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

Question

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.

(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.

egmat · Accepted Answer

Here is a  detailed video solution  for this interesting question.
See how this question can be solved in the test environment using " Owning the Dataset " approach.

https://www.youtube.com/watch?v=wzPUvczvrYc

Let us know if you have any questions.

GMATCoachBen · Answer

Video solution here:

https://www.youtube.com/watch?v=N2G2VbVesQ8

GMATinsight · Answer

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

Answer: Option B

Gemmie · Answer

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

Answer is B

Apk641 · Answer

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

aliddle22 · Answer

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.

Bunuel · Answer

It doesn't matter whether those specific books were returned. What we know is that the 100 books picked are from those borrowed during the past three weeks. Additionally, statement (2) tells us that exactly 15 books on history were borrowed in that time. Even if all of those books were returned and included in the sample, the percentage of history books in the 100 picked would be 15%, which is still less than 20%. Therefore, the answer to whether fewer than 20 percent of the books the librarian picks up are on history is YES.

minionbaba · Answer

Let's understand first what is SUFFICENT in the question: Number of history books picked out of 100 is less than 20% i.e. 19 or fewer -- If answer to this statement is YES; than the statement is sufficient.

Scenarios:

1. All the 15 History books borrowed during the last 3 weeks (& these are the only history books borrowed during last 3 weeks) were not returned & hence not included in 100 book, that means YES less than 20% of the books are on History -- Therefore, sufficient

2. All are returned, but none are picked up in that random lot of 100 books -- That means YES less than less 20% of the books are on History -- Therefore, sufficient

3. All are returned AND all are picked up in that random lot of 100 books i.e. 15 out of 100 are History books -- That means YES less than 20% of the books are on History -- Therefore, sufficient

Hence answer is Option B.

Shahp7 · Answer

I’m just wondering why no one ever mentions the possibility that **zero** history books were returned. When it says “fewer than 20% of the history books were returned,” it doesn’t necessarily mean *none* — it likely means *at least one*, since we’re dealing with whole numbers. But the GMAT seems to have its own internal logic that I have to somehow guess and follow, which feels unfair. After all, the statement doesn’t even specify that the books had to be returned within three weeks of being borrowed. You know what I mean? To me, answer would be E, because form all the statements above we cannot specify which is the correct answer logically, not mathematically

Bunuel · Answer

The stem already ties timing: all 100 returned today were borrowed in the past three weeks. Statement 2 fixes an absolute cap of 15 history books in that entire 3-week pool. The 100 come from that pool, so history among the 100 is at most 15, i.e., at most 15%. If zero history books were returned, it is 0%. Either way, the answer to “fewer than 20%?” is always Yes. Statement 2 is sufficient. Answer B.

Usernamevisible · Answer

Hi, I have a reading-related doubt about this question.

The stem says:

> "One afternoon, a librarian arbitrarily picks up 100 books for reshelving from among the books returned that day."

But the actual question asks:

> "Are fewer than 20 percent of the books the librarian picks up on history?"

How do we know that "the books the librarian picks up" still refers to the same 100 books picked from the returned books?

My confusion is that the question doesn't explicitly repeat "from among the books returned that day." Could "the books the librarian picks up" be interpreted as books picked from the entire library instead? What grammatical rule or reading principle tells us that it refers back to the previously defined group rather than introducing a new one?

manupoonia · Answer

I think it's just an assumption at this point, and it has become standard. Yeah, I understand what you mean, but yeah, I think this has just become an unsaid assumption.

egmat · Answer

Hi Usernamevisible,

This is a sharp reading question, and the good news is the stem leaves no ambiguity here.

The key is the phrase  "the books the librarian picks up."  There is only  one  act of picking up described anywhere in the stem: the librarian "arbitrarily picks up  100  books for reshelving from among the books returned that day." So when the question later says "the books the librarian picks up," it can only be pointing back to that exact action - the same  100  books.

The reading principle:  a  definite  noun phrase (" the  books the librarian picks up") refers to something already introduced in the text, not to a brand-new group. If the question wanted a different set - say, books drawn from the whole library - it would have to  define  that new act of picking (e.g., "if the librarian instead picked  100  books from the entire collection"). It never does. There is no second picking event to attach the phrase to, so it defaults to the one that was already set up.

That's why every solution in the thread treats the  100  as coming from the returned/borrowed pile - and why Statement ( 2 ) works: the  100  are a subset of the past-three-weeks borrows, only  15  of which are history, so at most  15  of the  100  can be history. That's under  20% .

A quick everyday parallel makes the grammar feel obvious:

"A shopper grabs  5  apples from the discount bin. Are  the apples the shopper grabs  ripe?"

Nobody reads that second sentence as "apples from anywhere in the store" - it's clearly the same  5  from the bin. Same mechanism here:  "the" locks the phrase onto the group already defined.

Answer: B

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

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

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