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Question from Gmat Prep- Help please! 2

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bobdylan Rising GMAT Star Default Avatar
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Question from Gmat Prep- Help please! 2 Post Fri Apr 13, 2012 2:12 pm
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If (1/5)^m . (1/4)^18= 1/2(10)^35, then m:
    a)17
    b)18
    c)34
    d)35
    e)36

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    Post Fri Apr 13, 2012 2:18 pm
    If (1/5)^m (1/4)^18 = 1/ 2(10)^35, then m =

    a.17
    b.18
    c.34
    d.35
    e.36

    (1/5)^m (1/4)^18 = 1/ 2(10)^35
    (1/5)^m * (1/2*2)^18 = 1/(2(2*5)^35)
    (1/5)^m * (1/2)^36 = 1/(2(2^35)(5^35))
    (1/5)^m * (1/2)^36 = 1/(2^36 * 5^35)
    multiply left hand side and right hand side with 2^36, leaving:
    1/5^m = 1/5^35
    Bases are equal, so should be exponents. Hence the value of m = 35
    Option D

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    Post Fri Apr 13, 2012 6:33 pm
    bobdylan wrote:
    If (1/5)^m . (1/4)^18= 1/2(10)^35, then m:
    a)17
    b)18
    c)34
    d)35
    e)36
    (1/5)^m * (1/4)^18= 1/2(10)^35
    (1/5)^m * (1/4)^18= 1/[2 * 2^35 * 5^35]
    Now all the answer choices are only integers, and power of 5 on both sides should be equal. The power of 5 is 35.

    The correct answer is D.

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    Post Fri Apr 13, 2012 7:04 pm
    Do only as much math as necessary. I posted a solution here:

    http://www.beatthegmat.com/pleasssseee-help-how-do-i-find-m-t95762.html

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