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(a X b) ^(c X d) = n

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sanju09 GMAT Instructor
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(a X b) ^(c X d) = n Post Sat Feb 11, 2012 3:19 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If a, b, c, and d are positive integers, and (a X b) ^(c X d) = n; then what is the unit’s digit of n?
    I. a^2 + b^2 = 41.
    II. a X b = 20.




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    Post Sat Feb 11, 2012 8:44 am
    sanju09 wrote:
    If a, b, c, and d are positive integers, and (a X b) ^(c X d) = n; then what is the unit’s digit of n?
    I. a^2 + b^2 = 41.
    II. a X b = 20.
    I'm not sure why the "X's" are added here. They could be mistaken for variables.
    How about . . .

    If a, b, c, and d are positive integers, and (ab)^(cd) = n, then what is the unit’s digit of n?
    1)a^2 + b^2 = 41
    2)ab = 20



    Target question: What is the unit’s digit of (ab)^(cd)?

    Statement 1: a^2 + b^2 = 41
    If a and b are positive integers, then it won't take long to check out the possible cases.
    We need only consider the following squares: 1, 4, 9, 16, 25, 36
    Given these squares, only 1 pair gives us a sum of 41 (16 and 25)
    So, either a=4 and b=5 or a=5 and b=4
    Either way, we now know that ab=20
    If ab=20, then (ab)^(cd) = (20)^(cd)
    If c and d are positive integers, then the units digit of (20)^(cd) must be 0
    As such, statement 1 is SUFFICIENT

    Statement 2:ab = 20
    If ab=20, then (ab)^(cd) = (20)^(cd)
    If c and d are positive integers, then the units digit of (20)^(cd) must be 0
    As such, statement 2 is SUFFICIENT

    The answer is D

    Cheers,
    Brent

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    Post Fri Feb 17, 2012 2:41 pm
    (D)

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    Post Sun Feb 19, 2012 12:26 am
    Yes (D) is the correct answer.

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