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Good inequality...

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amit.trivedi@ymail.com GMAT Destroyer!
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Good inequality... Post Mon May 07, 2012 1:30 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    "If x is negative, is x < -3 ?

    (1) x^2 > 9
    (2) x^3 < -9 "


    I donot have the OA but when I solved the question, I got the answer as E.

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    aneesh.kg GMAT Destroyer!
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    Post Mon May 07, 2012 1:53 am
    Statement (1):
    x^2 - 9 > 0
    Using critical points method for x < 0
    x < -3
    (You will get the same answer even by plugging-in numbers)
    SUFFICIENT

    Statement(2):
    x^3 + 9 < 0
    Plug-in negative values. The inequality does not hold true for -1 and -2. It holds true first when x^3 = - 9.
    x = - (9)^1/3
    Since (-2)^3 = - 8 and (-3)^3 = - 27, and
    -27 < - 9 < - 8,
    x is between -2 and -3 and slightly less than - 2.
    x = - 2.1 (approx)
    Below this value, the statement will always hold true.

    x < - 2.1

    i.e., x can be less than - 3 or even greater than it (for the values between - 2.1 and - 3).

    INSUFFICIENT.

    (A) is the answer.

    Traps in this problem:
    (1)The problem does not mention that x is an integer, so some people will fall into the trap of assuming x as an integer and go with (D)
    (2) x is negative. If you don't notice this you will go with (C).

    What is the Critical Points method?
    Read here:
    http://www.beatthegmat.com/critical-points-method-for-inequalities-explained-useful-t110450.html#465861

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    Anurag@Gurome GMAT Instructor
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    Post Tue May 08, 2012 9:39 pm
    amit.trivedi@ymail.com wrote:
    "If x is negative, is x < -3 ?

    (1) x^2 > 9
    (2) x^3 < -9 "


    I donot have the OA but when I solved the question, I got the answer as E.
    (1) x² > 9 implies x < -3 or x > 3
    It is given that x is negative or x < 0, so x < -3; SUFFICIENT.

    (2) x^3 < -9
    If x = -3, then x^3 = -27. Here x is equal to -3 and not less than -3.
    If x = -4, then x^3 = -64. Here x < -3.
    No definite answer; NOT sufficient.

    The correct answer is A.

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