Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
Jackie has two solutions (OG20160
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 93
- Joined: Mon Apr 25, 2016 2:22 pm
- Thanked: 1 times
- Followed by:1 members
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
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...boomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
Let x be the number of liters of 2% solution in the mixture
Since there are 60 liters in total, 60 - x will equal number of liters of 12% solution in the mixture
Now apply the formula:
5 = (x/60)(2) + [(60-x)/60](12)
Multiply both sides by 60 to get: 300 = 2x + (60-x)(12)
Expand: 300 = 2x + 720 - 12x
Rearrange: -420 = -10x
Solve: x = 42
Answer: E
For more information on weighted averages, you can watch this video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805
Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-av ... 17237.html
- https://www.beatthegmat.com/weighted-av ... 14506.html
- https://www.beatthegmat.com/average-wei ... 57853.html
- https://www.beatthegmat.com/averages-qu ... 87118.html
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
x + y = 60
and
.02x + .12y = .05*(x + y)
The second equation simplifies to 7y = 3x, or y = (3/7)x. Plugging that into the first gives
x + (3/7)x = 60, or x = 42.
and
.02x + .12y = .05*(x + y)
The second equation simplifies to 7y = 3x, or y = (3/7)x. Plugging that into the first gives
x + (3/7)x = 60, or x = 42.
-
- Senior | Next Rank: 100 Posts
- Posts: 38
- Joined: Thu Apr 28, 2016 7:17 pm
- Thanked: 1 times
Use allegation method for faster results
2-------------5--------------12
(Sol a) (Combined) (Sol b)
subtract 2 from 5 and 12 from 5 also ignore the signs and keep the result in opp direction
ie
2-------------5--------------12
(Sol a)=7 (Combined) (Sol b)=3
This gives you the ratio of the mixed sol ie 7:3.
Total sol is 60 also let the total sol be x
10(7+3)x=60 or x=6
multiply 7 by 6=42
2-------------5--------------12
(Sol a) (Combined) (Sol b)
subtract 2 from 5 and 12 from 5 also ignore the signs and keep the result in opp direction
ie
2-------------5--------------12
(Sol a)=7 (Combined) (Sol b)=3
This gives you the ratio of the mixed sol ie 7:3.
Total sol is 60 also let the total sol be x
10(7+3)x=60 or x=6
multiply 7 by 6=42
- DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
Or just use a little good old-fashioned logic. If the combined solution is 5%, you're going to have more than twice as much of the 2% solution as you will of the 12% solution. (5 is 3 units away from 2, and 7 units away from 12. 7/3 > 2. If you tested D, you'd have 36 liters of the 2% solution and 24 liters of the 12% solution, so 36 is too small, as it's not more than twice as much as 24. The answer must be larger than 36, so it's E.boomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
5% of 60 liters = (5/100)(60) = 3 liters of sulfuric acid.boomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
An alternate approach is to PLUG IN THE ANSWERS, which represent the amount of 2-percent solution in the mixture.
When the correct answer choice is plugged in, the total amount of sulfuric acid = 3 liters.
D: 36 liters of 2-percent solution, implying 24 liters of 12-percent solution
Total sulfuric acid = (2/100)(36) + (12/100)(24) = (18/25) + (72/25) = 90/25 = more than 3 liters.
The total amount of sulfuric acid is TOO HIGH.
Eliminate D.
To reduce the amount of sulfuric acid in the mixture, we must use MORE 2-percent solution, which contains LESS sulfuric acid than does the 12-percent solution.
The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
- 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
You've got the right idea for sure, but that line is red would need to be revised.Gurpreet singh wrote:Use allegation method for faster results
2-------------5--------------12
(Sol a) (Combined) (Sol b)
subtract 2 from 5 and 12 from 5 also ignore the signs and keep the result in opp direction
ie
2-------------5--------------12
(Sol a)=7 (Combined) (Sol b)=3
This gives you the ratio of the mixed sol ie 7:3.
Total sol is 60 also let the total sol be x
10(7+3)x=60 or x=6
multiply 7 by 6=42
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let the amount of 2% sulfuric acid solution = x and the amount of 12% sulfuric acid solution = y. Thus:boomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
x + y = 60
y = 60 - x
and
0.02x + 0.12y = 0.05(x + y)
2x + 12y = 5x + 5y
7y = 3x
Thus:
7(60 - x) = 3x
420 - 7x = 3x
420 = 10x
42 = x
Alternate Solution:
We will mix x liters of 2% sulfuric acid with (60 - x) liters of 12% sulfuric acid to produce 60 liters of 5% sulfuric acid. We can create an equation from this information and solve for x:
0.02x + 0.12(60 - x) = (0.05)(60)
0.02x + 7.2 - 0.12x = 3
-0.10x = -4.2
x = 42
Answer: E
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
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
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...boomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
Let x be the number of liters of 2% solution in the mixture
Since there are 60 liters in total, 60 - x will equal number of liters of 12% solution in the mixture
Now apply the formula:
5 = (x/60)(2) + [(60-x)/60](12)
Multiply both sides by 60 to get: 300 = 2x + (60-x)(12)
Expand: 300 = 2x + 720 - 12x
Rearrange: -420 = -10x
Solve: x = 42
Answer: E
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
Another approach is to keep track of the acidboomgoesthegmat wrote:Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid, approximately how many liters of the 2 percent solution will be required?
A) 18
B) 20
C) 24
D) 36
E) 42
OA: E
Let x = number of liters of 2% solution needed
So, 60 - x = number of liters of 12% solution needed
2% of x = 0.02x
So, 0.02x = the number of liters of PURE acid in the 2% solution
12% of 60 - x = 0.12(60 - x) = 7.2 - 0.12x
So, 7.2 - 0.12x = the number of liters of PURE acid in the 12% solution
Now let's COMBINE the two solutions.
Total volume of PURE acid = 0.02x + 7.2 - 0.12x
= 7.2 - 0.1x
So, our NEW solution contains 7.2 - 0.1x liters of PURE acid
Also, the NEW solution has a total volume of 60 liters
Since the NEW solution is 5% PURE acid, we can write: (7.2 - 0.1x)/60 = 5/100
Cross multiply to get: 100(7.2 - 0.1x) = 5(60)
Expand: 720 - 10x = 300
Add 10 x to both sides: 720 = 300 + 10x
Subtract 300 from both sides: 420 = 10x
Solve: x = 42
Answer: E
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 All,
This is essentially a Weighted Average question, but it can be solved in a variety of different ways. Since the answer choices are "spread out" numbers, there's actually a great 'brute force' approach that you can use to logically answer this question without doing that much math.
We're told to mix a 2% acid solution with a 12% acid solution and end up with 60 LITERS of 5% acid solution. We're asked how many liters (of the 60) would be the 2% solution.
IF....
we had 1 liter of each solution, then the acidity of the mixture would be (2% + 12%)/2 = 7%.... this is clearly too high (it's supposed to be 5%), so we need MORE of the 2% mixture.
IF....
we had 2 liters of the 2% solution and 1 liter of the 12% solution, then the acidity of the mixture would be (2% + 2% + 12%)/3 = 16/3% = 5 1/3%.... this is also clearly too high (it's supposed to be 5%), so we need even MORE of the 2% mixture. In this example, it's worth noting that 2/3 of the mixture is the 2% solution.
Since we need even MORE of that solution, we need MORE than 2/3 of the total to be that 2% mixture. There's only one answer that's more than 2/3 of 60....
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
This is essentially a Weighted Average question, but it can be solved in a variety of different ways. Since the answer choices are "spread out" numbers, there's actually a great 'brute force' approach that you can use to logically answer this question without doing that much math.
We're told to mix a 2% acid solution with a 12% acid solution and end up with 60 LITERS of 5% acid solution. We're asked how many liters (of the 60) would be the 2% solution.
IF....
we had 1 liter of each solution, then the acidity of the mixture would be (2% + 12%)/2 = 7%.... this is clearly too high (it's supposed to be 5%), so we need MORE of the 2% mixture.
IF....
we had 2 liters of the 2% solution and 1 liter of the 12% solution, then the acidity of the mixture would be (2% + 2% + 12%)/3 = 16/3% = 5 1/3%.... this is also clearly too high (it's supposed to be 5%), so we need even MORE of the 2% mixture. In this example, it's worth noting that 2/3 of the mixture is the 2% solution.
Since we need even MORE of that solution, we need MORE than 2/3 of the total to be that 2% mixture. There's only one answer that's more than 2/3 of 60....
Final Answer: E
GMAT assassins aren't born, they're made,
Rich