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Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code ## Ratios & Revenue (OG Quant Review #115) tagged by: Brent@GMATPrepNow This topic has 3 expert replies and 4 member replies bml1105 Master | Next Rank: 500 Posts Joined 24 Nov 2013 Posted: 113 messages Followed by: 5 members Upvotes: 1 #### Ratios & Revenue (OG Quant Review #115) Sun Apr 20, 2014 7:19 pm 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% Answer: C In the explanation, it says "the percent decrease in the royalties to sales ratios is 100 times the quotient of the difference in the ratios divided by the ratio of royalties to sales for the first$20 million in sales". What?? How did they get to this? Can anyone explain it a bit better?

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### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13605 messages
Followed by:
1796 members
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GMAT Score:
790
Mon Apr 21, 2014 2:21 am
bml1105 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%
Since the questions stem asks for an approximation, we can BALLPARK.

Original ratio = 3/20 = 15/100 = 15%..
Decreased ratio = 9/108 â‰ˆ 9/100 = 9%.
Percent decrease from 15 to 9 = (15 - 9)/15 * 100 = 6/15 * 100 = 40%.
Only C is viable.

If the answer choices are very close, the exact percent change can be calculated as follows.

Option 1: Denominator approach
Convert the ratios so that the denominators are the same.
Calculate the percent change in the numerators.

In the problem above:
Old ratio: 3/20 = 9/60.
New ratio: 9/108 = 1/12 = 5/60.
From 9 to 5, the percent change in the numerators = (9-5)/9 * 100 = 4/9 * 100 â‰ˆ 44.44.

Option 2: Numerator approach
Convert the ratios so that the numerators are the same.
Calculate the percent change in the denominators.

In the problem above:
Old ratio: 3/20 = 9/60.
New ratio = 9/108.
From 60 to 108, the percent change in the denominators = (108-60)/60 * 100 = 48/108 * 100 = 4/9 * 100 â‰ˆ 44.44.

But we should always check the answer choices BEFORE we calculate.
Here, the answer choices are NOT very close and the question stem asks for an APPROXIMATION.
Thus, we can save time by estimating, as I did in in my first solution above.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Thanked by: kolaalok
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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11032 messages
Followed by:
1217 members
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GMAT Score:
770
Mon Apr 21, 2014 8:46 am
bml1105 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%)

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13605 messages
Followed by:
1796 members
13060
GMAT Score:
790
Mon Apr 21, 2014 2:21 am
bml1105 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%
Since the questions stem asks for an approximation, we can BALLPARK.

Original ratio = 3/20 = 15/100 = 15%..
Decreased ratio = 9/108 â‰ˆ 9/100 = 9%.
Percent decrease from 15 to 9 = (15 - 9)/15 * 100 = 6/15 * 100 = 40%.
Only C is viable.

If the answer choices are very close, the exact percent change can be calculated as follows.

Option 1: Denominator approach
Convert the ratios so that the denominators are the same.
Calculate the percent change in the numerators.

In the problem above:
Old ratio: 3/20 = 9/60.
New ratio: 9/108 = 1/12 = 5/60.
From 9 to 5, the percent change in the numerators = (9-5)/9 * 100 = 4/9 * 100 â‰ˆ 44.44.

Option 2: Numerator approach
Convert the ratios so that the numerators are the same.
Calculate the percent change in the denominators.

In the problem above:
Old ratio: 3/20 = 9/60.
New ratio = 9/108.
From 60 to 108, the percent change in the denominators = (108-60)/60 * 100 = 48/108 * 100 = 4/9 * 100 â‰ˆ 44.44.

But we should always check the answer choices BEFORE we calculate.
Here, the answer choices are NOT very close and the question stem asks for an APPROXIMATION.
Thus, we can save time by estimating, as I did in in my first solution above.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Thanked by: kolaalok
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11032 messages
Followed by:
1217 members
5254
GMAT Score:
770
Mon Apr 21, 2014 8:46 am
bml1105 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%)

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

### GMAT/MBA Expert

Scott@TargetTestPrep GMAT Instructor
Joined
25 Apr 2015
Posted:
548 messages
Followed by:
3 members
43
Sat Jun 27, 2015 5:18 am
bml1105 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%

In the explanation, it says "the percent decrease in the royalties to sales ratios is 100 times the quotient of the difference in the ratios divided by the ratio of royalties to sales for the first $20 million in sales". What?? How did they get to this? Can anyone explain it a bit better? Thank you in advance! Solution: 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 the trailing zeroes in our ratios. First$20 Million

royalties/sales = 3/20

Next $108 Million royalties/sales = 9/108 = 1/12 We can plug 1/12 and 3/20 into our percent change formula: [(new - old)/old] x 100 [(1/12 - 3/20)/(3/20)] x 100 Because the first term is a complex fraction, we can simplify it by multiplying each fraction within the complex fraction by the LCM of 12 and 20, which is 60: 1/12 x 60 = 5 and 3/20 x 60 = 9 Therefore, we have: [(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 Â½, we know that (-4/9) x 100 is about a 45% decrease. Answer:C _________________ Scott Woodbury Stewart Founder & CEO GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions 5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT bml1105 Master | Next Rank: 500 Posts Joined 24 Nov 2013 Posted: 113 messages Followed by: 5 members Upvotes: 1 Sun Apr 20, 2014 8:14 pm Thanks Tushar! I feel like the OG Review over complicates its explanations. Tushar14 Senior | Next Rank: 100 Posts Joined 14 Feb 2014 Posted: 44 messages Upvotes: 12 Sun Apr 20, 2014 7:51 pm Tushar14 wrote: Hello, Please ignore the previous solution and consider this one as we need to calculate the % decrease in sales. Initially$3m royalty from $20m sales, So$ 1m sales = $3/20 Next,$9m royalty from $108m sales, So$ 1m sales = \$9/108

% Decrease = Change/Original * 100
% Decrease = (3/20 - 9/108)/ (3/20) * 100 = approx 45 %

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