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For a certain city's library, the average cost of purchasing each new

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For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 22 Jun 2017, 14:43
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For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year,the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000.Did the library receive the bonus last year ?

(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

(2) The lowest number of items checked out in one month was 459 .
[Reveal] Spoiler: OA

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For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 22 Jun 2017, 18:13
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Statement 1
Total cost of books purchased = 50 × 28 =16800
Total received = 15000
Because 15000 - 16800 = -1800
Statement state that library received enough $ to cover
Therefore, it must have received $2000. = Sufficient
Eliminate: B,C,E

Statement 2:
459 × 12 = 5508 > 5000 = Sufficient

Answer: D

Last edited by Valhalla on 23 Jun 2017, 18:34, edited 1 time in total.

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Re: For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 22 Jun 2017, 19:55
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Stmt 1.
Number of books purchased = 50*12 = 600
Total cost = 600*28 = 16800
Money received from the city = $15000
Since the library received enough money from the city to cover this cost, they must have received the bonus to cover the extra cost (16800 - 15000 = 1800)
Stmt 2.
The lowest number of items checked out in one month was 459. Considering this is the number of items checked out every month, number of items = 459 * 12 = 5508 which is more than the target 5000. So receives bonus.

Either of them is sufficient.
Ans D.

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Re: For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 22 Jun 2017, 20:24
AbdurRakib wrote:
For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year,the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000.Did the library receive the bonus last year ?

(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

(2) The lowest number of items checked out in one month was 459 .


(1):
Total number of books purchased last year \(= 12 * 50 = 600\).
Total cost of the books purchased \(= 600 * $28 = $16,800\).

So, (1) is sufficient to answer the question.

(2):
Lowest number of items bought in one month was \(459\), therefore, the MINIMUM number of books that must have been purchased would be \(11 * 460 = 5,060\), making the total number of books purchased \(= 459 + 5060 = 5,519\). Since the total number of items exceed \(5,000\) the library must have received the \($2,000\) bonus last year.

(2) is also sufficient to answer the question.

Hence, Ans-D.
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For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 22 Jun 2017, 23:35
Valhalla wrote:
Statement 1
Total cost of books purchased = 50 × 28 =16800
Total received = 15000
Because 15000 - 16800 = -1800
Statement state that library received enough $ to cover
Therefore, it must have received $2000. = Sufficient
Eliminate: B,C,E

Statement 2:
459 × 12 = 5508 > 5000 = Sufficient

Answer: E

Valhalla Your analysis is perfect
Since both the statements individually suffice to answer, the answer is D not E
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Re: For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 11 Oct 2017, 00:27
I know this is an Official question, but it is a very poorly written question, especially for a DS. I am sure that is why this question was more than likely a trial/test question that never got used and hint released by GMAC

(2) The lowest number of items checked out in one month was 459 .

I think you are incorrectly assuming this statement states the lowest number of items [to be] checked out in a one month was 459.

Which is different from what the statement states which says simply "checked out"... meaning the library no longer has the book and it's being rented out.
From my understanding, if there is any way you can prove a statement insufficient, then the statement is considered invalid.

So, for example, say John went to this library on January 1 and he himself checked out 459 books and he was the only person to go to the library. And say this library allows books to be checked out for a full year before the due date to be returned. In this case, the library only checked out 459 books the entire year.

Another example, say I went to the library on December 5 and asked for the Official GMAT 2017 book, and the library told me it's "checked out". Does this mean the book was check outed every month from January to December? (12 months total = 12 total check outs) or did someone borrow it in January and still has it (1 total check out).


"The lowest number of items checked out in one month was 459 . " this could mean 459 unique books checked out every month -OR- the library has lent out 459 books (at the least) in any given month, which could be counted twice from past months (for example John checked out 459 books in January and kept the all 459 books till December)

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Re: For a certain city's library, the average cost of purchasing each new [#permalink]

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New post 17 Nov 2017, 11:41
AbdurRakib wrote:
For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year,the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000.Did the library receive the bonus last year ?

(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

(2) The lowest number of items checked out in one month was 459 .


We need to determine whether the library received a bonus of $2,000 last year. Keep in mind that the library will only receive the bonus if the total number of items checked out out last year exceeded 5,000.

Statement One Alone:

The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

Since the library purchased 50 new books each month, it purchased 50 x 12 = 600 books last year. Since each new book cost $28, the total cost of the 600 books last year was 28 x 600 = $16,800. Since we are given that the library received enough money from the city to cover this cost, it must have received the $2,000 bonus in addition to the $15,000 from the city. Statement one alone is sufficient to answer the question.

Statement Two Alone:

The lowest number of items checked out in one month was 459.

Since the lowest number of items checked out in one month was 459, the minimum number of items checked out last year was 459 x 12 = 5,508. Since 5,508 is more than 5,000, the library did receive the $2,000 bonus from the city. Statement two alone is sufficient to answer the question.

Answer: D
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Re: For a certain city's library, the average cost of purchasing each new   [#permalink] 17 Nov 2017, 11:41
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