This is a classic style of Oxbridge interview question, where the candidate is presented with a question on a topic they won't have seen before, and is expected to work logically using the information provided by the tutor.
The final answer is a tumour of the pituitary gland. The optic nerves decussate above the pituitary gland, so a tumour will expand and impinge on the nerve, causing the loss of peripheral but not central vision.
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