Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register

BTG flashcards problem

This topic has 2 expert replies and 0 member replies
sparkles3144 Really wants to Beat The GMAT! Default Avatar
Joined
18 Jan 2013
Posted:
145 messages
Thanked:
7 times
BTG flashcards problem Post Sun Jun 15, 2014 1:09 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?

    Answer 14

    I disagree with the answer.
    Can someone show steps?

    Thanks!

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Jun 15, 2014 2:02 am
    Quote:
    How many liters of a solution that is
    10% alcohol by volume must be added
    to 2 liters of a solution that is 50%
    alcohol by volume to create a solution
    that is 15% alcohol by volume?
    A) 10
    B) 12
    C) 14
    D) 16
    E) 18
    We can use ALLIGATION -- a great way to handle MIXTURE PROBLEMS.

    Let X = the 10% solution and Y = the 50% solution.

    Step 1: Plot the 3 percentages on a number line, with the percentages for X and Y on the ends and the percentage for the mixture in the middle.
    X 10------------15------------50 Y

    Step 2: Calculate the distances between the percentages.
    X 10-----5-----15-----35-----50 Y

    Step 3: Determine the ratio in the mixture.
    The required ratio of X to Y is equal to the RECIPROCAL of the distances in red.
    X:Y = 35:5 = 7:1.

    Since X:Y = 7:1 = 14:2, 14 liters of X must be added to 2 liters of Y.

    The correct answer is C.

    An alternate approach is to PLUG IN THE ANSWERS, which represent the amount of 10% solution that must be added to 2 liters of 50% solution.

    Answer choice C: 14 liters
    Amount of alcohol in 14 liters of 10% solution = 10% of 14 = 1.4 liters.
    Amount of alcohol in 2 liters of 50% solution = 50% of 2 = 1 liter.
    (total alcohol)/(total volume) = (1.4 + 1)/(14 + 2) = (2.4)/16 = 24/160 = 3/20 = 15/100 = 15%.
    Success!

    The correct answer is C.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
    If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
    Available for tutoring in NYC and long-distance.
    For more information, please email me at GMATGuruNY@gmail.com.

    Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
    Post Sun Jun 15, 2014 5:06 am
    Quote:
    How many liters of a solution that is 10% alcohol by volume must be added to 2 liters of a solution that is 50% alcohol by volume to create a solution that is 15% alcohol by volume?
    A) 10
    B) 12
    C) 14
    D) 16
    E) 18
    When solving mixture questions, I find it useful to sketch the solutions with the ingredients SEPARATED.

    Start with 2 liters of solution that is 50% alcohol:

    When we draw this with the ingredients separated, we see we have 1 liter of alcohol in the mixture.


    Next, we'll let x = the number of liters of 10% solution we need to add.
    Since 10% of the mixture is alcohol, we know that 0.1x = the volume of alcohol in this solution:


    At this point, we can add the two solutions to get the following volumes:


    Since the resulting solution is 15% alcohol (i.e., 15/100 of the solution is alcohol), we can write the following equation:
    (1 + 0.1x)/(2 + x) = 15/100
    Simplify to get: (1 + 0.1x)/(2 + x) = 3/20
    Cross multiply to get: 20(1 + 0.1x) = 3(2 + x)
    Expand: 20 + 2x = 6 + 3x
    Rearrange/solve: 14 = x

    Answer: C

    Cheers,
    Brent

    Here are some additional mixture questions to practice with:
    http://www.beatthegmat.com/liters-of-mixture-x-in-the-50-mixture-t271387.html
    http://www.beatthegmat.com/percentage-mixture-t268631.html
    http://www.beatthegmat.com/rodrick-mixes-a-martini-that-has-a-volume-of-n-ounces-havi-t270387.html
    http://www.beatthegmat.com/mixure-problem-quite-confusing-t261767.html
    http://www.beatthegmat.com/mixture-ratio-problem-2-t191643.html

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Enter our contest to win a free course.

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

    Best Conversation Starters

    1 Mo2men 21 topics
    2 neeti2711 16 topics
    3 ziyuenlau 14 topics
    4 Donna@Stratus 9 topics
    5 vikkimba17 8 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    84 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    82 posts
    3 image description Rich.C@EMPOWERgma...

    EMPOWERgmat

    81 posts
    4 image description Matt@VeritasPrep

    Veritas Prep

    80 posts
    5 image description DavidG@VeritasPrep

    Veritas Prep

    70 posts
    See More Top Beat The GMAT Experts