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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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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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

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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Correct!

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