Answer: The right answer is the B) The apartment is inexpensive and run-down.
Explanation: Just to elaborate a little on the answer, it can also be added that if the apartment "did not exactly beggar description" it could still be somehow describable, but the fact that the place had "that word on the lookout for the mendicancy squad"—a police force that was in charge of arresting homeless people—does suggest that it was run-down. The weekly price for a furnished flat also suggests that it was not very expensive–even when "The Gift of the Magi," from which this excerpt has been taken, was written.