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Another ratio question :(

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Another ratio question :(

by hutch27 » Mon Feb 11, 2013 10:59 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 approx. 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

This is from the og 13th Ed. I'm not too strong at solving equivalent ratios but much better at portioning ratios. Any advice on innovative ways to tackle these problems would be helpful

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by Brent@GMATPrepNow » Mon Feb 11, 2013 11:17 am
hutch27 wrote: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 approx. 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
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.

Well, 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

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by GMATGuruNY » Mon Feb 11, 2013 11:56 am
hutch27 wrote: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 approx. 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
Since the question stem asks for an approximation, and there is sufficient distance between the answer choices, we can BALLPARK.

Case 1: royalties/sales = 3/20 = 15/100 = 15%.
Case 2: royalties/sales = 9/108 ≈ 9%.
Since 15% to 7.5% is a decrease of 50%, a decrease from 15% to 9% is a bit LESS than 50%.

The correct answer is C.
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