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The cost C

by shahfahad » Thu Nov 26, 2015 1:52 am
The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C=100,000p/100-p. According to the estimate, how much more would it cost to remove 90% of the pollutant from the pond than it would cost to remove 80% of the pollutant?

(A) $500,000
(B) $100,000
(C) $50,000
(D) $10,000
(E) $5,000

I solved the question first with 90%-80% = 10% method but it did not work. Then i calculated them separately and subtracted them and got the right answer. Why doesn't the 10% value works as it is the difference between 90 and 80%.
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by [email protected] » Thu Nov 26, 2015 11:07 am
Hi shahfahad,

If the question expected you to just subtract 80% from 90%, then none of that other information would have been provided. This is an example of a 'Symbolism' question - you're given a formula, and told what it means, and then you're expected to perform a calculation or two with it.

The reason why you won't get the correct answer by just subtracting the percents is that those two values impact the given equation in different ways (consider how the denominator changes relative to the numerator when you plug in 80% vs. 90%).

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by Brent@GMATPrepNow » Thu Nov 26, 2015 12:08 pm
shahfahad wrote:The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C=100,000p/(100-p). According to the estimate, how much more would it cost to remove 90% of the pollutant from the pond than it would cost to remove 80% of the pollutant?

(A) $500,000
(B) $100,000
(C) $50,000
(D) $10,000
(E) $5,000
Cost to remove 90%
p = 90
So, cost = 100,000(90)/(100-90)
= 9,000,000/10 = 900,000

Cost to remove 80%
p = 80
So, cost = 100,000(80)/(100-80)
= 8,000,000/20 = 400,000

DIFFERENCE = 900,000 - 400,000 = [spoiler]$500,000[/spoiler]

Answer: A

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by Matt@VeritasPrep » Thu Nov 26, 2015 11:54 pm
We've got

100,000(90)/(100 - 90) - 100,000(80)/(100 - 80),

or

100,000 * (90/10 - 80/20)

or

100,000 * (9 - 4),

so it's A.
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by rqmantovani » Mon Aug 01, 2016 8:19 am
If p is 90%, why p=90? Shouldn't it be 0.9?
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by [email protected] » Mon Aug 01, 2016 9:18 am
Hi rqmantovani,

The given equation expects us to plug in a value for P. The variable "P" will have to be a number (between 0 and 100, inclusive) since it's described in the context of "...P percent of a certain pollutant..."

IF... P = 90, then the sentence reads.... "to remove 90 percent of a certain pollutant..."
IF...P = .9, then the sentence reads... "to remove .9 percent of a certain pollutant..."

Given the wording of the rest of the prompt, we're expected to plug in P = 90 (and also P = 80) and complete the given calculations.

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by Jeff@TargetTestPrep » Mon Aug 01, 2016 3:38 pm
shahfahad wrote:The cost C, in dollars, to remove p percent of a certain pollutant from a pond is estimated by using the formula C=100,000p/100-p. According to the estimate, how much more would it cost to remove 90% of the pollutant from the pond than it would cost to remove 80% of the pollutant?

(A) $500,000
(B) $100,000
(C) $50,000
(D) $10,000
(E) $5,000
Here is my take:

The cost to remove 90 percent of the pollutant is determined by letting p = 90 in the cost formula:

100,000(90)/(100 - 90) = 9,000,000/10 = 900,000

Similarly, the cost to remove 80 percent of the pollutant is determined by letting p = 80 in the cost formula:

100,000(80)/(100 - 80) = 8,000,000/20 = 400,000

To determine how much more it costs to remove 90 percent of the pollutant than 80 percent of the pollutant, we calculate the difference of the two costs:

900,000 - 400,000 = 500,000

Answer: A

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by Matt@VeritasPrep » Thu Aug 04, 2016 8:39 pm
rqmantovani wrote:If p is 90%, why p=90? Shouldn't it be 0.9?
Since the stem gives it to us as "p percent", and we want "90 percent", we have p = 90, not p = .9. (Be careful not to convert to percentages if the word 'percent' is already attached to the variable!)
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