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Greatest Common Divisor

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dlencz Rising GMAT Star
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Greatest Common Divisor Post Mon Apr 23, 2012 11:58 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

    (1) x = 12u, where u is an integer
    (2) y = 12z, where z is an integer

    OA is B

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    Post Mon Apr 23, 2012 12:21 pm
    dlencz wrote:
    If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

    (1) x = 12u, where u is an integer
    (2) y = 12z, where z is an integer

    OA is B
    Pl. see here.

    http://www.beatthegmat.com/mba/2010/10/12/breaking-down-a-gmatprep-divisibility-problem

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    Post Mon Apr 23, 2012 8:27 pm
    dlencz wrote:
    If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

    (1) x = 12u, where u is an integer
    (2) y = 12z, where z is an integer

    OA is B
    For many test-takers, the most efficient approach on test day would be to plug in.

    Statement 1: x=12u, where u is an integer and x=8y+12.
    In other words, x is a multiple of 12.
    For x to be a multiple of 12, 8y must be a multiple of 12.

    If y=3, then x = 8*3 + 12 = 36.
    The GCD of 3 and 36 is 3.

    If y=6, then x = 8*6 + 12 = 60.
    The GCD of 6 and 60 is 6.

    Since the GCD can be different values, INSUFFICIENT.

    Statement 2: y=12z, where z is an integer and x=8y+12.
    In other words, y is a multiple of 12.
    Since we're looking for the GCD, view x in terms of its FACTORS.

    If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9.
    The GCD of 12 and 12*9 is 12.

    If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17.
    The GCD of 24 and 12*17 is 12.

    I'm almost convinced: the GCD is 12.
    Maybe one more just to be sure:

    If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25.
    The GCD of 36 and 12*25 is 12.
    SUFFICIENT.

    The correct answer is B.

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    amit28it Rising GMAT Star Default Avatar
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    Post Tue Apr 24, 2012 5:52 am
    The solution provided by GMATGuruNY is perfect there is no better solution for this problem,I have just completed the problem and follows the same procedure and the answer is Correct that is B.

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    Post Tue Apr 24, 2012 6:24 am
    The solution provided by GMATGuruNY is the simplest solution of this question,I have just completed the question and found that the procedure I am following is same and so is the answer.
    math problem solver

    shantanu86 Rising GMAT Star Default Avatar
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    Post Tue Apr 24, 2012 7:21 am
    dlencz wrote:
    If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?

    (1) x = 12u, where u is an integer
    (2) y = 12z, where z is an integer

    OA is B
    In general if a equation has the form -

    x = n*y +c

    It automatically implies that the HCF of x & y has to be a factor of 'c' resulting in
    x' * HCF = y'*HCF +c'*HCF.. here x', y' and c' are quotient when HCF divides x, y and c respectively.

    Thus, 12 will become HCF iff y has the form y= 12z.
    Hence B alone is sufficient.

    A implies that y =12(u-1)/8 = 4*(u-1)/3.. tells nothing.

    Hope it helps!!

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