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Ratios & Revenue (OG Quant Review #115)

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bml1105 Master | Next Rank: 500 Posts
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Ratios & Revenue (OG Quant Review #115)

Post Sun Apr 20, 2014 7:19 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    Thank you in advance!

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    Tushar14 Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Apr 20, 2014 7:39 pm
    Initially $3m royalty from $20m sales, So $ 1m royal = $20/3 = $ 6.66

    Next, $9m royalty from $108m sales, So $ 1m royal = $108/9 = $ 12

    % deccrease = (12 - 6.66)/ 12 * 100 = 44.5% so option C fits the best.

    Tushar14 Senior | Next Rank: 100 Posts Default Avatar
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    Post Sun Apr 20, 2014 7:49 pm
    Hello, Please ignore the previous solution and consider this one.

    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 %

    Thanked by: bml1105
    Tushar14 Senior | Next Rank: 100 Posts Default Avatar
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    Post 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 %

    bml1105 Master | Next Rank: 500 Posts
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    Post Sun Apr 20, 2014 8:14 pm
    Thanks Tushar! I feel like the OG Review over complicates its explanations.

    Post 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 ≈ 9/100 = 9%.
    Percent decrease from 15 to 9 = (15 - 9)/15 * 100 = 6/15 * 100 = 40%.
    Only C is viable.

    The correct answer is C.

    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 ≈ 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 ≈ 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.

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    Post 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%)
    Only one answer choice works.

    Answer: C

    Cheers,
    Brent

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    GMAT/MBA Expert

    Post 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%


    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?

    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 ½, we know that (-4/9) x 100 is about a 45% decrease.

    Answer:C

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