An author receives 10% of the publisher’s net receipts in royalties on

Question

An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter. By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

(A) 2%
(B) 10%
(C) 15%
(D) 20%
(E) 25%

pushpitkc · Answer

For the first 10000 copies, the author receives 10% of the publisher's net receipts in royalties.
The author receives 12% of the publisher's receipts for the next 15000 copies.

If the publisher made 1$ per copy sold, the first 10000 copies would bring in  1000$(\frac{10}{100} * 10000) 
The next 15000 copies would bring in  1800$(\frac{12}{100} * 15000)

The difference is  \frac{1800}{15000} - \frac{1000}{10000} = \frac{3600 - 3000}{30000} = \frac{600}{30000} = \frac{1}{50}

As a percentage, the ratio decreases from the first 10000 to the next 15000 is  (\frac{1}{50})/(\frac{1000}{10000}) = \frac{1}{50} * \frac{10000}{1000} * 100 = 20

Therefore, the percentage by which the ratio decreases from first 10000 to next 15000 is  20 %  (Option D)

generis · Answer

Method I  - Lengthy arithmetic
 (1)  Ratios of royalty percentage to book copies sold?
First set, 10% earned on 10,000 sold:  \frac{0.10}{10,000} 
Next set, 12% earned on 15,000 sold:  \frac{0.12}{15,000}

(2)  Rewrite ratios - LCD of 30,000
 \frac{0.10}{10,000}=\frac{0.3}{30,000}

\frac{0.12}{15,000}=\frac{0.24}{30,000}

(3)  "By what percent does ..." = Percent change (in this case, percent decrease)
 
Percent change:  (\frac{New-Old}{Old}*100) 
Calculate the change, then multiply by 100

\frac{(\frac{0.24}{30,000}-\frac{0.30}{30,000})}{(\frac{0.30}{30,000})}=

\frac{(-\frac{0.06}{30,000})}{(\frac{0.30}{30,000})}=(-\frac{0.06}{30,000}*\frac{30,000}{0.30})=

-\frac{0.06}{0.30}=-\frac{1}{5}=(-0.20*100) =

20  percent decrease

Answer D

Method II.  Faster arithmetic
We can treat ratios as fractions. Make these numbers more manageable. Multiply both ratios by (100*100 = 10,000). Result:
1) Decimal in both numerators moves two places to the right
2) Number in denominators loses 2 zeros, thus we have 
 \frac{10}{100}=\frac{5}{50}  
and 
 \frac{12}{150}=\frac{4}{50}

Percent decrease?  \frac{New-Old}{Old}*100

\frac{(\frac{4}{50}-\frac{5}{50})}{(\frac{5}{50})}=\frac{(-\frac{1}{50})}{(\frac{5}{50})}=(-\frac{1}{50}*\frac{50}{5})=

-\frac{1}{5}=(-0.20*100)=20  percent decrease

Answer D

JeffTargetTestPrep · Answer

The royalty percentage for the first 10,000 copies is:

0.10/10,000 = 10/1,000,000 = 5/500,000

The royalty percentage for the next 15,000 copies is:

0.12/15,000 = 12/1,500,000 4/500,000

The percent decrease is:

(4/500,000 - 5/500,000)/(5/500,000) x 100

(-1/500,000)/(5/500,000) x 100

-1/5 x 100 = -1/5 x 100 = -20 = 20 percent decrease

Answer: D

push12345 · Answer

First 10000 copies(A)= 10/10,000

Next 15000 copies(B)= 12/15,000

(B-A)*100/A
= 20 percent

Posted from my mobile device

AkshdeepS · Answer

Hey Pushpit,

I only understood for first case author receives = $ 1000

and for second he receives = $ 1800

Other than this I am not able to understand. Please see the highlighted part.

Can you explain to me what the question is asking for. Not able to decipher what the question is asking.

Akshdeep

SchruteDwight · Answer

Very unlike any question on the GMAT; too much unnecessary information. To the best of my knowledge, the GMAT does not do that

IanStewart · Answer

The author makes 10% on the first 10,000 copies, then 12% on the next 15,000 copies. We want to know the percent decrease going from 10/10,000 to 12/15,000, or from 5/5,000 to 4/5,000. We're just dealing with ratios, so we can multiply everything by whatever we want. So we'll have the same percent decrease going from 5 to 4, and the percent decrease is 1/5 = 20%.

Kinshook · Answer

Given:  An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold, 12% on the next 15,000 copies sold, and 15% on all copies sold thereafter.

Asked:  By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies?

An author receives 10% of the publisher’s net receipts in royalties on the first 10,000 copies of the author’s book sold
The ratio of the royalty percentage to number of copies = 10% / 10,000

An author receives 12% on the next 15,000 copies
The ratio of the royalty percentage to number of copies = 12% / 15,000

By what percent does the ratio of the royalty percentage to number of copies decrease from the first 10,000 copies to the next 15,000 copies  =\frac{\frac{12\%}{15,000} - \frac{10\%}{10,000}}{\frac{10\%}{10,000}}=\frac{8- 10}{10} = -20\%

IMO D

Kinshook · Answer

shahkevin99  Please see the solution for the question in PM

KarishmaB · Answer

Ratio of royalty percentage to number of copies in first case = 10/10,000 = 1/1000 = 15/15,000 (to make it comparable)
Ratio of royalty percentage to number of copies in second case = 12/15,000

So the ratio goes from 15/15000 to 12/15000. What percentage reduction is this? Since we are looking for percentage reduction, we can ignore the common denominator since it will anyway get cancelled to get (15 - 12)/15 * 100 = 20%

Answer (D)

If you are unsure, see this  \frac{\frac{15}{15000} - \frac{12}{15000}}{\frac{15}{15000} } * 100 = \frac{15 - 12}{15} * 100 = 20%

sayan640 · Answer

10/(100)*(10000) = m

12/(100)*(15000) = n

n/ m  = 120/150

Percentage decrease = (m-n)/ m * 100
                              = (1 - n/m )* 100 
                              = (1- 120/150) * 100
                             = (1-4/5) * 100
                               = 1/5 * 100 = 20%  ANs .  GMATinsight

pierjoejoe · Answer

i was solving this problem thinking that i needed to consider the royalties on ALL the copied sold up to 25.000 (first 10.000 and next 15.000)
in that case the royalties are

first 10.000 --> (10%*10000)/10.000 = 10%
next 15.000 --> (10%*10.000+12%*15000)/25.000 = 2800/25000 = 11.2%

so we have a absolute increase of 1.2%, with respect to the royalties of the first 10.000 we would have had --> 1.2%/10% = 12% increase

but  instead the problem was simply asking for the increase from the royalties in the first 10.000 (10%) to the royalties in the next 15.000 (12%)

--> (12% - 10%)/10% = 2%/10% = 1/50 / 1/10 = 1/5 = 20%

bumpbot · Answer

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An author receives 10% of the publisher’s net receipts in royalties on

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