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 .
Official Guide question
Answer: D
For a certain city's library, the average cost
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 83
- Joined: Mon Jul 24, 2017 8:16 am
- Followed by:1 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Given:jjjinapinch 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 .
Official Guide question
Answer: D
1. Average cost of each book = $28
2. Funds received per year = $15000
3. Bonus per month = $2000 if the number of booked checked out in a year > 5000.
Statement 1:
Cost of purchasing books = (50*12)*28 = $16800
Since the library received enough money from the city to cover this cost, the funds received must be at least $16800.
Fixed sum received = $15000 < $16800, thus to meet out an additional 16800 - 15000 = 1800, the library must have received the bonus. The answer is yes.
Statement 2:
Since the lowest number of items checked out in one month was 459, the library must have checked out at least 459*12 = 5508 books > 5000 books (number of books eligible to get the bonus). Thus, the library must have received the bonus. The answer is yes.
The correct answer: D
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Singapore | London | Dubai | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
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.jjjinapinch 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 .
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Hi All,
We're told that 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 and 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. We're asked if the library received the bonus last year. This is a YES/NO question and can be solved with some Arithmetic and 'rounding.'
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.
With the information in Fact 1, we know that the library purchased (12)(50) = 600 books last year. If we 'round down' $28 to $25 (which would make the following calculation a bit easier to deal with), then the cost of those 600 books would be (600)($25) = $15,000 exactly. Since $28 is more than $25, we know that the actual cost of those books was GREATER than $15,000, so the library had to have spent MORE than the $15,000 it was initially given by the city. That extra money - whatever the actual total is - had to have come from the 'bonus', so the answer to the question can only be YES.
Fact 1 is SUFFICIENT
2) The lowest number of items checked out in one month was 459.
Here, if we 'round down' to 450 - and we assume that 450 books were checked out each month, then the total for the year would be (12)(450) = (6)(900) = 5400. Since 459 is GREATER than 450, then we know that the actual number of books checked out for the year would be GREATER than 5400. That number - whatever it actually is - would end up earning the library the bonus, so the answer to the question can only be YES.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that 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 and 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. We're asked if the library received the bonus last year. This is a YES/NO question and can be solved with some Arithmetic and 'rounding.'
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.
With the information in Fact 1, we know that the library purchased (12)(50) = 600 books last year. If we 'round down' $28 to $25 (which would make the following calculation a bit easier to deal with), then the cost of those 600 books would be (600)($25) = $15,000 exactly. Since $28 is more than $25, we know that the actual cost of those books was GREATER than $15,000, so the library had to have spent MORE than the $15,000 it was initially given by the city. That extra money - whatever the actual total is - had to have come from the 'bonus', so the answer to the question can only be YES.
Fact 1 is SUFFICIENT
2) The lowest number of items checked out in one month was 459.
Here, if we 'round down' to 450 - and we assume that 450 books were checked out each month, then the total for the year would be (12)(450) = (6)(900) = 5400. Since 459 is GREATER than 450, then we know that the actual number of books checked out for the year would be GREATER than 5400. That number - whatever it actually is - would end up earning the library the bonus, so the answer to the question can only be YES.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich