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A pharmaceutical company received $3 million in royalties

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

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New post 01 Nov 2018, 22:46
kchen1994 wrote:

Isn't the formula (new - old)/old. why are you writing it (old - new)/old?


Hi,

If you know that it is a decrease, then you need to use (old – new)/old.

And, if you do not know whether it is a decrease or increase, then you need to use (new – old)/old
    • If this value is negative, then we can conclude that it is a decrease
    • If this value is positive, then we can conclude that it is an increase

Since, we are given that it is a decrease, in this question, we can use the formula: (old – new)/old

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

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New post 15 Nov 2018, 22:52
I get the math behind this question, but have a semantic clarification --

Is it safe to assume that when the gmat asks "by what percent did a ratio decrease?" they want a percentage decrease and not an absolute decrease? What if they ask "by what percentage did a percentage decrease?"

In this case, we're talking about a commission, which is almost always stated in percentage terms. In the real world, if you are running a commission based company and your commission goes from 5% to 4%, I think few people would say the decrease was 20% -- they would likely state the decrease in absolute terms, a 1% decrease. Should I basically ban this sort of thinking when taking the GMAT?
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Re: A pharmaceutical company received $3 million in royalties  [#permalink]

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New post 16 Nov 2018, 21:11
Hello, first time poster! Would someone be able to tell me if this way of solving this problem is correct?

So the standard ratio is 3/20 and you want to see with this ratio, how much you should have gotten at 108.

3 = X
20 108

X = 15

Then take the difference in ratios.

15-9 = 6/15 = ~40% which is close to 45
15
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Re: A pharmaceutical company received $3 million in royalties  [#permalink]

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New post 29 Dec 2018, 14:01
Key points -

1. Quick fraction to percentage: 3/20= 15 percent and 09/108= 1/12= 8.33 percent

2. Take advantage of the options since 15 goes down to 8.3, it can not be a slight decrease, hence A & B eliminated. Half of 15 is 7.5 so it can not be more than 50 percent, so options D & E not possible.

The use of analyzing the options before proceeding to the final equation/calculation can save a lot of time.
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Re: A pharmaceutical company received $3 million in royalties  [#permalink]

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New post 06 Apr 2019, 04:43
The question tricks with $9 million in royalties for $108 million in next sales. So made the ratio 9/128 in a hurry leading to longer solving time and the answer itself could have gone any way.
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A pharmaceutical company received $3 million in royalties  [#permalink]

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New post Updated on: 12 May 2019, 02:33
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%



Old Sales = $ 20 million

Old Royalties = $ 3 million

New Sales = $ 108 million

New Royalties = $ 9 million

Let us make both the sales approximately equal,

Old Sales = 20 * 5.5 = $ 110

Increase the Old Royalties equal times = 3*5.5 = $ 16.5 (say $ 17)

Say, New Sales also = $ 110

New Royalties = \($ 9\)

Percentage change = \(\frac{(Old - New)}{Old} * 100\)

\(17 - \frac{9}{17} * 100\)

\(47\) % approx

(C)

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Originally posted by AkshdeepS on 06 Apr 2019, 05:46.
Last edited by AkshdeepS on 12 May 2019, 02:33, 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 12 May 2019, 00:57
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%


Royalties decreased approximately:

3/20-9/108
----------*100=45%. Answer:C
3/20

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Re: A pharmaceutical company received $3 million in royalties   [#permalink] 12 May 2019, 00:57

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