This is a complete-the-passage item. The blank follows "The director's conclusion is questionable, however, because," so the credited choice must supply a reason the director's conclusion fails. First pin down that conclusion precisely: the longer evening hours brought in residents "who had not been using the library at all," that is, brand-new users. The only evidence offered is that weeknight visits rose 22%. The gap is that a rise in the number of weeknight visits is not the same as a rise in the number of distinct people using the library. The extra visits could come from people who already used the library and simply moved to evenings, in which case the user base did not expand at all.
(A) closes exactly that gap. If most of the additional weeknight visitors had already been visiting regularly at other times, then the evening surge reflects existing patrons shifting when they come, not new residents being reached. That is precisely the reason the new-patron conclusion is doubtful, and it is the credited answer.
(B) is wrong because a neighboring town with no rise in weeknight visits supports the idea that the extended hours caused Brideswell's increase, but it never addresses whether the visitors were new. It runs in the wrong direction for a sentence meant to challenge the director.
(C) is wrong because comparing Brideswell's rise to gains other libraries achieved through weekend programming says nothing about whether Brideswell's own weeknight visitors are new. It changes the subject to a different library and a different program.
(D) is wrong because a slight decline in daytime visits is consistent both with a genuine shift from day to evening and with genuinely new evening users plus an unrelated daytime dip. It does not establish that the weeknight visitors were prior users, so it does not speak to the actual gap.
(E) is wrong because saying the longer hours made visiting more convenient merely restates why visits rose and is fully compatible with the hours attracting new patrons. It supports the director's conclusion rather than casting doubt on it.
On a complete-the-passage item, read the connector first to fix the direction the blank must run, then find the choice that targets the specific gap between the evidence, which shows only that visits went up, and the conclusion, which claims the library reached users who are new.