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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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New post 07 Jul 2017, 02:13
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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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New post 07 Jul 2017, 03:35
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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New post 07 Jul 2017, 04:22
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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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New post 08 Jul 2017, 11:43
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.)
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The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 09 Jul 2017, 08:49
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
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 10 Jul 2017, 20:05
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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 :)
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 12 Jul 2017, 16:35
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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
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 11 Aug 2017, 01:30
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?
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 05 Jan 2018, 21:00
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
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Re: The price of a diamond varies inversely with the square of the percent [#permalink]

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New post 06 Jan 2018, 04:33
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

Answer (A)
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Re: The price of a diamond varies inversely with the square of the percent   [#permalink] 06 Jan 2018, 04:33
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