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Percents of Ratio

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Percents of Ratio

by leumas » Sun Sep 11, 2011 1:32 am
A pharmaceutical company received $3 million in
royalties on the fi rst $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 fi rst $20 million in sales to
the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

OA is C
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by Geva@EconomistGMAT » Sun Sep 11, 2011 1:42 am
leumas wrote:A pharmaceutical company received $3 million in
royalties on the fi rst $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 fi rst $20 million in sales to
the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

OA is C
In order to even compare the two ratios, you need to bring them to the same base.

First ratio: 3:20, or 3/20
Second ratio: 9:108, or 9/108.

Expand the first ratio to a denominator of 108: from 20 to 108 you need to multiply times ~5.5, so the nuemrator needs to be multipled by that as well:
3/20 = ~3*5.5/108 = ~16/108.

So now the two ratios are:

16/108 decrease to 9/108. A decrease of 7 "points" from the original "16" points is slightly less than 50% - only answer choice C matches that description.
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by GMATGuruNY » Sun Sep 11, 2011 3:29 am
leumas wrote:A pharmaceutical company received $3 million in
royalties on the fi rst $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%

OA is C
Geva's solution is great. I just want to point out something important: always be aware when a question asks for an APPROXIMATION.
Don't do any more math than is needed.

Original ratio = royalties/sales = 3/20 = 15%.
New ratio = royalties/sales = 9/108 ≈ 9%.
Difference = 15-9 = 6.
Difference/Original = 6/15 = 2/5 = 40%.

Only one answer choice is close enough.
The correct answer is C.
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by mehrasa » Sun Sep 11, 2011 11:50 am
the easy and time consuming method is to find the ration of 2 different part then find the amount of change

new/original(status 2/status 1)= 9/108/3/20= 9/108*20/3= 5/9 = 0.55 ==> %55
the second royalties is %55 of first royalties ==> decline change= 100-55= %45

OA: C
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by Brent@GMATPrepNow » Thu Jan 09, 2020 6:33 am
leumas wrote:A pharmaceutical company received $3 million in
royalties on the fi rst $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 fi rst $20 million in sales to
the next $108 million in sales?
(A) 8%
(B) 15%
(C) 45%
(D) 52%
(E) 56%

OA is C
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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