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If x is negative, is x < 3 ? [#permalink]
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02 Jan 2011, 08:47
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If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9
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Last edited by Engr2012 on 12 Sep 2015, 09:44, edited 2 times in total.
Renamed the topic and edited the question.



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Re: If x is negative, is x < 3 ? [#permalink]
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02 Jan 2011, 08:57
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Re: If x is negative, is x < 3 ? [#permalink]
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24 Feb 2011, 05:11
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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]
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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]
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Re: If x is negative, is x < 3 ? [#permalink]
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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]
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10 Mar 2013, 22:49
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]
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20 Jun 2013, 14:37
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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]
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Re: If x is negative, is x < 3 ? [#permalink]
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If x is negative, is x < 3 ? [#permalink]
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02 Dec 2015, 23:31
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St1) Quite obviously SUFF St2) x^3<9. First of all x has to be negative as cube root of a negative number will be negative. Now lets take cube root of both sides: x< (~2.1) ...[we know than cube root of 8 is 2, so cube root of of 9 will be just slightly smaller than 2] So our ballpark estimate is that x lies to the left of 2.1 we don't know if it will lie to the left of 3. INSUF Alternatively Stem: If x is negative, is x < 3 ? In other words, i) is x^2>9? (Inequality sign will flip) ii) is x^3<27? (Ineqality sign doesnt change) ii) is x^4> 81? (Inequality sign will flip) etc etc . . . st1) Straight away yes from i)...SUF St2) only tells us x^3 is less than 9 so x^3 could be less than 27 or not. INSUF Ans: A
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Re: If x is negative, is x < 3 ? [#permalink]
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10 Jan 2017, 08:27
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Re: If x is negative, is x < 3 ? [#permalink]
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20 Jan 2017, 05:25
(1) says that x^2 > 9
I thought that this would mean that x > 3 or x < 3 and hence, (1) is insufficient.
However, I missed out that question itself says that x < 0. So, this rules out x > 3. Hence, (1) itself says that x < 3.



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Re: If x is negative, is x < 3 ? [#permalink]
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17 Jun 2017, 05:22
Hi guys...this is how i solved the question... plz correct me,wher i am wrong... For statement 1: x^2>9, x^29>0 , (x+3)(x3)>0 , {x>3 & x>3} or {x<3 & x<3} Now considering only negative values i get x>3 or x<3.. Since answer is not consistent A is not sufficient...
Thanks in advance



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Re: If x is negative, is x < 3 ? [#permalink]
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17 Jun 2017, 05:32



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Re: If x is negative, is x < 3 ? [#permalink]
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17 Jun 2017, 05:33
JJSHHShank wrote: Hi guys...this is how i solved the question... plz correct me,wher i am wrong... For statement 1: x^2>9, x^29>0 , (x+3)(x3)>0 , {x>3 & x>3} or {x<3 & x<3} Now considering only negative values i get x>3 or x<3.. Since answer is not consistent A is not sufficient...
Thanks in advance Hey Mate, If x^2 > 9 x > 3 or x < 3 With what you're saying is x > 3 then x = 2 for example and x^2 = 4 which is not in line with the equation, and this is also incorrect. In terms of solving an inequality equation, If x^2 > 9 then x > 3 or x < 3 If x^2 < 9 then 3<x<3 Try to input value of x in the range, and it'll always be true. Hope this helps.



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Re: If x is negative, is x < 3 ? [#permalink]
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18 Jun 2017, 04:38
Thanks Bunuel and akshayk for the quick response... The links given were bible for inequalities...Thanks a lot. Understood that we cannot just solve taking a pen and a scratch pad... we need to think tooat every step, especially when dealing with inequalities...




Re: If x is negative, is x < 3 ?
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