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If x is negative, is x < 3 ? [#permalink]
 02 Jan 2011, 08:47
Question Stats:
44% (01:54) correct
55% (00:42) wrong based on 70 sessions
If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9
Last edited by Bunuel on 01 Nov 2012, 15:28, edited 1 time in total.
Renamed the topic and edited the question.
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1. x^2>9|x|>3x>3 \hspace{3} or \hspace{3} x<-3We know that x is -ve. Thus; x<-3Sufficient. 2. x^3<-9x^3 can be -27 making x=-3 or x^3 can be -64 making x=-4[/m] We can't conclude that x is definitely smaller than -3. Not Sufficient. Ans:"A"
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Re: If x is negative, is x < 3 ? [#permalink]
09 Mar 2013, 11:41
I'm not seeing something in testing out statement 2.
Would someone be able to illustrate on a number line when testing out x=-3 and x=-4 only -64 <-3 and not -27?
And if you have a similar problem, please post.
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Re: If x is negative, is x < 3 ? [#permalink]
10 Mar 2013, 06:07
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Re: If x is negative, is x < 3 ? [#permalink]
10 Mar 2013, 12:03
Bunuel wrote: DelSingh wrote: I'm not seeing something in testing out statement 2.
Would someone be able to illustrate on a number line when testing out x=-3 and x=-4 only -64 <-3 and not -27?
And if you have a similar problem, please post. Not sure I understand what you mean there. Can you please elaborate? Thank you. Anyway both -64 and -27 are less than -3, since both are negative and further from 0 than -3 is. Hopefully this will show what I am doing wrong in statement two:  I had sufficient for statement 2 but that was wrong
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Re: If x is negative, is x < 3 ? [#permalink]
10 Mar 2013, 16:02
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they are asking is x<-3, not if x^3<-3. -27 and -64 are the values of x^3. so x=-3 and x=-4. negative 3 isn't less than negative 3, so answer is no. negative 4 is less than negative 3, so answer is yes. insufficient.
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Re: If x is negative, is x < 3 ? [#permalink]
10 Mar 2013, 22:49
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DelSingh wrote: Bunuel wrote: DelSingh wrote: I'm not seeing something in testing out statement 2.
Would someone be able to illustrate on a number line when testing out x=-3 and x=-4 only -64 <-3 and not -27?
And if you have a similar problem, please post. Not sure I understand what you mean there. Can you please elaborate? Thank you. Anyway both -64 and -27 are less than -3, since both are negative and further from 0 than -3 is. Hopefully this will show what I am doing wrong in statement two: I had sufficient for statement 2 but that was wrong x = -3 and x = -4 satisfy the second statement: (-3)^3 < -9 and (-4)^3 < -9. Now, if x = -4 we have an YES answer because -4 < -3; But if x = -3 we have a NO answer because -3 = -3 (x equals to -3 and is not less than -3). Hope it's clear.
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Re: If x is negative, is x < 3 ? [#permalink]
11 Mar 2013, 09:49
Now I see, I just got lost in translation and calculation, and didn't remember the actual question stem. Thank you both
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Re: If x is negative, is x < 3 ?
[#permalink]
11 Mar 2013, 09:49
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