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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Checked. Yours is good too! Just dropped an alternative way.

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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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

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%.

Please advise where am I going wrong. thanks

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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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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Let the total number of books originally be 1000, which means there were 800 non-biographies in the library. Now, this figure does not change, i.e., even after more biographies have been added, there have been no more additions of non-biographies.

So, 0.8 * 1000 = 0.625 * (1000+X), where 'X' is the number of new books added. Solving this (using fractions), we arrive at the value of X = 280. This means 280 books were added to the library, and all of them were biographies. This is also the difference between the no. of biographies originally and the total no. of biographies after the addition.

Now, it's a simple percentage increase calculation, which is (280/200) * 100 = 140%.

The equation 0.8 * 1000 = 0.625 * (1000+X) is basically saying that the no. of biographies does not change, even though the no. of biographies as a percentage of the total no. of books may change. I prefer this method because it's fast, and if you know your fractions, the calculations are very easy.

Hi Bunuel VeritasKarishma -

I also made the mistake and calculated the difference between 37.5 % and 20 % to get 17.5 % and calculated the resulting % change ( I ended up picking C incorrectly)

I now understand why my logic does not work because of the example posted in the purple font above

Can you provide a link / problem that flushes out this logic a bit more ?

While I have understood it, i want to perhaps read more about this logical fallacy or do some problems w.r.t this logical fallacy in order to imbibe it completely.

Before you add/subtract percentages, you need to ensure that the bases of the percentages are the same.
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