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Register now and save up to $200 Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code ## Jackie has two solutions (OG20160 tagged by: Brent@GMATPrepNow This topic has 8 expert replies and 1 member reply boomgoesthegmat Senior | Next Rank: 100 Posts Joined 25 Apr 2016 Posted: 93 messages Upvotes: 1 #### Jackie has two solutions (OG20160 Fri May 06, 2016 12:34 pm 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 ### GMAT/MBA Expert Scott@TargetTestPrep GMAT Instructor Joined 25 Apr 2015 Posted: 773 messages Followed by: 3 members Upvotes: 43 Fri Jan 05, 2018 6:35 am 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 We can let the amount of 2% sulfuric acid solution = x and the amount of 12% sulfuric acid solution = y. Thus: 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 ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11275 messages Followed by: 1225 members Upvotes: 5254 GMAT Score: 770 Fri Jan 05, 2018 7:17 am 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 Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... 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 _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 11275 messages Followed by: 1225 members Upvotes: 5254 GMAT Score: 770 Sat May 07, 2016 6:54 am 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 Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ... 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: http://www.gmatprepnow.com/module/gmat-statistics?id=805 Here are some additional practice questions related to weighted averages: - http://www.beatthegmat.com/weighted-averages-t117237.html - http://www.beatthegmat.com/weighted-average-t114506.html - http://www.beatthegmat.com/average-weight-of-men-and-women-t57853.html - http://www.beatthegmat.com/averages-question-t87118.html Cheers, Brent _________________ Brent Hanneson â€“ Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Matt@VeritasPrep GMAT Instructor Joined 12 Sep 2012 Posted: 2640 messages Followed by: 113 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Thu May 12, 2016 12:38 am 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. Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Gurpreet singh Senior | Next Rank: 100 Posts Joined 28 Apr 2016 Posted: 38 messages Upvotes: 1 Mon Jun 20, 2016 11:41 pm 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 DavidG@VeritasPrep Legendary Member Joined 14 Jan 2015 Posted: 2613 messages Followed by: 118 members Upvotes: 1153 GMAT Score: 770 Tue Jun 21, 2016 4:34 am 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 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. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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Tue Jun 21, 2016 5:22 am
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
5% of 60 liters = (5/100)(60) = 3 liters of sulfuric acid.
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.

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Thu Jun 23, 2016 4:08 pm
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
You've got the right idea for sure, but that line is red would need to be revised.

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Brent@GMATPrepNow GMAT Instructor
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Fri Jan 05, 2018 7:18 am
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
Another approach is to keep track of the acid
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

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