Problem Solving

Vincen wrote: ↑

Fri Jan 28, 2022 4:50 am

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