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If |x| > 3

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massi2884 Rising GMAT Star Default Avatar
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If |x| > 3 Post Thu Apr 12, 2012 11:34 am
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  • Lap #[LAPCOUNT] ([LAPTIME])
    If |x| > 3, which of the following must be true?

    1) x > 3
    2) x^2 > 9
    3) |x - 1| > 2

    I only
    II only
    I and II only
    II and III only
    I, II, and III

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    massi2884 Rising GMAT Star Default Avatar
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    Post Thu Apr 12, 2012 11:46 am
    OA is D
    Thanks

    neelgandham Community Manager
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    Post Thu Apr 12, 2012 11:47 am
    |x| > 3
    From the definition of mod, if |x| > 3, x>3 or x<-3

    1) x > 3 - Is not a 'must-be-true' condition as x can be less than -3
    2) x^2 > 9 - Is a 'must-be-true condition as if x>3, then x^2>9 and if x<-3, x^2>9
    3) |x - 1| > 2 => x-1>2 or x-1<-2 => x>3 and x<-1 - Is not a 'must-be-true' condition as x can be a value between -1 and -3, say -2.

    IMO B)II only

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    Post Thu Apr 12, 2012 11:50 am
    Only II and III are correct.

    |x|>3. That is, x>3 or x<-3
    but it is still must be true question.
    I. x>3 but what if x=-4? |-4|=4<3 but x is not bigger than 3
    II. it is true. if x=4 x^2=16 - true. if x=4, x^2=16, true.
    III. two possibilities x<-1 and x>3 (Drow 2 lines to see that if x<-3 x will always be < -1)

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    Post Thu Apr 12, 2012 11:55 am
    If x =-2, |-2 - 1| = 3 > 2. So x=-2 satisfies the equation III but |x| = 2<3 and doesn't satisfy the inequation.

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    Post Thu Apr 12, 2012 12:09 pm
    neelgandham wrote:
    If x =-2, |-2 - 1| = 3 > 2. So x=-2 satisfies the equation III but |x| = 2<3 and doesn't satisfy the inequation.
    Look carefully at the stimulus. x is less than 3 or more than 3. It can`t be -2.

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    Post Thu Apr 12, 2012 12:15 pm
    katrin - I

    Option 3 reads |x - 1| > 2,So x = -2 is one of the solutions for this in-equation. Agreed?
    So is x=-2 a solution of the stimulus |x|>3 ?

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    Post Thu Apr 12, 2012 1:36 pm
    massi2884 wrote:
    If |x| > 3, which of the following must be true?

    1) x > 3
    2) x^2 > 9
    3) |x - 1| > 2

    I only
    II only
    I and II only
    II and III only
    I, II, and III
    Plug in a value that satisfies the condition that |x| > 3.
    Let x=-4.
    Eliminate any statement that is not valid for x=-4.

    Statement I: x > 3
    -4 > 3
    Not true.
    Eliminate any answer choice that includes I.
    Eliminate A, C and E.

    Compare the remaining answer choices.
    B and D each include II.
    Thus, II must be true, since it is included in both of the remaining answer choices.
    Thus, we need to evaluate only statement III.

    Statement III: |x-1| > 2
    |x-1| > 2 implies that the distance between x and 1 is more than 2 units.
    |x| > 3 implies that x is more that 3 units from 0.
    Since x is more than 3 units from 0 -- in other words, x<-3 or x>3 -- the distance between x and 1 must be more than 2 units.
    Thus, III must be true.
    Eliminate B, which doesn't include III.

    The correct answer is D.

    Please note the following:
    If |x| > 3, then statement III must be true: |x-1| > 2.
    This does NOT imply the reverse.
    If |x-1| > 2, it does NOT have to be true that |x| > 3.
    For example, x=-2 satisfies |x-1| > 2 but not |x| > 3.

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    neelgandham Community Manager
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    Post Thu Apr 12, 2012 3:24 pm
    Thanks for the explanation Mitch! I was solving the other way.

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    ronnie1985 GMAT Destroyer!
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    Post Thu Apr 12, 2012 10:04 pm
    IMO (B) only x^2>9 is correct.

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    harsha.198004@gmail.com Just gettin' started! Default Avatar
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    Post Fri Apr 13, 2012 7:06 am
    I went by substitution method and i get II and III as answer

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