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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]

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New post 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) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%
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A pharmaceutical company received $3 million in royalties [#permalink]

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New post 12 Dec 2012, 05:32
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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.

P.S. How to calculate:

\(\frac{\frac{3}{20}-\frac{1}{12}}{\frac{3}{20}}*100=\frac{\frac{9}{60}-\frac{5}{60}}{\frac{3}{20}}*100=\frac{\frac{4}{60}}{\frac{3}{20}}*100=\frac{4}{60}*\frac{20}{3}*100=\frac{4}{9}*100\approx{0.44*100}=44\)
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 14 Dec 2012, 03:18
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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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A pharmaceutical company received $3 million in royalties [#permalink]

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New post 11 Sep 2014, 12:15
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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]

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New post 29 May 2015, 15:53
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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]

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New post 02 Jun 2015, 05:48
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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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 23 Nov 2015, 15:55
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% change also equals :
\(\frac{new}{old}\)\(- 1\)

\(\frac{9}{108}\)*\(\frac{20}{3}\)\(- 1\)

= \(\frac{-4}{9}\) ==> since 1/9 = 0,11 ==> -44%
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A pharmaceutical company received $3 million in royalties [#permalink]

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New post Updated on: 09 Oct 2016, 20:30
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 :x . Lesson learnt.)
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Originally posted by colorblind on 17 Jan 2016, 20:55.
Last edited by colorblind on 09 Oct 2016, 20:30, edited 1 time in total.
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 10 Apr 2016, 10:43
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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%


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

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

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New post 23 Mar 2017, 17:01
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umaa wrote:
A pharmaceutical company received $3 million in royalties on the first $20 million in sales of 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%


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

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New post 25 Mar 2017, 10:01
let's write this translation problem from the beginning into formula:
3/20-9/108 or 3/20-1/12 or 9/60-5/60=4/60

(4/60)/(9/60)=4/9 hence cca 44%
Answer is C
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 11 Jun 2017, 04:15
I did this by "Long hand", Of course it eat up more time! :(

Just sharing in case someone interested.

For the first 20 Million, \(\frac{Royalty}{sales}= \frac{3}{20}\)

For the next 108 Million, \(\frac{Royalty}{sales} = \frac{9}{108}\)

Required percentage

= \((\frac{3}{20}- \frac{9}{108})/\frac{3}{20} * 100\)

= \((\frac{3}{20} - \frac{9}{108})* \frac{20}{3} * 100\)

= \(3* (\frac{1}{20}-\frac{3}{108}) * \frac{20}{3} * 100\)

= \((1 - \frac{5}{9}) * 100\)

= \(\frac{4}{9} * 100\)

= 44.44444

Final answer : Option C
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 13 Jan 2018, 23:54
Bunuel chetan2u amanvermagmat niks18

Quote:

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


Is below approach the most efficient for simplification:
Taking 1/4 common after simplifying(3/20 - 1/12)
in numerator which finally simplifies to 2/3 and then multiplying by 20/3
which approx to 40/9. Now since denominator is slightly less than 10
and 40/10 is 4 so we shall get fraction as slightly more than 4.xx as a value.
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 14 Jan 2018, 00:22
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adkikani wrote:
Bunuel chetan2u amanvermagmat niks18

Quote:

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


Is below approach the most efficient for simplification:
Taking 1/4 common after simplifying(3/20 - 1/12)
in numerator which finally simplifies to 2/3 and then multiplying by 20/3
which approx to 40/9. Now since denominator is slightly less than 10
and 40/10 is 4 so we shall get fraction as slightly more than 4.xx as a value.


I'd suggest another way:

\(\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}=(\frac{3}{20}-\frac{1}{12})*\frac{20}{3}=1 -\frac{1}{12}*\frac{20}{3}=1-\frac{5}{9}=\frac{4}{9}=0.444....\)
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 14 Jan 2018, 06:00
adkikani wrote:
Bunuel chetan2u amanvermagmat niks18

Quote:

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


Is below approach the most efficient for simplification:
Taking 1/4 common after simplifying(3/20 - 1/12)
in numerator which finally simplifies to 2/3 and then multiplying by 20/3
which approx to 40/9. Now since denominator is slightly less than 10
and 40/10 is 4 so we shall get fraction as slightly more than 4.xx as a value.


since the choices are slightly away, even approximation would do...

get the denominator close by to compare the numerator..
\(\frac{3}{20}=\frac{3*5.5}{20*5.5}=\frac{16.5}{110}~\frac{16.5}{108}\)
compare 16.5/108 with 9/108
so Now we are looking at 16.5 coming down to 9.... \(\frac{16.5-9}{16.5}=7.5/16.5\)
half of 16.5 is 8.xx so 7.5 should be closer to 50% but <50%
ans 44%

Ofcourse the method above by Bunuel is simple and accurate BUT a lot depends on your ease with a method..
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A pharmaceutical company received $3 million in royalties [#permalink]

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New post 06 May 2018, 06:45
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%



here is my approach, not sure though if it is correct though, niks18 can you please confirm it :)

\(20=100%\)
\(3=x\)

cross multiply \(x = 15\)

\(108=100%\)
\(9 = x\)
cross multiply \(x = 8\)

now to calculate the difference in % decrease

\(\frac{15-8}{15}\) = \(\frac{7}{15}\) approx i get 0.47 % which is closer to option C :)
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Re: A pharmaceutical company received $3 million in royalties [#permalink]

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New post 06 May 2018, 10:02
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dave13 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%



here is my approach, not sure though if it is correct though, niks18 can you please confirm it :)

\(20=100%\)
\(3=x\)

cross multiply \(x = 15\)

\(108=100%\)
\(9 = x\)
cross multiply \(x = 8\)

now to calculate the difference in % decrease

\(\frac{15-8}{15}\) = \(\frac{7}{15}\) approx i get 0.47 % which is closer to option C :)


Hi dave13

Sorry but your method is incorrect. if you have assigned a value to the variable, then it should remain same. What is x here? and if you say x=3, then x cannot take any other value. Can you explain the reason to cross-multiply?

Refer to Bunuel 's solution above for correct approach.

Note the question is asking decrease in "Ratio". So try to find out the two ratios and then simply calculate the % decrease.
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A pharmaceutical company received $3 million in royalties [#permalink]

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New post 21 May 2018, 22:25
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Please advise whether the below given way of calculation is acceptable

I calculated using the percentage value's of the commission in both the numbers.

First 20 million = 3 million royalties = 15% of the sales.
Next 108 million = 9 million royalties = 8.33% of the sales

Now i calculated the reduction in percentage values = 15% reduced to 8.33% , which is 44.46% reduction, approximately 45%

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

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New post 22 May 2018, 11:23
Hi akadiyan,

Yes - your approach/calculations are perfect for this question!

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Re: A pharmaceutical company received $3 million in royalties   [#permalink] 22 May 2018, 11:23
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