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A pharmaceutical company received $3 million in royalties [#permalink]

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12 Dec 2012, 05:29

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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 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 \(=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}\).

Re: A pharmaceutical company received $3 million in royalties [#permalink]

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14 Dec 2012, 03:18

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Ans:

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]

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26 Feb 2013, 11:34

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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]

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26 Jun 2014, 22:19

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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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11 Sep 2014, 12:15

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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 \(=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}\).

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...

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'

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.

A pharmaceutical company received $3 million in royalties [#permalink]

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17 Jan 2016, 20:55

Used normal percentage method but approximated cause I was trying to complete this in 1 min \([\frac{3}{20} - \frac{9}{100}]*\frac{20}{3}*100\) \(\frac{(15-9)}{100} *\frac{20}{3}*100\) \(\frac{6}{100}*\frac{20}{3}*100\) =40% = ~44% (again, I approximated 108 to 100, I was lucky, if the answer choice was either 52% & 56%, I would be pulling my hair . Lesson learnt.)
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Last edited by colorblind on 09 Oct 2016, 20:30, edited 1 time in total.

A pharmaceutical company received $3 million in royalties [#permalink]

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08 Mar 2016, 00:30

To Bunuel:

I tend to get confused when estimating in certain scenarios and select the wrong answer. In this case I took denominator 20 as 18 so that 3/20 becomes 3/18 = 1/6 and 9/108 = 1/12 so 1/6-1/12 =1/12 and now (1/12)/(1/6)*100 = 50% so I would have selected (D) - 52% which is the closest. In another case had I taken 20 as 21(more convenient) the fraction would have been 3/21 = 1/7 and to balance the round off I would have taken 12 as 10 (one increase other decrease) so (1/7-1/10)/(1/7) = (3/70)*7 = 30% its quite far apart from the options so either 15 or 45 although we are actually reducing the 108 mn to 90 mn which is a huge difference so the overall result should be higher so 45 should be the case. In the next scenario I took 20 mn as 21 mn and then ratio became (1/7) so ({1/7-1/12}/(1/7))*100 = 5/12*100 = 42% approx so again option C (45%). So in these cases the answers are different so then how to reach the correct answer in quick time if choices are quite close, there is a high chance of error. Kindly advise the extent to which we can approximate values of fractions as answers can be a huge difference in the answers arrived by taking multiple scenarios as if one scenario leads us to one choice we will quickly select it and move on as there is the time factor.
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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%

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

Related Resource The following free video covers the concepts/strategies that are useful for answering this question:

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%

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.
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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24 Sep 2017, 22:33

Percentage change = (3/20*100 -9/108*100) / (3/20*100) = only percentage change to near to 50 and less that 50 is 45% hence answer must be C
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