VeritasPrepKarishma 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%
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)
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?