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A small library has books on twenty different subjects including, most prominently, history. One afternoon, a librarian arbitrarily picks up 100 books for reshelving from among the books returned that day. All the books returned that day were borrowed during the past three weeks. Are fewer than 20 percent of the books the librarian picks up on history?
We need to determine if fewer than 20% of the 100 books picked by the librarian are history books. Since the librarian picks exactly 100 books, this translates to: Are there fewer than 20 history books among the 100 picked?
This is a yes/no question. We need a definitive answer:
For sufficiency, we need information that allows us to answer this question with certainty.
Statement 1: "Fewer than 20% of the books in the library are on history."
This might seem helpful, but here's the crucial insight: the librarian isn't picking from all library books—she's picking from books that were returned that day, which were all borrowed in the past 3 weeks.
The overall library composition tells us nothing definitive about recent borrowing patterns. Let's see why:
Scenario A - History is trending:
Scenario B - History is unpopular lately:
Since we can get different answers depending on borrowing patterns, Statement 1 is NOT sufficient.
[STOP - Not Sufficient!] This eliminates choices A and D.
Forget Statement 1. We're analyzing Statement 2 independently.
Statement 2: "During the past three weeks, exactly 15 books on history were borrowed from the library."
This statement provides a powerful constraint:
Since the librarian picks from the returned books, and there are at most 15 history books available to pick, it's impossible for her to pick 20 or more history books. Even if she picked every single history book that was returned, she'd get at most 15.
Since \(15 < 20\), we can definitively answer: YES, fewer than 20% of the picked books are history books.
[STOP - Sufficient!] Statement 2 alone is sufficient.
Statement 2 alone provides a definitive YES answer by establishing an absolute upper limit: at most 15 history books could be picked, which is less than 20.
Answer Choice B: Statement 2 alone is sufficient, but Statement 1 alone is not sufficient.