A 4-year-old boy of Indian descent presents with orange-colored crystals in his diapers, developmental delay, and involuntary writhing movements. On examination, he has self-inflicted bite wounds on his lips and fingers. Genetic testing reveals a loss-of-function mutation in the HPRT1 gene. The enzyme marked **B** in the purine salvage pathway diagram is deficient. Which of the following best explains the hyperuricemia and gout observed in this patient?