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Was trying to plug in this one

This topic has 1 expert reply and 2 member replies
shibsriz@gmail.com Master | Next Rank: 500 Posts Default Avatar
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Was trying to plug in this one

Post Tue Apr 08, 2014 9:24 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If 5 - 6/x = x, then x has how many possible values?

    (A) None
    (B) One
    (C) Two
    (D) A finite number greater than two
    (E) An infinite number

    Not sure how the answer is C

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    Post Tue Apr 08, 2014 9:37 pm
    Hi shibsriz,

    You'll have to do a bit of algebra to deduce the number of solutions to this equation…

    5 - 6/x = x

    First, multiply everything by x…

    5x - 6 = x^2

    Now, move everything "to the right"….

    0 = x^2 - 5x + 6

    You can now factor this into two terms…

    0 = (x -2)(x - 3)

    And answer the question…

    Final Answer: C

    GMAT assassins aren't born, they're made,
    Rich

    _________________
    Contact Rich at Rich.C@empowergmat.com



    Last edited by Rich.C@EMPOWERgmat.com on Wed Apr 09, 2014 12:59 pm; edited 1 time in total

    Thanked by: shibsriz@gmail.com
    Post Wed Apr 09, 2014 7:48 am
    I just have one small point to make.
    Rich's approach is great, but his factorization of x² - 5x + 6 should be (x - 2)(x - 3), rather than (x - 6)(x +1)

    So, the two solutions are actually x = 2 and x = 3

    Cheers,
    Brent

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    Post Wed Apr 09, 2014 12:58 pm
    Hi All,

    Brent is absolutely correct - I rushed it and made a silly mistake (I've edited the original post). As it stands, my mistake doesn't actually affect the answer to this question, but it's worth noting that the details DO matter on Test Day.

    GMAT assassins aren't born, they're made,
    Rich

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