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A pharmaceutical company received $3 million in royalties

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A pharmaceutical company received $3 million in royalties [#permalink] New post 12 Dec 2012, 04:29
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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%
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 12 Dec 2012, 04:32
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Walkabout 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 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%


General formula for percent increase or decrease, (percent change) is \(Percent=\frac{Change}{Original}*100\).

Thus, the royalties decreased by approximately \(=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}\).

Answer: C.
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 14 Dec 2012, 02:18
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for this kind of percentage change questions we apply the formula (change/original)x100, so here we have initial ratio=3/20 final ratio=1/12 . now change = 3/20-1/12=1/15 , putting these values in the formula we get the answer as (C).
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 15 Dec 2012, 08:17
To Brunuel:

Thanks for the sharing, I'm wondering whether your formula shouldn't be (9/108-3/20) / (3/20) ? This doesn't change the final answer anyway.

BTW thanks for all the great job you have been doing so far! I'm new to the forum and I'm just speechless.

cheer Mate
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 26 Feb 2013, 10:34
carloswn wrote:
To Brunuel:

Thanks for the sharing, I'm wondering whether your formula shouldn't be (9/108-3/20) / (3/20) ? This doesn't change the final answer anyway.



I don't think it'll make a difference because in the numerator we are just looking for the difference between the two amounts. Just make sure that in the denominator you have the original value.

For better understanding:

\(Percent Change = \frac{Change in Value}{Original Value}\)

Hence, the "change in value" is just the difference. I wouldn't worry about a negative here.
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 26 Jun 2014, 21:19
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 11 Sep 2014, 11:15
Bunuel wrote:
Walkabout 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 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%


General formula for percent increase or decrease, (percent change) is \(Percent=\frac{Change}{Original}*100\).

Thus, the royalties decreased by approximately \(=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}\).

Answer: C.




Hi Bunuel,

please confirm on this..

for first one --15%

for the second one approx. 8 %

so (15-8)/15 = 7/15 approx = 45
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 29 May 2015, 01:57
For me, percentage questions seem time consuming ..not sure if I am the only one feel this way..
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Re: A pharmaceutical company received $3 million in royalties [#permalink] New post 29 May 2015, 14:53
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Hi katzzzz,

Percent questions come from the broader family of 'ratio-based' questions and you're going to see a bunch of those on Test Day, so you have to make sure that you're ready for them. While some of these questions can be wordier/longer than average, the 'key' to answering these types of questions quicker is to organize information in the most effective way possible (for the question that is asked and for the answer choices that are given).

For example, ALL of the following examples mean the same thing, so you have to decide which would be easiest to work with...

Men/Women = 1 to 10 = 1:10 = 1/10 = 0.1 = 10%
10M = 1W

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A pharmaceutical company received $3 million in royalties [#permalink] New post 02 Jun 2015, 04:48
Expert's post
katzzzz wrote:
For me, percentage questions seem time consuming ..not sure if I am the only one feel this way..


Dear katzzzz

One reason why percentage questions may seem time consuming to you is that they usually have multiple data points (for example, the current question has earlier royalty, earlier sales, new royalty, new sales, the percentage change between earlier ratio of royalty:sales to new royalty:sales. That may seem quite a handful of quantities to track and tackle! :) )

Here's an approach that I suggest to you for questions that seem to have lots of information: Always go from the unknown to the known.

By Unknown, I mean what the question is asking.
By known, I mean the given information.

Let me illustrate this approach here.

The question is asking about the % decrease in some ratio.

So, my first step is to let this % decrease be P.

So, I can write:

\(Later Ratio = (1 - \frac{P}{100})(Earlier Ratio)\)

Now, what is the Ratio being considered here? It is the ratio of 'Royalty to Sales'

So, the above equation becomes:

\(\frac{(Later Royalty)}{(Later Sales)} = (1 - \frac{P}{100})\frac{(Earlier Royalty)}{(Earlier Sales)}\)

Now the question is easy to solve. You simply substitute the values of earlier and later royalty, and earlier and later sales, and you get the value of P.

As you can see, this approach of going 'From Unknown to Known' gave us a sense of direction to wade through the given information.

I hope this helped. :)

Best Regards

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A pharmaceutical company received $3 million in royalties   [#permalink] 02 Jun 2015, 04:48
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