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# A small library has books on twenty different subjects including, most

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Re: A small library has books on twenty different subjects including, most [#permalink]

GMATCoachBen
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?

(1) Fewer than 20 percent of the books in the library are on history.

(2) During the past three weeks, exactly 15 books on history were borrowed from the library.­­
­Question: Are fewer than 20 percent of the books the librarian picks up on history?

For this to be true the subject-wise composition of books to reshelve is required

Statement 1: Fewer than 20 percent of the books in the library are on history.

Total percentage of history books in library does NOT confirm their percentage in 100 books to be reshelved hence

NOT SUFFICIENT

Statement 2: During the past three weeks, exactly 15 books on history were borrowed from the library.­­

i.e. out of total 100 books to be reshelved, the history books can NOT exceed 15 which is 15% hence the percentage of history books to be reshelved is definitely less than 20% hence
SUFFICIENT

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Re: A small library has books on twenty different subjects including, most [#permalink]
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100 books among the books borrowed during the past 3 weeks are picked up

­Statement 1: Fewer than 20 percent of the books in the library are on history.

Suppose that there are 1000 books in the library and 400 books were borrowed during the past 3 weeks

Fewer than 20% of the books in the library are on history ==> Suppose there were 190 books (19%)

It could have been that
(i) all 100 books which were picked up are history ==> 100% > 20%
or
(2) 19 out of the 100 books which were picked up were on history => 19% < 20%

==> Not sufficient

Statement 2: During the past three weeks, exactly 15 books on history were borrowed from the library.

Even if all 15 history books were among the 100 books which are picked up
% = $$\frac{15}{100}$$ < 20%

==> Sufficient

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A small library has books on twenty different subjects including, most [#permalink]
GMATCoachBen
Video solution here:

­
In principle, you don’t even need to think too much. If a maximum of 15 history books were returned in the last three weeks, and from these books the librarian selects 100 books at random, then in a sample of 100 books there will be a maximum of 15 history books. This is 15 percent, which is less than 20 percent. And many are ready to order case study writing services for this; they use https://ca.edubirdie.com/case-study-writing-services for this. I myself like to read something about history. For me, this is the best genre, it is less fictitious, and in some places only embellished.

­
­Subscribed to you. Cool! Thank you!­
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Re: A small library has books on twenty different subjects including, most [#permalink]
Statement 1. We don't know how many total books are in the library. insufficient BCE

Statement 2. Out of 100 books being re-shelved, the maximum amount can be 15 history books. 15 is 15% of 100, therefore there are fewer than 20%. Sufficient B is correct
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Re: A small library has books on twenty different subjects including, most [#permalink]
How do we know the books referenced in statement 2 were even returned to the library? I believe this is leads to E being correct.
Re: A small library has books on twenty different subjects including, most [#permalink]
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