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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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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  [#permalink]

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New post 17 Nov 2017, 12:41
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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  [#permalink]

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New post Updated on: 23 Jun 2017, 19:34
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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

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  [#permalink]

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New post 22 Jun 2017, 20:55
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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, 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, 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 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  [#permalink]

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New post 11 Oct 2017, 01:27
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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 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  [#permalink]

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New post 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  [#permalink]

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New post 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  [#permalink]

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New post 29 Jul 2019, 04:36
What put me off in this question was St 1. St 2 can be solved using worst case scenario method.

The question explicitly says that the bonus is given if the total number of items checked out over the course of the year exceeds 5,000.

1) In St1, we do not know whether the library received the bonus. What if the fund of 15,000 dollars was increased this year to cover the cost?

2) Also, since in question statement, the condition of providing bonus is explicitly mentioned, how can we just assume that the bonus was provided in St 1 without even knowing the number of items checked out?

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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 30 Jul 2019, 02:34
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578vishnu wrote:
What put me off in this question was St 1. St 2 can be solved using worst case scenario method.

The question explicitly says that the bonus is given if the total number of items checked out over the course of the year exceeds 5,000.

1) In St1, we do not know whether the library received the bonus. What if the fund of 15,000 dollars was increased this year to cover the cost?

2) Also, since in question statement, the condition of providing bonus is explicitly mentioned, how can we just assume that the bonus was provided in St 1 without even knowing the number of items checked out?

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As per stmnt 1, the total money spent on buying the books during the year = 50*12 *28 = 16,800
We are given that the library received enough money from the city to cover this cost. So it received at least $16,800 from the city. But the city gives only $15,000 per year (given in the question). A bonus is given only if more than 5000 books are checked out. Since the city gave $16,800, the city must have given the bonus 2000. So more than 5000 books must have been checked out.
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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 05 Aug 2019, 19:12
578vishnu wrote:
What put me off in this question was St 1. St 2 can be solved using worst case scenario method.

The question explicitly says that the bonus is given if the total number of items checked out over the course of the year exceeds 5,000.

1) In St1, we do not know whether the library received the bonus. What if the fund of 15,000 dollars was increased this year to cover the cost?

2) Also, since in question statement, the condition of providing bonus is explicitly mentioned, how can we just assume that the bonus was provided in St 1 without even knowing the number of items checked out?

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1) For statement 1, we need to figure out how many books were purchased and how much they cost. Since 50 x 12 = 600 books were purchased and each book cost $28, the total cost was $16,800. There is no way the library can spend this much money unless they received the bonus. The fund of 15,000 is the same each year. It won’t increase; any extra money is from the bonus.

2) Because statement 1 states that “[the library] received enough money from the city to cover this cost,” which implies they did receive the bonus. Again, they spent $16,800 on books, but the regular amount they received is $15,000. So they must also received $2000 bonus in order to have $17,000 and spend $16,800 on books.
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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 23 Aug 2019, 03:44
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 .


Responding to a pm:

Quote:
i am not able to understand this question, it is mentioned in the question stem that the library receives bonus only if the total number of items checked out over the course of the year exceeds 5,000.
From statement 1 we know that the number of new books purchased were 600, which is less than 5000, i stopped solving further after i knew that number of new books purchased was 600.
is the number of new books purchased different from the total number of items purchases, should i not consider items equivalent to books.
Please help me understand this.


We are talking about a library. People check out books from it and then return them after a few days. The library's stock doesn't dwindle. Then the library may buy some new books which increases its stock. But it only rents out books.
The library gets a bonus if the total number of items checked out (and eventually returned) over the course of the year exceeds 5,000. The purchase of new books has nothing to do with this number. It just tells us the money the library spent in increasing its stock.
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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 01 Sep 2019, 22:33
poor verbiage question.

st2:
(2) The lowest number of items checked out in one month was 459 .

The correct ans for this question is option D. I would have arrived at the correct answer if not for ambiguity of statement 2.

I think the more appropriate statement would be.

The lowest number of items checked out in any month was 459.
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Re: For a certain city's library, the average cost of purchasing each new   [#permalink] 01 Sep 2019, 22:33
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