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# If x is negative, is x < 3 ?

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If x is negative, is x < 3 ? [#permalink]  02 Jan 2011, 07:47
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If x is negative, is x < –3 ?

(1) x^2 > 9
(2) x^3 < –9
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Nov 2012, 14:28, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Inequalities [#permalink]  02 Jan 2011, 07:57
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If x is negative, is x < –3 ?

(1) x^2 > 9 --> $$x<-3$$ or $$x>3$$ as given that $$x<0$$ then we have that $$x<-3$$. Sufficient.

(2) x^3 < –9 --> if $$x=-3$$ ($$x^3=-27<-9$$) then the answer will be NO (as $$x$$ equals to -3 and is not less than -3) but if $$x=-4$$ ($$x^3=-64<-9$$) then the answer will be YES. Not sufficient.

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Re: Inequalities [#permalink]  24 Feb 2011, 04:11
1.
$$x^2>9$$
$$|x|>3$$
$$x>3 \hspace{3} or \hspace{3} x<-3$$
We know that x is -ve.
Thus;
$$x<-3$$
Sufficient.

2.
$$x^3<-9$$
$$x^3$$ 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, 10:41
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, 05:07
Expert's post
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.
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Re: If x is negative, is x < 3 ? [#permalink]  10 Mar 2013, 11:03
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, 15:02
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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, 21:49
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Expert's post
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, 08:49
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]  20 Jun 2013, 13:37
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Statement 2 : X^3<-9
=> We know (-2)^3 = -8 and (-3)^3= -27
=> it isnt given in the q that x has to be an integer
=> x can be any decimal slightly less than -2.0 ie. -2.5^3 (-15) and thus give an answer NO
& x can be any number <-3 (=>x^3 <-27)and give an answer YES.
Thus, insufficient
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Re: If x is negative, is x < 3 ? [#permalink]  12 Aug 2014, 09:12
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Re: If x is negative, is x < 3 ?   [#permalink] 12 Aug 2014, 09:12
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