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Is b < 0 ?

This topic has 2 expert replies and 0 member replies

Is b < 0 ?

Post Fri Nov 10, 2017 6:15 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is b < 0 ?

    (1) b^3 < b
    (2) b^2 > b

    The OA is C .

    I don't have this DS question clear. Experts, may you clarify this to me?

    Thanks.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Fri Nov 10, 2017 7:56 am
    Vincen wrote:
    Is b < 0 ?

    (1) b³ < b
    (2) b² > b
    Target question: Is b < 0 ?

    Statement 1: b³ < b
    There are several values of b that satisfy statement 1. Here are two:
    Case a: b = -2 (which means b³ = -8, and -8 < -2). In this case, the answer to the target question is YES, b IS less than 0
    Case b: b = 1/2 (which means b³ = 1/8, and 1/8 < 1/2). In this case, the answer to the target question is NO, b is NOT less than 0
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: b² > b
    There are several values of b that satisfy statement 2. Here are two:
    Case a: b = -1 (which means b² = 1, and 1 > -1). In this case, the answer to the target question is YES, b IS less than 0
    Case b: b = 2 (which means b² = 4, and 4 > 2). In this case, the answer to the target question is NO, b is NOT less than 0
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 tells us that b³ < b
    Statement 2 tells us that b² > b
    Combine the inequalities to get: b³ < b < b²
    This tells us that b³ < b²
    Subtract b² from both sides to get: b³ - b² < 0
    Factor to get: b(b² - b) < 0
    If b(b² - b) < 0, then there are TWO POSSIBLE CASES:
    Case a: b < 0 and (b² - b) > 0
    OR
    Case b: b > 0 and (b² - b) < 0
    If we take statement 2 (b² > b) and subtract b from both sides, we get: b² - b > 0
    This RULES OUT case b (above), which means case a must be true.
    If case a is true, then it must be the case that b < 0
    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer: C

    Cheers,
    Brent

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    Post Fri Nov 10, 2017 10:47 am
    Hi Vincen,

    We're asked if B is less than 0. This is a YES/NO question. You can solve it by TESTing VALUES and/or by using Number Property Rules.

    1) B^3 < B

    There are two types of numbers that fit the inequality we're given in Fact 1:
    -Negative numbers that are LESS than -1 (using any of these values would get us a YES answer).
    -Positive fractions (using any of these values would get us a NO answer).
    Fact 1 is INSUFFICIENT

    2) B^2 > B

    There are two types of numbers that fit the inequality we're given in Fact 2:
    -Positive numbers that are GREATER than 1 (using any of these values would get us a NO answer).
    -ANY Negative numbers (using any of these values would get us a YES answer).
    Fact 2 is INSUFFICIENT

    Combined, we have to look for 'overlap' between the two Facts (what groups of numbers fit BOTH Facts?). There's only one group that fits both:
    -Negative numbers that are LESS than -1.
    Since we're limited to just these values, the answer to the question is ALWAYS YES).
    Combined, SUFFICIENT

    Final Answer: C

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

    _________________
    Contact Rich at Rich.C@empowergmat.com

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