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

Question

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%

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

Bunuel · Accepted Answer

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.

manugmat123 · Answer

the OE is attached .....

manugmat123 · Answer

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.......?????

Bunuel · Answer

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

manugmat123 · Answer

ooooooh... yes yes :-D

thanks a lot

JBGMAT · Answer

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%

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

Bunuel · Answer

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.

JBGMAT · Answer

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%

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.

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

JBGMAT · Answer

Yes, its clear now. Many thanks Bunuel.

Regards,

bekerman · Answer

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?

Bunuel · Answer

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.

KarishmaB · Answer

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)

kiranm · Answer

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?

KarishmaB · Answer

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...

JeffTargetTestPrep · Answer

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

standyonda · Answer

--EASY SOLUTION-- 25 sec

We know that 37.5% = 3/8 and 20% = 1/5

Also we have:

{1} -- (b’+b)/(b’+b+t) = 3/8
{2}   -- b/(b+t) = 1/5

We are looking for: b'/b = x

Divide everything in {1} with b then use the reciprocal of {2} and replace everything replaceable and also replace b'/b with x (for simpler calc.) and you will find x easily!

Bunuel ,  VeritasPrepKarishma  check

KarishmaB · Answer

Yes, the method looks fine though cumbersome. I don't like to deal with so many variables or, if possible, any variables. Take a look at the weighted averages approach I discussed in a comment on the previous page.

GMATGuruNY · Answer

Let the number of books prior to the purchase of new biographies = 100, implying that the number of biographies prior to the purchase = 20% of 100 = 20.
We can PLUG IN THE ANSWERS, which represent the percent increase in the number of biographies.
Percents on the GMAT tend to be round numbers.
Thus, the correct answer is probably D or E.
When the correct answer is plugged in:

\frac{(new-total-biographies)}{(new-total-books)}  = 37.5% =  \frac{3}{8} .

D: 140% 
Here, the increase in the number of biographies =  \frac{140}{100}  * 20 = 28.
Thus:

\frac{(new-total-biographies)}{(new-total-books)}  =  \frac{(20+28)}{(100+28)} =  \frac{48}{128}  =  \frac{3}{8} .

Success!

D

Mo2men · Answer

Dear  GMATGuruNY

How to solve this problem if treated a mix problem using the Alligation method? Is ti applicable in this case?
Thanks

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

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