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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)?

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

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

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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.)

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

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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)

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

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10 Jul 2017, 20:05

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

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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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

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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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