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12 Dec 2012, 04:29
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Difficulty:

65% (hard)

Question Stats:

67% (02:40) correct 33% (02:02) wrong based on 1537 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%
[Reveal] Spoiler: OA

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14 Dec 2012, 02:18
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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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26 Feb 2013, 10:34
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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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11 Sep 2014, 11:15
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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 $$=\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}*100\approx{44%}$$.

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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29 May 2015, 14:53
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Expert's post
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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02 Jun 2015, 04:48
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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

Japinder
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17 Jan 2016, 19:55
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, 19:30, edited 1 time in total.

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10 Apr 2016, 09:43
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Expert's post
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

Related Resource
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25 Mar 2017, 09:01
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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09 Jul 2017, 01:04
Hi:)
another way...
20---->3
108--->9

If in the same ratio as the 1st one, royalty calculated for 108 would be 16.2

so (16.2 - 9)/16.2.... approx 16.2 to 16...
7/16 = 0.4375
approx 45%...
Hope it helps

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Re: A pharmaceutical company received $3 million in royalties [#permalink] ### Show Tags 24 Sep 2017, 21:33 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 _________________ Regards, Naveen email: nkmungila@gmail.com Please press kudos if you like this post Kudos [?]: 102 [0], given: 59 Re: A pharmaceutical company received$3 million in royalties   [#permalink] 24 Sep 2017, 21:33
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