**Core Concept**
The question requires knowledge of enzymes involved in purine metabolism. Hypoxanthine-guanine phosphoribosyltransferase (HGPRTase) is a crucial enzyme in the salvage pathway of purine metabolism, which recycles purine bases to form nucleotides. A deficiency in this enzyme leads to the accumulation of uric acid and its metabolites, causing a specific genetic disorder.

**Why the Correct Answer is Right**
The child is likely to have Lesch-Nyhan syndrome, a rare genetic disorder caused by a deficiency of the HGPRTase enzyme. This enzyme is necessary for the conversion of hypoxanthine and guanine to their respective monophosphate derivatives, which are then converted to nucleotides. In its absence, uric acid production increases, leading to severe neurological symptoms, gouty arthritis, and renal damage. The HGPRTase deficiency impairs the body's ability to recycle purine bases, resulting in an accumulation of uric acid and its toxic metabolites.

**Why Each Wrong Option is Incorrect**
**Option B:** Adenosine deaminase deficiency is associated with severe combined immunodeficiency (SCID), characterized by a lack of B and T cells, leading to recurrent infections and failure to thrive. This condition is distinct from Lesch-Nyhan syndrome.
**Option C:** Alkaline phosphatase (APRTase) is another enzyme involved in purine metabolism, but its deficiency is associated with a different condition, called APRT deficiency, which leads to kidney stones and gout. However, it is not linked to Lesch-Nyhan syndrome.
**Option D:** Acid maltase deficiency is the cause of Pompe disease, a glycogen storage disorder characterized by the accumulation of glycogen in muscles, leading to muscle weakness, hypertrophy, and cardiomegaly. This condition is unrelated to purine metabolism.

**Clinical Pearl / High-Yield Fact**
Lesch-Nyhan syndrome is an X-linked recessive disorder, meaning it primarily affects males, as they have only one X chromosome. Females can be carriers of the disease but typically do not exhibit symptoms due to the presence of another X chromosome with a normal HGPRTase gene.

**✓ Correct Answer: A. HGPRTase**