A pharmaceutical company received $3 million in royalties

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

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).

For me, percentage questions seem time consuming ..not sure if I am the only one feel this way..

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

GMAT assassins aren't born, they're made,
Rich

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

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 of the trailing zeros in our ratios.

First 20 Million

royalties/sales = 3/20

Next 108 Million

royalties/sales = 9/108 = 1/12

Because each ratio is not an easy number to use, we can simplify them by multiplying each by the LCM of the two denominators, which is 60. Keep in mind that we are able to do this only because our answer choices are expressed in percentages.

First 20 Million

royalties/sales = (3/20) x 60 = 9

Next 108 Million

royalties/sales = (1/12) x 60 = 5

We can plug 9 and 5 into our percent change formula:

(new – old)/old x 100

[(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

Bunuel chetan2u amanvermagmat niks18



Is below approach the most efficient for simplification:
Taking 1/4 common after simplifying(3/20 - 1/12)
in numerator which finally simplifies to 2/3 and then multiplying by 20/3
which approx to 40/9. Now since denominator is slightly less than 10
and 40/10 is 4 so we shall get fraction as slightly more than 4.xx as a value.

I'd suggest another way:

\(\frac{\frac{3}{20}-\frac{9}{108}}{\frac{3}{20}}=(\frac{3}{20}-\frac{1}{12})*\frac{20}{3}=1 -\frac{1}{12}*\frac{20}{3}=1-\frac{5}{9}=\frac{4}{9}=0.444....\)

since the choices are slightly away, even approximation would do...

get the denominator close by to compare the numerator..
\(\frac{3}{20}=\frac{3*5.5}{20*5.5}=\frac{16.5}{110}~\frac{16.5}{108}\)
compare 16.5/108 with 9/108
so Now we are looking at 16.5 coming down to 9.... \(\frac{16.5-9}{16.5}=7.5/16.5\)
half of 16.5 is 8.xx so 7.5 should be closer to 50% but <50%
ans 44%

Ofcourse the method above by Bunuel is simple and accurate BUT a lot depends on your ease with a method..

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,
e-GMAT

Per million for first 20 million \(=\frac{3}{20}\)

Per million for the next 108 million \(= \frac{9}{108}=\frac{1}{12}\)

The royalty reduce \(=\frac{3}{20}-\frac{1}{12}\)

\(⇒ \frac{3}{20}*60-\frac{1}{12}*60\)

\(⇒ 9-5=4\)

The percentage: \(\frac{4}{9}*100\)

\(=4*11^+\)

\(≈44^+\)

The answer is \(C\)

Given: 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.
Asked: 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?

Ratio of royalty of one of pharmaceutical company product = 3/20 = 15%
Ratio of royalty of next pharmaceutical company product = 9/108 = 1/12 = 8.33%

The percent with which ratio of royalties to sales decrease from the first $20 million in sales to the next $108 million in sales = (3/20 - 1/12)/(3/20) * 100% = {(9-5)/60}/(9/60) * 100% = 400/9 % = 44.44% ~ 45%

IMO C

Hi All,

We’re told that a pharmaceutical company received $3 million in royalties on the FIRST $20 million in sales and then $9 million in royalties on the NEXT $108 million in sales. We’re asked by what APPROXIMATE percentage did the ratio of royalties on the first $20 million DECREASE to the ratio of royalties on the next $108 million.

The question clearly refers to Percentage Change, so we’ll need to use the Percentage Change Formula to answer it.

Percent Change = (New – Old)/Old = Difference/Original

First though, we need to define the two ratios involved:

$3 million/$20 million = 3/20 = .15

$9 million/$108 million = 9/108 = 1/12 = .083333

Instead of directly placing those decimals into the Percentage Change Formula, I’m going to multiply them both by 100 (which will make the final calculation easier to look at…

Old = 15
New = 8.333

(New – Old)/Old = (8.3333 – 15)/15 = -6.6666/15

Since -6/15 would be a 40% decrease, we know that -6.6666/15 would be a bit more of a decrease (but not a 50% decrease, since that would be -7.5/15) …

Final Answer:

GMAT Assassins aren’t born, they’re made,
Rich

I used this method with the exact same numbers.

It boils down to a decrease from 16,5 to 9. Less than fifty percent but way more than 15 %. Only one option fits.

Video solution from Quant Reasoning:
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Correct Option C : 44%

Ratio of: (Royalties) / (Sales)

Original ——-> 3/20 * (5/5) = 15/100 = .15


New ————-> 9/108 = 1/12

1/12 = One-half of (1/6)

———> 1/6 = .16666

One-half of (1/6) = .08333


Fractional Decrease = (15 - 8.3) / 15 ~ 7/15

Since 7.5 / 15 is equivalent to 50%

The percentage decrease is going to be just a little less than 50%

(C) 45%





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