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A certain truck uses 1/12 + kv^2 gallons of fuel

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jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
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A certain truck uses 1/12 + kv^2 gallons of fuel

Post Tue Aug 01, 2017 10:11 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A certain truck uses 1/12 + kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?
    (1) The value of k is 1/10,800
    (2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

    Official Guide question
    Answer: D

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    Post Tue Aug 01, 2017 12:25 pm
    Hi jjjinapinch,

    We're told that a truck uses 1/12 + (K)(V^2) gallons of fuel per mile when its speed is V miles per hour and that K is a constant.
    We're asked for the speed at which the truck travels so that it uses 5/12 gallon of fuel per mile.

    To start, we can input the specific 'fuel usage' that the question asks us to deal with into the given equation:

    5/12 = 1/12 + (K)(V^2)

    Thus, to figure out the speed (V), we need to know the constant (K).

    1) The value of K is 1/10,800

    Fact 1 gives us the constant, we can figure out the value of V (and since we can't have a "negative speed", there's only one value for V^2 - the positive one).
    Fact 1 is SUFFICIENT

    2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

    We can plug this information into the equation, which gives us...

    1/6 = 1/2 + (K)(30^2)

    With this equation, we can then solve for K (which we could then plug back into the original question and solve for V).
    Fact 2 is SUFFICIENT

    Final Answer: D

    GMAT assassins aren't born, they're made,
    Rich

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    Post Wed Aug 09, 2017 11:09 am
    jjjinapinch wrote:
    A certain truck uses 1/12 + kv^2 gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses 5/12 gallon of fuel per mile?
    (1) The value of k is 1/10,800
    (2) When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

    Official Guide question
    Answer: D
    We need to determine v when:

    5/12 = 1/12 + kv^2

    4/12 = kv^2

    1/3 = kv^2

    Statement One Alone:

    The value of k is 1/10,800.

    Thus, we have:

    1/3 = (1/10,800)v^2

    3600 = v^2

    60 = v

    Statement one alone is sufficient to answer the question.

    Statement Two Alone:

    When the truck travels at 30 miles per hour, it uses 1/6 gallon of fuel per mile.

    Thus:

    1/6 = 1/12 + k(30)^2

    1/12 = 900k

    1/10,800 = k

    Since we have determined the value of k (the very same value of k in statement one), we can determine v. Statement two alone is sufficient to answer the question.

    Answer: D

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