Step 1: Lesch-Nyhan syndrome is an X-linked disorder of purine metabolism caused by complete deficiency of hypoxanthine-guanine phosphoribosyltransferase (HGPRT), the key enzyme of the purine salvage pathway.
Step 2: HGPRT normally recycles hypoxanthine and guanine back into nucleotides using PRPP. When it is absent, PRPP is no longer consumed by salvage, so PRPP levels rise and drive the de-novo purine synthesis pathway.
Step 3: Overproduction of purine nucleotides plus unsalvaged bases funnel into uric acid, producing hyperuricemia, gouty arthritis, and urinary stones, along with the classic neurological picture (choreoathetosis, spasticity, self-mutilation). This pins the answer to (d).
Step 4: The other options are pyrimidine or NAD pathway transferases (orotate PRT in pyrimidine synthesis, quinolinate PRT in NAD synthesis) and do not produce this syndrome.