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GMAT PREP PS Problem

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alex.gellatly GMAT Destroyer! Default Avatar
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GMAT PREP PS Problem Post Sat Apr 21, 2012 5:05 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    (A) 25%
    (B) 33 1/3%
    (C) 50%
    (D) 66 2/3%
    (E) 75%

    Thanks

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    Post Sat Apr 21, 2012 6:45 am
    In 8 hours, the faster machine will seal 2k cartons and the slower machine will seal k cartons

    Total sealed = 3k.

    Percentage sealed by the faster machine = 2k/3k = 66 2/3%.

    Hence, D!

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    Post Sat Apr 21, 2012 7:33 am
    In any period of time, the second machine seals double the number cartons than the first machine.
    If, in a certain period of time, the first machine seals 'x' number of machines, the second machine will seal '2x' number of machines.

    Percent of cartons sealed by the second machine = (Number of cartons sealed by the second machine)/ (Total number of cartons sealed)
    = (2x)/(2x + x)]*100
    = 66 2/3 %

    [D] is the answer

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    Brent@GMATPrepNow GMAT Instructor
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    Post Sat Apr 21, 2012 11:02 am
    alex.gellatly wrote:
    Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    (A) 25%
    (B) 33 1/3%
    (C) 50%
    (D) 66 2/3%
    (E) 75%

    Thanks
    We can also solve this question by plugging in a convenient value for k.

    Let's say that k=8.
    So, the slower machine seals 8 cartons in 8 hours, which means it seals 1 carton per hour.
    This also means that the faster machine seals 8 cartons in 2 hours, which means it seals 2 carton per hour.

    Now the question considers a scenario in which the 2 machines, working together, and for the same period of time, sealed a certain number of cartons.

    Well, let's say they worked for one hour.
    This means they sealed a total of 3 cartons, and the faster machine sealed 2 of those cartons.
    So, the faster machine sealed 2/3 (66 2/3%) of the cartons.

    So, the answer is D

    Cheers,
    Brent

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    Post Sun Apr 22, 2012 6:50 pm
    alex.gellatly wrote:
    Working alone at its own constant rate, a machine seals k cartons in 8 hours, and working alone at its own constant rate, a second machine seals k cartons in 4 hours. If the two machines, each working at its own constant rate and for the same period of time, together sealed a certain number of cartons, what percent of the cartons were sealed by the machine working at the faster rate?

    (A) 25%
    (B) 33 1/3%
    (C) 50%
    (D) 66 2/3%
    (E) 75%

    Thanks
    1st machine seals k cartons in 8 hours.
    2nd machine seals k cartons in 4 hours OR 2k cartons in 8 hours.
    If both the machines are working for the same time, say, 8 hours, then together they seal 3k cartons
    2nd machine is the faster machine of the two machines.
    So, 2nd machine seals 2k out of 3k cartons, that is it seals 2/3 = 66.66% of the total cartons

    The correct answer is D.

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