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12 Dec 2012, 05:29
10
1
74
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Difficulty:

55% (hard)

Question Stats:

68% (02:22) correct 32% (02:26) wrong based on 2543 sessions

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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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23 Nov 2015, 15:55
7
6
% 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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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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02 Jun 2015, 05:48
2
4
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.

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

Japinder
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10 Apr 2016, 10:43
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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%)

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

Cheers,
Brent
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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%
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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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14 Jan 2018, 06:00
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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06 May 2018, 10:02
1
dave13 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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22 May 2018, 11:23

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

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Re: A pharmaceutical company received $3 million in royalties [#permalink] ### Show Tags 01 Nov 2018, 22:27 $$=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}$$.[/quote] 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.[/quote] I'd suggest another way: $$\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}=(\frac{3}{20}-\frac{1}{12})*\frac{20}{3}=1 -\frac{1}{12}*\frac{20}{3}=1-\frac{5}{9}=\frac{4}{9}=0.444....$$[/quote] Isn't the formula (new-old)/old. why are you writing it (old-new)/old? Re: A pharmaceutical company received$3 million in royalties   [#permalink] 01 Nov 2018, 22:27

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