The cost C, in dollars, to remove p percent of a certain pollutant fro

Question

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 this estimate, how much more would it cost to remove 90 percent of the pollutant from the pond than it would cost to remove 80 percent of the pollutant?

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

Kudos for a correct solution.

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

mcelroytutoring · Accepted Answer

Hi  diegocml , "per cent" means "per hundred." So when I say "90 percent," I am actually saying "90/100". Thus, if you plug the number .9 into this formula, which is already formatted for a percent input (in other words, the equation itself has already taken the division by 100 into account), then it will become .9/100 = .009, which is less than one percent!

Lesson learned : if the question or formula already includes the word "percent," then don't divide by 100, because you will be dividing by 100 twice.

m2k · Answer

It has to be A...

C = (100000*p)/100-p
Here we can check puuting the values for 90 and 80 i.e.

Let 100000 be x so
for 90 its => 90x/10 =>9x ----1

for 80 its => 80x/20 =>4x ------2

Now , subtracting 2 from 1 we get => 9x - 4x = 5x or 5*100000 => 500,000

v12345 · Answer

required cost = (100,000 * 90)/(100 - 90) - (100,000 * 80) /(100 - 80)
 = 100,000 * (90/10 - 80/20)
 = 100,000 * (9 - 4)
 = 100,000 * (5)
 = 500,000
 
answer choice A

ScottTargetTestPrep · Answer

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

mcelroytutoring · Answer

Attached is a visual that should help. In order to solve this question correctly, you must realize that  p  is expressed as a percent and thus should not be converted to a decimal.

diegocml · Answer

After checking the solution for this exercise, it looks quite easy. I just don't understand one thing. Why can I just plug the 90 and the 80 for p in the formula and not 90% (90/100) or 80% (80/100)?

i.e.: 100,000(90/100) / 100 - (90/100)

Thanks a lot.

Diwabag · Answer

Hi  Bunuel  ,

Why not just plug in the difference (10%) into the equation? That's what I did first but I got a wrong answer. I read  Hero8888  's explanation but I don't understand.

How come getting the percent difference here will not work? For me it seems logically sound. Where does this logic go wrong here?

Thanks.

jabhatta2 · Answer

Hi - the only way plugging in 10 % (difference between 90 and 80) will work is if the variable x is attached to ALL elements of the equation ...example below

A) 10 x - (4/5) x --> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer 
 B) 18x + 5x ------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer 
 C) 10 x - 6x --------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer 
 D) 125 x / 6 --------> if you plug in 90 and 80 separately and subtract or just plug in 10 %, you will get the same answer

However If you have the following equation where X is not attached to the constant -- plugging in 10 % will fail 
example :  100  + (x) --> if you plug in 90 and 80 separately and subtract or just plug in 10 , you will get DIFFERENT answers

Logic : when you are subtracting (90 - 80) to give you 10 % --> you are getting rid of the constant within the equation (in above case, 100 in blue color) ..when you plug in 10 %, the constant remains...

In this equation, the numerator has the x attached to it, but the 100 underline does not and thus will fail if you put in just a 10 
 I) 100,000 * X / (  100  -X)

MHIKER · Answer

Don't we think that 90 percent means  \frac{90}{100}=0.90 ?

Hope help from you.

ScottTargetTestPrep · Answer

Solution:

“90 percent” indeed means 90/100 = 0.9; however, we can’t replace p by “90/100”” or “0.9”, each of which is equivalent to “90 percent.” Recall that the sentence describing the formula is “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)”. From the wording of the sentence, we see that “p percent” requires that p be the actual percent value, not its decimal or fractional equivalent.

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=hIKtLe1lYPw

saynchalk · Answer

I still don't get it, please help?

harvinderkaurprep · Answer

Can someone please explain why are we not taking 90/100?

Bunuel · Answer

Check the question:
 
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 this estimate, how much more would it cost to remove  90 percent  of the pollutant from the pond than it would cost to remove  80 percent  of the pollutant?
 
As you can see, the stem mentions "p percent" and then inquires about "90 percent" and "80 percent." Simply substitute p with 90 and 80 to obtain p = 90 and p = 80.

Hope it helps.

harshchougule · Answer

Does it also apply for "%" symbol too?

Bunuel · Answer

Yes, the "%" symbol and the word "percent" mean the same thing, so they are used interchangeably.

Ilanchezhiyan · Answer

Sir, substituted p for 90/100 and 80/100, can you explain why this is wrong

egmat · Answer

Ilanchezhiyan

I completely understand your confusion - converting percentages to decimals (like 90% = 0.9) is the standard approach in most math problems, so your instinct was actually correct for typical situations!

The Key Issue:

In this specific formula  C = \frac{100,000p}{100 - p} , the variable  p  represents the  percentage value itself  (90 or 80), not the decimal form (0.9 or 0.8).

How to Recognize This:

Look at the denominator:  (100 - p)

If we used  p = 0.9 , the denominator would become:  100 - 0.9 = 99.1  ✗ 
 This doesn't make logical sense in the context. The formula is designed so that when removing 90% of pollutant:  100 - 90 = 10  ✓

This represents the remaining 10% of pollutant, which makes the formula meaningful.

Correct Solution:

For 90% removal:  C_{90} = \frac{100,000(90)}{100 - 90} = \frac{9,000,000}{10} = 900,000 
For 80% removal:  C_{80} = \frac{100,000(80)}{100 - 80} = \frac{8,000,000}{20} = 400,000

Difference:  900,000 - 400,000 = 500,000 
 
Quick Check for Future Problems:  When you see a formula with terms like  (100 - p)  or  (1 - p) , check which makes sense:
 
 If it's  (100 - p) , use percentage form (p = 90) 
 If it's  (1 - p) , use decimal form (p = 0.9)  
 
Answer: (A) $500,000

The cost C, in dollars, to remove p percent of a certain pollutant fro

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The cost C, in dollars, to remove p percent of a certain pollutant fro

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