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OG Is x|x| < 2^x?

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AbeNeedsAnswers Master | Next Rank: 500 Posts Default Avatar
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OG Is x|x| < 2^x?

Post Tue Aug 22, 2017 7:34 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x is an integer, is x|x|<2^x ?

    (1) x < 0
    (2) x = -10

    D

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    Post Wed Aug 23, 2017 9:46 am
    Hi AbeNeedsAnswers,

    We're told that X is an integer. We're asked if X|X| < 2^X. This is a YES/NO question. We can answer it with a bit of Number Property knowledge.

    1) X < 0

    With Fact 1, we know that X is NEGATIVE. By definition, that means...
    X|X| = (Neg)|Neg| = Negative
    2^(Negative) = Positive
    Thus, X|X| will ALWAYS be less than 2^X and the answer to the question is ALWAYS YES.
    Fact 1 is SUFFICIENT

    2) X = -10

    With the value of X, we can absolutely answer the question (we would just need to plug in that value:
    Is (-10)|-10| < 2^(-10)?
    The answer to the question IS yes, but we don't have to actually do that work. There would be just one answer to the question, so it doesn't really matter what that one answer is.
    Fact 2 is SUFFICIENT

    Final Answer: D

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

    Post Wed Aug 23, 2017 12:50 pm
    AbeNeedsAnswers wrote:
    If x is an integer, is x|x|<2^x ?

    (1) x < 0
    (2) x = -10

    D
    Target question: Is x|x|< 2^x ?

    Given: x is an integer

    Statement 1: x < 0
    In other words, x is NEGATIVE
    So, x|x| = (NEGATIVE)(|NEGATIVE|) = (NEGATIVE)(POSITIVE) = NEGATIVE

    IMPORTANT: 2^x will be POSITIVE for all values of x.

    Since x|x| must be NEGATIVE, and since 2^x must be POSITIVE, we can be certain that x|x|< 2^x
    Since we can answer the target question with certainty, statement 1 is SUFFICIENT

    Statement 2: x = -10
    So, x|x| = (-10)(|-10|) = (-10)(10) = -100 = a NEGATIVE
    On the other hand, 2^x = 2^(-10) = 1/(2^10) = some POSITIVE number
    Since x|x| is NEGATIVE, and since 2^x must be POSITIVE, we can be certain that x|x|< 2^x
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: D

    Cheers,
    Brent

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