characterized by the classic triad of **self-mutilation**, **aggressive behavior**, and **renal impairment** due to uric acid overproduction. Early recognition of these symptoms can lead to genetic testing for HGPRT deficiency.

## Correct Answer: C. HGPRT (Hypoxanthine-Guanine Phosphoribosyltransferase).