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Number Property Question

This topic has 1 expert reply and 0 member replies
nbalow Newbie | Next Rank: 10 Posts Default Avatar
Joined
22 Dec 2014
Posted:
4 messages
Thanked:
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Test Date:
May 2015
Target GMAT Score:
750

Number Property Question

Post Wed Mar 25, 2015 3:11 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Could one of the experts give me a quick way to get through a problem such as the following:

    Which of the following integers is NOT a divisor of x if x = (21)(3^7) - (112)?
    A. 7
    B. 11
    C. 15
    D. 17
    E. 35

    Please walk me through how you would attack this.

    Thank you
    Nick

    Thanked by: Gurpreet singh
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    Post Wed Mar 25, 2015 3:41 pm
    nbalow wrote:
    Could one of the experts give me a quick way to get through a problem such as the following:

    Which of the following integers is NOT a divisor of x if x = (21)(3^7) - (112)?
    A. 7
    B. 11
    C. 15
    D. 17
    E. 35
    Let's factor this thing like crazy.
    (21)(3^7) - (112) = (3)(7)(3^7) - (7)(2)(2)(2)(2)
    = (7)(3^8) - (7)(2^4)
    = 7(3^8 - 2^4) NOTE: The part in the brackets is a difference of squares, since 3^8 = (3^4)^2 and 2^4 = (2^2)^2
    = 7(3^4 + 2^2)(3^4 - 2^2) we factored the difference of squares
    = 7(3^4 + 2^2)(3^2 - 2)(3^2 + 2) we factored another difference of squares
    = 7(81 + 4)(9 - 2)(9 + 2) evaluated
    = 7(85)(7)(11) evaluated
    = (7)(5)(17)(7)(11)

    We can see that the above product is divisible by 7, 11, 17, and 35
    BUT it is not divisible by 15

    Answer: C

    Cheers,
    Brent

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