Trace the missing molecule.
Ask: what does the stomach uniquely provide for vitamin absorption? Answer: intrinsic factor from parietal cells.
Consequence of gastrectomy.
No stomach → no parietal cells → no intrinsic factor. Which vitamin absolutely needs intrinsic factor to be absorbed in the terminal ileum? Only $Vitamin\ B_{12}$. So removing the stomach selectively cuts off B12 uptake.
Time course explains the clinical need.
Hepatic B12 stores cover roughly 2-4 years, so deficiency (megaloblastic anaemia, glossitis, subacute combined degeneration of the cord) appears late. To prevent this, patients receive lifelong B12 - typically intramuscular, because the IF-dependent oral pathway no longer works.
Screening the distractors against the "needs intrinsic factor?" test:
Vit A - no (fat-soluble, small-bowel absorption).
Vit C - no (water-soluble, small-bowel absorption).
Vit D - no (fat-soluble, bile-dependent, small bowel).
Vit B12 - YES.
Hence the supplement after gastrectomy is Vitamin B12 - Option C.