Final answer:
Elevated vanillylmandelic acid (VMA) urinary levels are most specifically related to neuroblastoma, as VMA is a breakdown product of catecholamines, which are often overproduced by neuroblastomas.
Step-by-step explanation:
A 1-year-old child with suspected neuroblastoma would most specifically have elevated levels of vanillylmandelic acid (VMA) in the urine. This metabolite is a breakdown product of catecholamines, which are often produced in excess by neuroblastomas. In contrast, a positive Babinski's sign would be more indicative of an upper motor neuron lesion rather than specifically to neuroblastoma. The presence of blast cells in the bone marrow could suggest a hematological malignancy rather than neuroblastoma. Projectile vomiting is a common sign of increased intracranial pressure, which may or may not be related to neuroblastoma. Therefore, elevated VMA is the finding most specifically associated with neuroblastoma.