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

Question

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

(A) $400
(B) $500
(C) $1000
(D) $4000
(E) $8000

TimeTraveller · Accepted Answer

p = k/(impurity)^2
2500 = k/(0.02)^2
k = 1

p = 1/(o.o5)^2
p = 1/0.0025 = 400. Ans - A.

JeffTargetTestPrep · Answer

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

jedit · Answer

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.

generis · Answer

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.) 
 
 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.)

mohshu · Answer

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

Blackbox · Answer

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

pclawong · Answer

For this part that you did  0.025/0.04 = 6.25. ,
Do you actually mean--> 0.0025/ 0.0004?

luffy_ueki · Answer

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

KarishmaB · Answer

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)

Rajat1998 · Answer

I think my way is a little simpler

2500*0.2*0.2 = c*0.5*0.5

C= 2500*2*2/5*5 = 400

Posted from my mobile device

Sreeragc · Answer

Even i got this answer in these simple steps and wonder is this really a 700+ question as its categorized as one. I've just started the preparations and really don't know where each questions ranges in. This question seems rather simple comparatively, so is this a 700+ question or 600+ question? Just curious to set the standards and any help will be much appreciated.

Thanks.

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

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