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

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An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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18 Apr 2018, 18:20
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35% (medium)

Question Stats:

72% (02:13) correct 28% (02:26) wrong based on 87 sessions

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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%

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An author receives 10% of the publisher’s net receipts in royalties on  [#permalink]

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19 Apr 2018, 00:37
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Bunuel wrote:
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%

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) _________________ You've got what it takes, but it will take everything you've got Senior SC Moderator Joined: 22 May 2016 Posts: 2033 An author receives 10% of the publisher’s net receipts in royalties on [#permalink] ### Show Tags 19 Apr 2018, 01:31 Bunuel wrote: 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% 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 _________________ The only thing more dangerous than ignorance is arrogance. -- Albert Einstein Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2830 Re: An author receives 10% of the publisher’s net receipts in royalties on [#permalink] ### Show Tags 23 Apr 2018, 16:52 Bunuel wrote: 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% 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 _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Director Joined: 02 Oct 2017 Posts: 645 Re: An author receives 10% of the publisher’s net receipts in royalties on [#permalink] ### Show Tags 05 May 2018, 07:48 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 _________________ Give kudos if you like the post VP Status: It's near - I can see. Joined: 13 Apr 2013 Posts: 1265 Location: India Concentration: International Business, Operations GMAT 1: 480 Q38 V22 GPA: 3.01 WE: Engineering (Consulting) Re: An author receives 10% of the publisher’s net receipts in royalties on [#permalink] ### Show Tags 02 Aug 2018, 00:00 pushpitkc wrote: Bunuel wrote: 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% 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
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Re: An author receives 10% of the publisher’s net receipts in royalties on &nbs [#permalink] 02 Aug 2018, 00:00
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