A pharmaceutical company received $3 million in royalties

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:49 pm

A pharmaceutical company received $3 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?

(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

Answer: C
Source: Official guide

First $20 million: royalties/sales ratio = 3/20 = 36/240
Next $108 million: royalties/sales ratio = 9/108 = 1/12 = 20/240

Noticed that I rewrote both with the SAME DENOMINATOR.
So, now all we need to is determine the percent change from 36 to 20.
To do so, we could use some more lengthy calculations [e.g., 100(36-20)/36]
HOWEVER, notice that, if we start at 36, a 50% decrease would give us 18.
So going from 36 to 20, must be a decrease that's LESS THAN 50% (but also pretty close to 50%)
Only one answer choice works.

Answer: C


Cheers,
Brent

BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:49 pm

A pharmaceutical company received $3 million in royalties on the first $20 million in sales of the generic equivalent of one of its products and then $9 million in royalties on the next $108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales?

(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

Answer: C
Source: Official guide

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 of 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 them 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 percentages.

First 20 Million

royalties/sales = (3/20) x 60 = 9

Next 108 Million

royalties/sales = (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