The question is badly worded. For starters, you have the correct article. But it speaks of entrances to the working space, not to the room. This has been the subject of some debate. What I mean is that I could, if I wished, say that the correct answer to the question is "none," since the article does not tell us about doors leading out of the room.
I suspect that the question's author wants you to say "one entrance." The reasoning is that that article gives criteria for needing a second entrance, and you don't meet those criteria, so only a single entrance is needed.
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