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Jackie has two solutions (OG20160

This topic has 5 expert replies and 1 member reply
boomgoesthegmat Senior | Next Rank: 100 Posts Default Avatar
Joined
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Jackie has two solutions (OG20160

Post Fri May 06, 2016 12:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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

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    Post 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

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    Post 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.

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    Gurpreet singh Senior | Next Rank: 100 Posts Default Avatar
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    Post 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

    Post 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.

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    Post 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.

    The correct answer is E.

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    GMAT/MBA Expert

    Post 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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