It is currently 17 Oct 2017, 04:48

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Keats Library purchases a number of new books, all in the ca

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

5 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 13

Kudos [?]: 194 [5], given: 2

Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 26 Jun 2013, 05:00
5
This post received
KUDOS
17
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:08) correct 55% (01:21) wrong based on 546 sessions

HideShow timer Statistics

Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%
[Reveal] Spoiler: OA

Kudos [?]: 194 [5], given: 2

Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 13

Kudos [?]: 194 [0], given: 2

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 26 Jun 2013, 05:09
1
This post was
BOOKMARKED
Since the the biography collection of the library amounts to 37.5%

I thought of assuming the actual number to be 75.

and thus the total number of new books would come to 200

Thus the number of books before the purchase would be 200-75 = 125 (Since only the biographies were added)

thus 20% of 125 = 25

therefore the % increase in biographies would be (75-25)/25 = 200% (which is no where in the answer choices....


Can someone plz tell me where am I going wrong.......?????

Kudos [?]: 194 [0], given: 2

1 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 13

Kudos [?]: 194 [1], given: 2

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 26 Jun 2013, 05:13
1
This post received
KUDOS
4
This post was
BOOKMARKED
the OE is attached .....
Attachments

OE.jpg
OE.jpg [ 93.86 KiB | Viewed 12507 times ]

Kudos [?]: 194 [1], given: 2

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128525 [1], given: 12180

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 26 Jun 2013, 05:23
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
manugmat123 wrote:
Since the the biography collection of the library amounts to 37.5%

I thought of assuming the actual number to be 75.

and thus the total number of new books would come to 200

Thus the number of books before the purchase would be 200-75 = 125 (Since only the biographies were added)

thus 20% of 125 = 25

therefore the % increase in biographies would be (75-25)/25 = 200% (which is no where in the answer choices....


Can someone plz tell me where am I going wrong.......?????


The red part is not correct. Out of 75 biographies not all of them were recently purchased.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128525 [1], given: 12180

Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 13

Kudos [?]: 194 [0], given: 2

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 26 Jun 2013, 05:30
ooooooh...

yes yes :-D :-D

thanks a lot

Kudos [?]: 194 [0], given: 2

Intern
Intern
avatar
Joined: 31 Dec 2012
Posts: 10

Kudos [?]: [0], given: 4

WE: Analyst (Consulting)
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 16 Dec 2013, 04:34
Bunuel wrote:
manugmat123 wrote:
Since the the biography collection of the library amounts to 37.5%

I thought of assuming the actual number to be 75.

and thus the total number of new books would come to 200

Thus the number of books before the purchase would be 200-75 = 125 (Since only the biographies were added)

thus 20% of 125 = 25

therefore the % increase in biographies would be (75-25)/25 = 200% (which is no where in the answer choices....


Can someone plz tell me where am I going wrong.......?????


The red part is not correct. Out of 75 biographies not all of them were recently purchased.



Hi,

Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%

Pls throw some more light on this part. "With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books"

I didn't get the answer.

Thanks in advance!!

Regards,

Jasmine

Kudos [?]: [0], given: 4

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128525 [1], given: 12180

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 16 Dec 2013, 04:49
1
This post received
KUDOS
Expert's post
JBGMAT wrote:
Bunuel wrote:
manugmat123 wrote:
Since the the biography collection of the library amounts to 37.5%

I thought of assuming the actual number to be 75.

and thus the total number of new books would come to 200

Thus the number of books before the purchase would be 200-75 = 125 (Since only the biographies were added)

thus 20% of 125 = 25

therefore the % increase in biographies would be (75-25)/25 = 200% (which is no where in the answer choices....


Can someone plz tell me where am I going wrong.......?????


The red part is not correct. Out of 75 biographies not all of them were recently purchased.



Hi,

Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%

Pls throw some more light on this part. "With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books"

I didn't get the answer.

Thanks in advance!!

Regards,

Jasmine


Before the purchase: the biography collection of the library amounted to 20% (1/5 th) of the total number of books. So, before the purchase, 1 out of 5 books were biographies.

After the purchase: the biography collection of the library amounted to 37.5% (3/8 th) of the NEW total number of books. So, after the purchase, 3 out of 8 books were biographies.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128525 [1], given: 12180

Intern
Intern
avatar
Joined: 31 Dec 2012
Posts: 10

Kudos [?]: [0], given: 4

WE: Analyst (Consulting)
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 16 Dec 2013, 06:12
Hi,

Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%

Pls throw some more light on this part. "With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books"

I didn't get the answer.

Thanks in advance!!

Regards,

Jasmine[/quote]

Before the purchase: the biography collection of the library amounted to 20% (1/5 th) of the total number of books. So, before the purchase, 1 out of 5 books were biographies.

After the purchase: the biography collection of the library amounted to 37.5% (3/8 th) of the NEW total number of books. So, after the purchase, 3 out of 8 books were biographies.

Hope it's clear.[/quote]


I am not convinced with the MGMAT's solution presented above. Would be nice if you could present more detailed calculations. Thanks

Kudos [?]: [0], given: 4

Expert Post
5 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128525 [5], given: 12180

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 16 Dec 2013, 07:39
5
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
JBGMAT wrote:
Before the purchase: the biography collection of the library amounted to 20% (1/5 th) of the total number of books. So, before the purchase, 1 out of 5 books were biographies.

After the purchase: the biography collection of the library amounted to 37.5% (3/8 th) of the NEW total number of books. So, after the purchase, 3 out of 8 books were biographies.

Hope it's clear.


I am not convinced with the MGMAT's solution presented above. Would be nice if you could present more detailed calculations. Thanks


Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?
A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%

Say prior to the purchase, there were total of 100 books. We are told that, by that time, the biography collection of the library amounted to 20% (1/5 th) of the total number of books, thus there were 20 biographies.

After that, x biography books were purchased, thus the total number of books became 100+x, out of which 20+x were biographies. Since after the purchase the biography collection of the library amounted to 37.5% (3/8 th) of the NEW total number of book, then \(20+x=\frac{3}{8}*(100+x)\) --> \(x=28\).

So, we have that initially there were 20 biography books and after the purchase there were 20+28=48 biography books --> % increase = \(\frac{difference}{original}*100 = \frac{28}{20}*100=140%\).

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128525 [5], given: 12180

Intern
Intern
avatar
Joined: 31 Dec 2012
Posts: 10

Kudos [?]: [0], given: 4

WE: Analyst (Consulting)
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 16 Dec 2013, 07:45
Yes, its clear now. Many thanks Bunuel.

Regards,

Kudos [?]: [0], given: 4

Intern
Intern
avatar
Joined: 12 Dec 2013
Posts: 25

Kudos [?]: 22 [0], given: 22

GMAT ToolKit User
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 07 Jun 2014, 15:03
The mistake I made on this problem was that I took (37.5% - 20%) / 20% = 17.5/20 = 87.5%. Can someone explain why this is not correct?
_________________

Please +1 KUDOS if my post helps. Thank you.

Kudos [?]: 22 [0], given: 22

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128525 [1], given: 12180

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 08 Jun 2014, 03:31
1
This post received
KUDOS
Expert's post
bekerman wrote:
The mistake I made on this problem was that I took (37.5% - 20%) / 20% = 17.5/20 = 87.5%. Can someone explain why this is not correct?


That's wrong because 37.5% and 20% are from different quantities.

Consider this, if biography books were 10% of 100 books and then became 50% of 1,000,000 books would it be correct to say that the increase in the number of biographies was (50-10)/10 = 400%?

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128525 [1], given: 12180

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7670

Kudos [?]: 17326 [1], given: 232

Location: Pune, India
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 21 Sep 2014, 20:17
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
manugmat123 wrote:
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%


Responding to a pm:

Yes, you can do it using weighted averages:

You are mixing a collection consisting of 20% biographies with a collection consisting of 100% biographies to give a collection consisting of 37.5% biographies. The weights of the two collections will be:

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (1 - 3/8)/(3/8 - 1/5) = (5/8)/(7/40) = 25/7

So if initial collection had a total of 25 books (including 1/5th biographies i.e. 5 biographies), 7 new biographies were added.

Biographies have increased by (7/5)*100 = 140%

Answer (D)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17326 [1], given: 232

Intern
Intern
avatar
Joined: 14 Feb 2014
Posts: 7

Kudos [?]: [0], given: 258

GMAT 1: 550 Q45 V21
GMAT 2: 690 Q49 V35
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 22 Sep 2014, 01:27
VeritasPrepKarishma wrote:
manugmat123 wrote:
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%


Responding to a pm:

Yes, you can do it using weighted averages:

You are mixing a collection consisting of 20% biographies with a collection consisting of 100% biographies to give a collection consisting of 37.5% biographies. The weights of the two collections will be:

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (1 - 3/8)/(3/8 - 1/5) = (5/8)/(7/40) = 25/7

So if initial collection had a total of 25 books (including 1/5th biographies i.e. 5 biographies), 7 new biographies were added.

Biographies have increased by (7/5)*100 = 140%

Answer (D)


Thanks a lot Karishma for the quick response. That made my life much easier.
Highlighted above in red is where I went wrong earlier.
After reaching w1/w2=25/7 I considered that number of biographies in earlier collection is 25 (vs 5 in your solution)
Is there a technique to identify if w1 refers to the whole collection or only the biographies?

Kudos [?]: [0], given: 258

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7670

Kudos [?]: 17326 [1], given: 232

Location: Pune, India
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 22 Sep 2014, 03:16
1
This post received
KUDOS
Expert's post
keyrun wrote:
VeritasPrepKarishma wrote:
manugmat123 wrote:
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%


Responding to a pm:

Yes, you can do it using weighted averages:

You are mixing a collection consisting of 20% biographies with a collection consisting of 100% biographies to give a collection consisting of 37.5% biographies. The weights of the two collections will be:

w1/w2 = (A2 - Aavg)/(Aavg - A1) = (1 - 3/8)/(3/8 - 1/5) = (5/8)/(7/40) = 25/7

So if initial collection had a total of 25 books (including 1/5th biographies i.e. 5 biographies), 7 new biographies were added.

Biographies have increased by (7/5)*100 = 140%

Answer (D)


Thanks a lot Karishma for the quick response. That made my life much easier.
Highlighted above in red is where I went wrong earlier.
After reaching w1/w2=25/7 I considered that number of biographies in earlier collection is 25 (vs 5 in your solution)
Is there a technique to identify if w1 refers to the whole collection or only the biographies?


When you say the concentration (for lack of a better term) is 20%, ask yourself - of what? 20% of what? It is 20% of the original collection. It means the weight w1 is original collection. When you say A2 is 100%, ask yourself - 100% of what? 100% of the new addition (which are all biographies). So the new addition is w2.

The formula is just a rephrasing of

Cavg = (C1*w1 + C2*w2)/(w1 + w2)

If C1 is 20%, you need w1 to be the original collection.

20% of original collection.

20% * Original Collection

and so on...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Kudos [?]: 17326 [1], given: 232

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16766

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 21 Feb 2016, 13:58
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16766

Kudos [?]: 273 [0], given: 0

Premium Member
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 08 May 2017, 12:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Senior Manager
Senior Manager
avatar
G
Joined: 26 Dec 2015
Posts: 254

Kudos [?]: 52 [0], given: 1

Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 05 Jun 2017, 17:49
Bunuel wrote:
bekerman wrote:
The mistake I made on this problem was that I took (37.5% - 20%) / 20% = 17.5/20 = 87.5%. Can someone explain why this is not correct?


That's wrong because 37.5% and 20% are from different quantities.

Consider this, if biography books were 10% of 100 books and then became 50% of 1,000,000 books would it be correct to say that the increase in the number of biographies was (50-10)/10 = 400%?

Hope it's clear.


Bunuel, is the tip-off here (re: unknown quantities) that the equation uses %s instead of absolute numbers?
- meaning, 20% can be 1/5 or 20/100 (quantities changed)

Kudos [?]: 52 [0], given: 1

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 827 [1], given: 5

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 08 Jun 2017, 17:05
1
This post received
KUDOS
Expert's post
manugmat123 wrote:
Keats Library purchases a number of new books, all in the category of biography; the library does not acquire any other books. With the addition of the new biographies, the biography collection of the library amounts to 37.5% of the new total number of books in the library. If prior to the purchase, only 20% of the books in Keats Library were biographies, by what percent has the number of biographies in the library increased?

A. 17.5%
B. 62.5%
C. 87.5%
D. 140%
E. 150%


We can let the original number of books = 100. Thus, there were 20 biographies in the collection and 80 non-biographies. We can also let x = the number of new biographies and we can create the following equation:

(20 + x)/(100 + x) = 0.375

20 + x = 37.5 + 0.375x

0.625x = 17.5

x = 28

So, now we have 20 + 28 = 48 biographies. We use the formula percent increase = (new - old)/old x 100 to determine the percentage increase:

(48 - 20)/20 x 100

28/20 x 100

7/5 x 100 = 140%

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 827 [1], given: 5

Intern
Intern
avatar
B
Joined: 06 Apr 2017
Posts: 27

Kudos [?]: 7 [0], given: 38

GMAT ToolKit User CAT Tests
Re: Keats Library purchases a number of new books, all in the ca [#permalink]

Show Tags

New post 17 Jul 2017, 10:17
When dealing with ratios, proportions, and percentages don't forget that each can be satisfied by an infinite number of combinations. Take \(\frac{1}{5}\) for example:

There could be \(1\) biography and \(5\) total books \(\frac{1}{5}=20\%\)

There could be \(2\) biography and \(10\) total books \(\frac{2}{10}=20\%\)

There could be \(3\) biography and \(15\) total books \(\frac{3}{15}=20\%\)

This pattern proceeds into positive infinite. MANY of the questions related to ratios, proportions, and percentages will ask you about the nature of the relationship after some change. You can use some variable multiplier to handle the fact that infinite numbers could satisfy the relationship described by the ratio, proportion, or percentage. I'll call the multiplier \(m\) and the discrete number of biographies added \(x\)

\(\frac{m+x}{5m+x}=\frac{3}{8}\)

\(8m + 8x=15m+3x\)

\(5x=7m\)

\(\frac{x}{m}=\frac{7}{5}\)

So the multiplier is some multiple of 5 and the number of books added is the same multiple of 7.

Test that out to be sure.

\(\frac{5}{25}=20\%\)

\(\frac{5+7}{25+7}=\frac{12}{32}=\frac{3}{8}\)

So if you have \(5\) biographies of \(25\) total books, and you add \(7\) biographies, you'll then have \(12\) biographies in \(32\) total books. This satisfies the questions constraints.

\(\frac{12}{5}-1=140\%\)

Answer D

Kudos [?]: 7 [0], given: 38

Re: Keats Library purchases a number of new books, all in the ca   [#permalink] 17 Jul 2017, 10:17

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

Keats Library purchases a number of new books, all in the ca

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.