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%.
The cost C
This topic has expert replies
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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%).
GMAT assassins aren't born, they're made,
Rich
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%).
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Cost to remove 90%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
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
Cheers,
Brent
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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.
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.
- rqmantovani
- Newbie | Next Rank: 10 Posts
- Posts: 1
- Joined: Sun Jan 11, 2015 1:18 pm
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
Here is my take: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
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
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
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!)rqmantovani wrote:If p is 90%, why p=90? Shouldn't it be 0.9?