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Ratio Problem

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vinay1983 GMAT Destroyer!
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Ratio Problem Post Mon Aug 19, 2013 1:42 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    This is the question:

    Of the new vehicles registered in a week, 300 were neither SUVs nor were they powered by diesel. 3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs. If SUVs not powered by diesel were a sixth of non SUVs not powered by diesel, how many vehicles registered in the week were powered by diesel?
    A. 200
    B. 50
    C. 250
    D. 150
    E. 400


    Vinay

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    Post Mon Aug 19, 2013 3:08 am
    vinay1983 wrote:
    This is the question:

    Of the new vehicles registered in a week, 300 were neither SUVs nor were they powered by diesel. 3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs. If SUVs not powered by diesel were a sixth of non SUVs not powered by diesel, how many vehicles registered in the week were powered by diesel?
    A. 200
    B. 50
    C. 250
    D. 150
    E. 400
    This is an EITHER/OR problem.
    Every vehicle is EITHER an SUV OR a non-SUV.
    Every vehicle is EITHER diesel OR non-diesel.
    Use a GROUP GRID (also known as a double-matrix) to organize the data.
    The key to the grid is the following:
    The values in any row or column must add up to the TOTAL of that row or column.

    300 were neither SUVs nor were they powered by diesel:


    3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs.
    Let total SUVs = 4x.
    Since 3/4 of the SUVs are diesel, diesel SUVs = (3/4)(4x) = x.
    Since there 1/2 as many SUVs as non-SUVs, non-SUVs = 8x.
    Enter this information into the grid:


    SUVs not powered by diesel were a sixth of non SUVs not powered by diesel.
    Thus, the x SUVS that are not diesel are equal to 1/6 of the 300 non-SUVS that are not diesel:
    x = 1/6 * 300
    x = 50.
    Resulting grid:


    Total diesels = 250.

    The correct answer is C.

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    Last edited by GMATGuruNY on Mon Aug 19, 2013 1:30 pm; edited 1 time in total

    Thanked by: tarik, sakre
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    Post Mon Aug 19, 2013 5:44 am
    vinay1983 wrote:
    This is the question:

    Of the new vehicles registered in a week, 300 were neither SUVs nor were they powered by diesel. 3/4th of the SUVs registered were diesel powered and there were half as many SUVs as there were non SUVs. If SUVs not powered by diesel were a sixth of non SUVs not powered by diesel, how many vehicles registered in the week were powered by diesel?
    A. 200
    B. 50
    C. 250
    D. 150
    E. 400

    I thought I'd point out that Mitch's "group grid" approach (aka "Double Matrix Method") can be used for most questions featuring a population in which each member has two characteristics associated with it (e.g., diesel and SUV)

    To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

    Then try these additional practice questions that can be solved using the Double Matrix Method:
    - http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
    - http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
    - http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
    - http://www.beatthegmat.com/ds-quest-t187706.html
    - http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
    - http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
    - http://www.beatthegmat.com/ds-french-japanese-t222297.html

    Cheers,
    Brent

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    tarik Rising GMAT Star Default Avatar
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    Posted:
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    Post Mon Aug 19, 2013 1:03 pm
    Thank you for the explanation. I will try to use this technique for similar problem

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