GMATGuruNY wrote:Since the question stem asks for a PERCENT CHANGE, we can make the math easier by using easier values.
The percent change will remain constant as long as the first set of copies and the second set of copies are in the following ratio:
10000:15000 = 10:15.
Thus, the prompt can be rephrased as follows:
gmattoend wrote:An author receives 10% of the publisher's net receipts in royalties on the first 10 copies of the author's book sold, 12% on the next 15 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10 copies to the next 15 copies?
(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%
Since a 10% royalty is earned on the first 10 copies, we get the following royalty-to-copies ratio:
10/10 = 1.
Since a 12% royalty is earned on the next 15 copies, we get the following royalty-to-copies ratio:
12/15 = 4/5.
Since the ratio decreases from 1 to 4/5, it decreases by 1/5 = 20%.
The correct answer is
D.
Dear GMATGuru Sir,
I try to solve the question with another way but I still confused.
I assumed the copy price is $1, So
the total price 10,000 copies = $10,000,
Then, The 10% royalty of 10,000 copies = $1000, therefore, the percentage = 1000/10000 = 0.1
the total price 15,000 copies = $15,000
Then, The 12% royalty of 15,000 copies = $1800, therefore,the percentage = 1800/15000 = 0.12
Percentage change = (New value - Initial value) /Initial value
Apply in formula = (0.12 - 0.1)/ 0.1 = 0.2. This means it s 20%
Although the answer is correct, why did not my formula or answer produce negative sign to indicate decrease change? However, I applied the values in your solution, It did produce negative sign: ( 4/5 -1) /1 = -1/5 = -0.2
Many appreciate
Gmattoend
