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For a certain city's library, the average cost of purchasing each new
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22 Jun 2017, 15:43
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60% (02:12) correct 40% (02:11) wrong based on 821 sessions
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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 .
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Re: For a certain city's library, the average cost of purchasing each new
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17 Nov 2017, 12:41
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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For a certain city's library, the average cost of purchasing each new
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Updated on: 23 Jun 2017, 19:34
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
Originally posted by Valhalla on 22 Jun 2017, 19:13.
Last edited by Valhalla on 23 Jun 2017, 19:34, edited 1 time in total.




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Re: For a certain city's library, the average cost of purchasing each new
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22 Jun 2017, 20:55
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
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22 Jun 2017, 21:24
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, AnsD.
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For a certain city's library, the average cost of purchasing each new
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23 Jun 2017, 00:35
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
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11 Oct 2017, 01:27
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
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04 Nov 2018, 16:23
How can I assume that the lowest numbers of books checked out in ONE month equals the others 11 months lowest numbers?



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Re: For a certain city's library, the average cost of purchasing each new
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22 May 2019, 06:21
ScottTargetTestPrep wrote: 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 The question stem says the "average price" of a book purchased is $28. So for Statement 1, how can we assume that the price of the books purchases was $28? What if the library purchased just 15 books at $1,000 each? Surely then the library wouldn't have been able to meet the target for the bonus. Even if it did purchase more than 50 books, how do we know that the library was able to meet its target of checking out 50 books?



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Re: For a certain city's library, the average cost of purchasing each new
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27 May 2019, 05:19
sterlingarcher123 wrote: ScottTargetTestPrep wrote: 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 The question stem says the "average price" of a book purchased is $28. So for Statement 1, how can we assume that the price of the books purchases was $28? What if the library purchased just 15 books at $1,000 each? Surely then the library wouldn't have been able to meet the target for the bonus. Even if it did purchase more than 50 books, how do we know that the library was able to meet its target of checking out 50 books? On the first question: We can assume each book is the average price since the total cost of the books purchased (regardless of the actual price of each book) is always equal to the average price times the number of books purchased. For example, statement 1 just said an average of 50 books were purchased each month, but the total number of books purchased for the year must be 50 x 12 = 600 even though we don’t know the actual number of books purchased in any particular month. Therefore, even though we don’t know the actual price of each book, we make the same argument: that the library must have spent a total of 600 x 28 = $16,800 on the books. On the second question: We don’t know how many books are actually checked out. But the number of books (5000) required to be checked out to receive the bonus is like a red herring in the problem. Because in statement 1, it says “[the library] received enough money from the city to cover this cost.” Well, the total cost of the books is $16,800, and the routine receipt of $15,000 from the city would not be able to cover the total $16,800 spent unless the library also receive the $2000 bonus.
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Re: For a certain city's library, the average cost of purchasing each new
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