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

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Intern
Joined: 31 Aug 2016
Posts: 45
Keats Library purchases a number of new books, all in the ca  [#permalink]

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06 Jun 2018, 22:16
--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
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Location: Pune, India
Re: Keats Library purchases a number of new books, all in the ca  [#permalink]

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07 Jun 2018, 20:56
standyonda wrote:
--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

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

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08 Jun 2018, 07:04
VeritasPrepKarishma wrote:
standyonda wrote:
--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

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.

Checked. Yours is good too! Just dropped an alternative way.
Director
Joined: 04 Aug 2010
Posts: 609
Schools: Dartmouth College
Keats Library purchases a number of new books, all in the ca  [#permalink]

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08 Jun 2018, 07:41
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%

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!

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13 Jun 2018, 14:29
N= New biographies
X= Old Biographies
R = Non- biography

Equation 1: N+X = 3/8 (N+X+R) -> 5N/8 + 5X/8 = 3R/8 - > 5N+5X = 3R (1)
This means new bio + old bio = 3/8 of all books in the library ( new bio + old bio + non-bio)

Equation 2: X = 1/5(X+R) -> 4X/R = R/5 -> X= R/4 (2)
This equation means old biographies = 1/5 of old bio + Non-bio books
Percent change = ((New - Old)/Old) *100 -> N-X/X *100

Using equation (1) -> N= 3R/5 - X
Using equation (2) -> X = R/4

Percent Change = ((3R/5 - R/4)/ R/4) *100 -> 7R/20 * 4/R *100 = 700/5 = 140
Intern
Joined: 28 Feb 2017
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13 Jun 2018, 19:28
Hi, I had a different approach to the question

For e.g. Earlier I had 40 books so of which 20% were biographies = 8 books of biographies
Now I add 40 more books to my collections so in total I have 80 books of which 3/8 or 37.5% of total are biographies = 30 books.

So the number of biographies have increased by 22. So the percentage change is $$\frac{(22-8)}{8}$$
= $$\frac{7}{4}$$ which is not equal to 140%.

RSM Erasmus Moderator
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Posts: 2439
Concentration: Operations, Strategy
Schools: Erasmus
Keats Library purchases a number of new books, all in the ca  [#permalink]

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14 Jun 2018, 20:45
GMATGuruNY 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%

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!

Dear GMATGuruNY

How to solve this problem if treated a mix problem using the Alligation method? Is ti applicable in this case?
Thanks
Director
Joined: 04 Aug 2010
Posts: 609
Schools: Dartmouth College
Re: Keats Library purchases a number of new books, all in the ca  [#permalink]

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15 Jun 2018, 03:15
2
Mo2men wrote:
Dear GMATGuruNY

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

Let C = the current number of books and B = the number of added biographies.

C = 20% biographies.
B = 100% biographies.
The MIXTURE of C and B = 37.5% biographies.

To determine the required ratio of C to B, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for C and B on the ends and the percentage for the mixture in the middle.
C 20%---------------37.5%---------------100% B

Step 2: Calculate the distances between the percentages.
C 20%-----17.5-----37.5%-----62.5-----100% B

Step 3: Determine the ratio in the mixture.
The ratio of C to B is equal to the RECIPROCAL of the distances in red.
$$\frac{C}{B}$$ = $$\frac{62.5}{17.5}$$= $$\frac{125}{35}$$ = $$\frac{25}{7}$$= $$\frac{100}{28}$$.

The resulting ratio implies that the number of biographies must increase by 28 if there are currently 100 books.
Since 20% of these 100 books would be biographies -- implying a present tally of 20 biographies -- we get:
$$\frac{increase-in-biographies}{current-number-of-biographies}$$= $$\frac{28}{20}$$ = $$\frac{140}{100}$$ = 140%.

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

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15 Jun 2018, 17:09
GMATGuruNY wrote:
Mo2men wrote:
Dear GMATGuruNY

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

Let C = the current number of books and B = the number of added biographies.

C = 20% biographies.
B = 100% biographies.
The MIXTURE of C and B = 37.5% biographies.

To determine the required ratio of C to B, we can use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for C and B on the ends and the percentage for the mixture in the middle.
C 20%---------------37.5%---------------100% B

Step 2: Calculate the distances between the percentages.
C 20%-----17.5-----37.5%-----62.5-----100% B

Step 3: Determine the ratio in the mixture.
The ratio of C to B is equal to the RECIPROCAL of the distances in red.
$$\frac{C}{B}$$ = $$\frac{62.5}{17.5}$$= $$\frac{125}{35}$$ = $$\frac{25}{7}$$= $$\frac{100}{28}$$.

The resulting ratio implies that the number of biographies must increase by 28 if there are currently 100 books.
Since 20% of these 100 books would be biographies -- implying a present tally of 20 biographies -- we get:
$$\frac{increase-in-biographies}{current-number-of-biographies}$$= $$\frac{28}{20}$$ = $$\frac{140}{100}$$ = 140%.

Thanks GMATGuru

What if the question were to be to calculate the change increase in the total books in the library after the purchase? Based on the calculation above:

$$\frac{B}{C}$$ = $$\frac{28}{100}$$ = 28%

Is it correct?
Director
Joined: 04 Aug 2010
Posts: 609
Schools: Dartmouth College
Re: Keats Library purchases a number of new books, all in the ca  [#permalink]

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16 Jun 2018, 01:48
Mo2men wrote:
Thanks GMATGuru

What if the question were to be to calculate the change increase in the total books in the library after the purchase? Based on the calculation above:

$$\frac{B}{C}$$ = $$\frac{28}{100}$$ = 28%

Is it correct?

Correct!

$$\frac{increase-in-biographies}{original-number-of-books}$$= $$\frac{28}{100}$$ = 28%.
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