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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