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A
The library was usually empty
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B
There was very high demand for study space during exams
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C
The library was closing down
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D
Students preferred studying at home
Why this is the answer
The clues — extended hours, every seat taken by 8 a.m., students on the floor, and a line at the door — all point to very high demand for study space during finals. The passage doesn't state this directly, but the crowded conditions clearly support it. The other options are contradicted (usually empty, prefer home) or unsupported (closing down). Inference questions ask you to combine the described details into a reasonable conclusion: the overcrowding indicates intense demand for places to study during exams.
Source: ASVAB Paragraph Comprehension — Inference