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If b is an even integer is b < 0 ?

This topic has 1 expert reply and 2 member replies

If b is an even integer is b < 0 ?

Post Fri Sep 15, 2017 7:13 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If b is an even integer is b < 0 ?

    (1) b^2 - 4b + 4 < 16
    (2) b^2 > 9

    The OA is A.

    I know the option (2) alone is not sufficient, but I could not determine if the statement (1) is sufficient. Can any expert help me here.

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    Post Fri Sep 15, 2017 7:36 pm
    Vincen wrote:
    If b is an even integer is b < 0 ?

    (1) b^2 - 4b + 4 < 16
    (2) b^2 > 9

    The OA is A.

    I know the option (2) alone is not sufficient, but I could not determine if the statement (1) is sufficient. Can any expert help me here.
    Statement 1: b² - 4b + 4 < 16
    Rephrased:
    (b-2)² < 16.
    If b=-2, then (b-2)² = (-2-2)² = (-4)² = 16.
    If b=-4, then (b-2)² = (-4-2)² = (-6)² = 36.
    If b=-6, then (b-2)² = (-6-2)² = (-8)² = 64.
    Notice the PATTERN.
    When b=-2, (b-2)² = 16.
    As b becomes more negative, (b-2)² becomes BIGGER.
    Implication:
    There is no negative even value for b such that (b-2)² < 16.
    Since b cannot be negative, the answer to the question stem is NO.
    SUFFICIENT.

    _________________
    Mitch Hunt
    GMAT Private Tutor
    GMATGuruNY@gmail.com
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    For more information, please email me at GMATGuruNY@gmail.com.

    Thanked by: Vincen
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    Top Member

    Post Sat Sep 16, 2017 6:45 am
    GMATGuruNY wrote:
    Vincen wrote:
    If b is an even integer is b < 0 ?

    (1) b^2 - 4b + 4 < 16
    (2) b^2 > 9

    The OA is A.

    I know the option (2) alone is not sufficient, but I could not determine if the statement (1) is sufficient. Can any expert help me here.
    Statement 1: b² - 4b + 4 < 16
    Rephrased:
    (b-2)² < 16.
    If b=-2, then (b-2)² = (-2-2)² = (-4)² = 16.
    If b=-4, then (b-2)² = (-4-2)² = (-6)² = 36.
    If b=-6, then (b-2)² = (-6-2)² = (-8)² = 64.
    Notice the PATTERN.
    When b=-2, (b-2)² = 16.
    As b becomes more negative, (b-2)² becomes BIGGER.
    Implication:
    There is no negative even value for b such that (b-2)² < 16.
    Since b cannot be negative, the answer to the question stem is NO.
    SUFFICIENT.
    Dear Mitch,

    For statement 1:

    If b = 0 ..........then 4 < 16

    If b = 2...........then 0 < 16

    If b = 4............then 4 <16

    How come A is sufficient?????

    Top Member

    Post Sat Sep 16, 2017 6:49 am
    Mo2men wrote:
    GMATGuruNY wrote:
    Vincen wrote:
    If b is an even integer is b < 0 ?

    (1) b^2 - 4b + 4 < 16
    (2) b^2 > 9

    The OA is A.

    I know the option (2) alone is not sufficient, but I could not determine if the statement (1) is sufficient. Can any expert help me here.
    Statement 1: b² - 4b + 4 < 16
    Rephrased:
    (b-2)² < 16.
    If b=-2, then (b-2)² = (-2-2)² = (-4)² = 16.
    If b=-4, then (b-2)² = (-4-2)² = (-6)² = 36.
    If b=-6, then (b-2)² = (-6-2)² = (-8)² = 64.
    Notice the PATTERN.
    When b=-2, (b-2)² = 16.
    As b becomes more negative, (b-2)² becomes BIGGER.
    Implication:
    There is no negative even value for b such that (b-2)² < 16.
    Since b cannot be negative, the answer to the question stem is NO.
    SUFFICIENT.
    Dear Mitch,

    For statement 1:

    If b = 0 ..........then 4 < 16

    If b = 2...........then 0 < 16

    If b = 4............then 4 <16

    How come A is sufficient?????
    Sorry Mitch, I did not read your post thoroughly. SmileSmile

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