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The price of a diamond varies inversely with the square of the percent

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The price of a diamond varies inversely with the square of the percent [#permalink]

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07 Jul 2017, 01:13
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The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)? (A)$400
(B) $500 (C)$1000
(D) $4000 (E)$8000
[Reveal] Spoiler: OA

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The price of a diamond varies inversely with the square of the percent [#permalink]

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07 Jul 2017, 02:35
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)? (A)$400
(B) $500 (C)$1000
(D) $4000 (E)$8000

It should be A.

P is proportional to square of impurities.

First Diamond
$$0.02^2 = 0.0004$$

Second Diamond
$$0.05^2 = 0.025$$

Ratio of square of increase in impurities = $$0.025/0.04 = 6.25.$$

Price of diamond would decrease by the same ratio -> $$2500/6.25 = 400$$

This is a very crude calculation and I would appreciate someone providing a proper mathematical equation for this.
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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07 Jul 2017, 03:22
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p = k/(impurity)^2
2500 = k/(0.02)^2
k = 1

p = 1/(o.o5)^2
p = 1/0.0025 = 400. Ans - A.
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The price of a diamond varies inversely with the square of the percent [#permalink]

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08 Jul 2017, 10:43
Bunuel wrote:
The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is $2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)? (A)$400
(B) $500 (C)$1000
(D) $4000 (E)$8000

Hmm. I got D. I translated .02% to .0002. (Initially I got A, but then it occurred to me that the problem says .02% -- not .02.)
Quote:
The price of a diamond varies inversely with the square of the percentage of impurities

1. Where P is price, k is constant, and x is the square of the percentage of impurities

$$P = \frac{k}{x}$$, or $$P*x = k$$

2. Find k from "the cost of a diamond with .02% impurities is $2500." .02% = $$.0002$$, and $$(.0002)^2 = .00000004$$, or $$4 * 10^{-8}$$, thus: $$2500 * 4 * 10^{-8} = .001$$ = $$k$$ 3. What is the cost of a diamond with 0.05% impurities? Start with x. .05% = .0005 $$x = (.0005)^2$$ = $$.00000025$$, or $$25 * 10^{-8}$$ 4. Find price. $$P = \frac{k}{x}$$ Make k easier to work with: .001 = $$100 * 10^{-5}$$ P = $$100 * 10^{-5}$$ / $$25 * 10^{-8}$$ = $$4 * 10^{-5 - (-8)}$$ = $$4 * 10^3 = 4,000$$ Answer D? (Seems a little odd that a larger percentage of impurities -- prior to squaring -- would yield a more expensive diamond. Once squared, however, .05% impurities < .02% impurities.) _________________ At the still point, there the dance is. -- T.S. Eliot Formerly genxer123 Director Joined: 21 Mar 2016 Posts: 549 The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 09 Jul 2017, 07:49 Bunuel wrote: The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is$2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400 (B)$500
(C) $1000 (D)$4000
(E) $8000 can be solved with ratios.. let the price be x 2500 -->> 1/0.0004 ..(1) x--> 1/0.0025 ..(2) divide both the equations 2500/x = 25/4 x = 2500 *4 /25 x = 400 ans A Manager Joined: 30 May 2012 Posts: 217 Location: United States (TX) Concentration: Finance, Marketing GPA: 3.3 WE: Information Technology (Consulting) Re: The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 10 Jul 2017, 19:05 1 This post received KUDOS Here's how I solved it: Given, price of the diamond decreases as the square of impurities increase. $$Diamond_{0.0004%}$$ = 2500 So, obviously if the impurities increase, the price MUST be less than 2500. So, rule out option D and E Now, how much of 0.0004 is 0.0025 [I have squared both the impurities as per the given info]? That will be 6.25. In other words, if you multiplied 0.0004 by 6.25, you will get 0.0025. Since, the price and impurities and inversely proportional - I will divide the price by 6.25 $$Diamond_{0.0025%}$$ = $$\frac{2500}{6.25}$$, which is 400. Hope what I did was correct Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 1835 Re: The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 12 Jul 2017, 15:35 3 This post received KUDOS Expert's post Bunuel wrote: The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is$2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400 (B)$500
(C) $1000 (D)$4000
(E) $8000 We can let k = the constant of proportionality, and we have: k/(0.0002)^2 = 2500 k/0.00000004 = 2500 k = 0.0001 Thus: 0.0001/(0.0005)^2 = 0.0001/0.00000025 = 400 Answer: A _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Manager Joined: 07 Jun 2017 Posts: 109 Re: The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 11 Aug 2017, 00:30 jedit wrote: Bunuel wrote: The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is$2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400 (B)$500
(C) $1000 (D)$4000
(E) $8000 It should be A. P is proportional to square of impurities. First Diamond $$0.02^2 = 0.0004$$ Second Diamond $$0.05^2 = 0.025$$ Ratio of square of increase in impurities = $$0.025/0.04 = 6.25.$$ Price of diamond would decrease by the same ratio -> $$2500/6.25 = 400$$ This is a very crude calculation and I would appreciate someone providing a proper mathematical equation for this. For this part that you did $$0.025/0.04 = 6.25.$$, Do you actually mean--> 0.0025/ 0.0004? Manager Joined: 23 Oct 2017 Posts: 63 Re: The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 05 Jan 2018, 20:00 Based on the question: price = k/(i*i) where i = % of impurities and k = some constant Now substituing values: 2500 = k/(0.02*0.02) For 0.05 % impurity, let the price be x x = k/(0.05*0.05) On solving, k gets out of the picture 2500/x = 25/4 x= 400 Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7878 Location: Pune, India Re: The price of a diamond varies inversely with the square of the percent [#permalink] Show Tags 06 Jan 2018, 03:33 Bunuel wrote: The price of a diamond varies inversely with the square of the percentage of impurities. The cost of a diamond with 0.02% impurities is$2500. What is the cost of a diamond with 0.05% impurities (keeping everything else constant)?

(A) $400 (B)$500
(C) $1000 (D)$4000
(E) $8000 Since price varies inversely as square of impurities, their product will be constant: Price * Impurities^2 = k 2500 * (.02)^2 = k = P2 * (.05)^2 P2 =$400

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Re: The price of a diamond varies inversely with the square of the percent   [#permalink] 06 Jan 2018, 03:33
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