Last Updated on May 3, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This is a percent decrease problem. We will use the formula: percent change = (new – old)/old x 100 to calculate the final answer.
We first set up the ratios of royalties to sales. The first ratio will be for the first 20 million in sales, and the second ratio will be for the next 108 million in sales. Because all of the sales are in millions, we do not have to express all the trailing zeros in our ratios.
First 20 Million
royalties/sales = 3/20
Next 108 Million
royalties/sales = 9/108 = 1/12
Because each ratio is not an easy number to use, we can simplify each one by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percents.
First 20 Million
royalties/sales = (3/20) x 60 = 9
Next 108 Million
royalties/sales = 9/108 = (1/12) x 60 = 5
We can plug 9 and 5 into our percent change formula:
(new – old)/old x 100
[(5 – 9)/9] x 100-4/9 x 100
At this point we can stop and consider the answer choices. Since we know that 4/9 is just a bit less than ½, we know that -4/9 x 100 is about a 45% decrease.
Answer: C
