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



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Keats Library purchases a number of new books, all in the ca
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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: \(\frac{(newtotalbiographies)}{(newtotalbooks)}\) = 37.5% = \(\frac{3}{8}\). D: 140%Here, the increase in the number of biographies = \(\frac{140}{100}\) * 20 = 28. Thus: \(\frac{(newtotalbiographies)}{(newtotalbooks)}\) = \(\frac{(20+28)}{(100+28)}\)= \(\frac{48}{128}\) = \(\frac{3}{8}\). Success!
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Keats Library purchases a number of new books, all in the ca
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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 + nonbio)
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 + Nonbio books Percent change = ((New  Old)/Old) *100 > NX/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



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Keats Library purchases a number of new books, all in the ca
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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 \(\frac{(228)}{8}\) = \(\frac{7}{4}\) which is not equal to 140%.
Please advise where am I going wrong. thanks



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Keats Library purchases a number of new books, all in the ca
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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: \(\frac{(newtotalbiographies)}{(newtotalbooks)}\) = 37.5% = \(\frac{3}{8}\). D: 140%Here, the increase in the number of biographies = \(\frac{140}{100}\) * 20 = 28. Thus: \(\frac{(newtotalbiographies)}{(newtotalbooks)}\) = \(\frac{(20+28)}{(100+28)}\)= \(\frac{48}{128}\) = \(\frac{3}{8}\). Success! Dear GMATGuruNY How to solve this problem if treated a mix problem using the Alligation method? Is ti applicable in this case? Thanks



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Re: Keats Library purchases a number of new books, all in the ca
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15 Jun 2018, 03:15
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% 17.537.5% 62.5100% 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: \(\frac{increaseinbiographies}{currentnumberofbiographies}\)= \(\frac{28}{20}\) = \(\frac{140}{100}\) = 140%.
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Re: Keats Library purchases a number of new books, all in the ca
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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% 17.537.5% 62.5100% 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: \(\frac{increaseinbiographies}{currentnumberofbiographies}\)= \(\frac{28}{20}\) = \(\frac{140}{100}\) = 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?



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Re: Keats Library purchases a number of new books, all in the ca
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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! \(\frac{increaseinbiographies}{originalnumberofbooks}\)= \(\frac{28}{100}\) = 28%.
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Re: Keats Library purchases a number of new books, all in the ca
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