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Percent problem

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GmatKiss GMAT Titan Default Avatar
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Percent problem Post Sat May 05, 2012 5:10 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

    A.50
    B.100
    C.200
    D.1,000
    E.2,000

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    Post Sat May 05, 2012 5:31 am
    GmatKiss wrote:
    Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 100. What is the value of x?

    A.50
    B.100
    C.200
    D.1,000
    E.2,000
    We can plug in the answers.

    Answer choice C: 200
    y = 50% of 50% of x = (1/2)(1/2)200 = 50.
    y% of x = 50% of 200 = 100.
    Success!

    The correct answer is C.

    Algebraically:
    y = 50% of 50% of x = (1/2)(1/2)x = x/4.

    Since y% of x = 100:
    (x/4)/100 * x = 100
    x² = 100*100*4
    x = 10*10*2 = 200.

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