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If x is negative, is x < 3 ?
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If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9
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Originally posted by surendar26 on 02 Jan 2011, 08:47.
Last edited by ENGRTOMBA2018 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 ?
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02 Jan 2011, 08:57
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. Answer: A.
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Re: If x is negative, is x < 3 ?
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24 Feb 2011, 05:11
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 ?
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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 ?
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10 Mar 2013, 16:02
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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If x is negative, is x < 3 ?
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05 Oct 2017, 01:20
siddyj94 wrote: I know this is a lame question but i am trying to get into my head this topic. For the second statement can we pick values other than 3 and 4 like 2 and 5 and prove that the statement is not sufficient Numbers you pick to get that a statement is NOT sufficient, should a. satisfy that statement and b. should give a NO and an YES answer to the question. x = 2 does not satisfy x^3 < 9, because x^3 in this case is 8, which is greater than 9, not less than it. (2) x^3 < –9, implies that \(x < (\approx 2.1)\) (of course you are not expected to know what is \(\sqrt[3]{9}\) but you can get that since (2)^3 = 8, then \(\sqrt[3]{9}\) will be LESS than 2 but greater than 3 (3^3 = 27)). So any number from 2.1 to 3, inclusive, will give a No answer to the question and any number less than 3 will give an YES answer to the question. Hope it helps.
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Re: If x is negative, is x < 3 ?
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20 Jun 2013, 14:37
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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If x is negative, is x < 3 ?
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02 Dec 2015, 23:31
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 ?
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17 Jun 2017, 05:32
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 This is not correct. x^2 > 9 x > 3 (by taking the square root from both sides, notice that we can safely do that because both sides are nonnegative); x < 3 or x > 3. You should brush up fundamentals on inequalities: Inequalities Made Easy!Solving Quadratic Inequalities  Graphic ApproachInequality tipsWavy Line Method Application  Complex Algebraic InequalitiesDS Inequalities Problems PS Inequalities Problems 700+ Inequalities problemshttp://gmatclub.com/forum/inequalitiestrick91482.htmlhttp://gmatclub.com/forum/datasuffine ... 09078.htmlhttp://gmatclub.com/forum/rangeforvar ... 09468.htmlhttp://gmatclub.com/forum/everythingis ... 08884.htmlhttp://gmatclub.com/forum/graphicappro ... 68037.htmlHope this helps.
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Re: If x is negative, is x < 3 ?
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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 ?
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11 Sep 2017, 20:50
shinrai15 wrote: Bunnel,
Can you please explain why we should consider statement 1 as sufficient? I eliminated it thinking there two different values and not 1 value.
What am I missing here!
Thanks in advance! Shinrai 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. Please tell if anything is unclear above.
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Re: If x is negative, is x < 3 ?
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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 ?
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10 Mar 2013, 06:07
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 ?
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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 ?
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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...



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Re: If x is negative, is x < 3 ?
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11 Sep 2017, 19:10
Bunnel,
Can you please explain why we should consider statement 1 as sufficient? I eliminated it thinking there two different values and not 1 value.
What am I missing here!
Thanks in advance! Shinrai



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If x is negative, is x < 3 ?
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24 Sep 2017, 07:51
There are no doubts about 1 as it is obviously sufficient . I want to discuss more about 2. 2. Is x<3 if x=3 then x^3=27, 27<9 which is very true . This is the very point where the option 2 fails. Is X<3 ? No because 2 becomes true at x=3 as27<9, so x cannot be <3.If the question was is x<= 3 then it would have been sufficient. Ans  A Hope this helps Kudos if you like the solution



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Re: If x is negative, is x < 3 ?
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05 Oct 2017, 01:06
I know this is a lame question but i am trying to get into my head this topic. For the second statement can we pick values other than 3 and 4 like 2 and 5 and prove that the statement is not sufficient



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Re: If x is negative, is x < 3 ?
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05 Oct 2017, 01:29
Thanks Bunuel. Doubt is cleared.



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Re: If x is negative, is x < 3 ?
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05 Dec 2017, 19:32
surendar26 wrote: If x is negative, is x < –3 ?
(1) x^2 > 9 (2) x^3 < –9 We are given that x is negative, and we must determine whether x < 3. Statement One Alone: x^2 > 9 Taking the square root of both sides of the inequality in statement one we have: √x^2 > √9 x > 3 x > 3 OR x > 3 x > 3 OR x < 3 Since we are given that x is negative, we see that x must be less than 3. Statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E. Statement Two Alone: x^3 < 9 Using the information in statement two, we see that x can be less than 3 or not be less than 3. For example, if x = 4, (4)^3 = 64, (which fulfills the statement) and 4 is less than 3. However, if x = 3, (3)^3 = 27, (which fulfills the statement) but 3 is not less than 3. Statement two alone is not sufficient to answer the question. The answer is A.
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Re: If x is negative, is x < 3 ?
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