Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 30 Sep 2010
Posts: 19

If x is negative, is x < 3 ? [#permalink]
Show Tags
02 Jan 2011, 07:47
4
This post received KUDOS
52
This post was BOOKMARKED
Question Stats:
56% (01:06) correct 44% (01:05) wrong based on 1644 sessions
HideShow timer Statistics
If x is negative, is x < –3 ? (1) x^2 > 9 (2) x^3 < –9
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by ENGRTOMBA2018 on 12 Sep 2015, 08:44, edited 2 times in total.
Renamed the topic and edited the question.



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
02 Jan 2011, 07:57
3
This post received KUDOS
Expert's post
13
This post was BOOKMARKED



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1945

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
24 Feb 2011, 04:11
2
This post received KUDOS
1
This post was BOOKMARKED
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"
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 25 Jul 2012
Posts: 73
Location: United States

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
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.
_________________
If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
10 Mar 2013, 05:07



Intern
Joined: 09 Mar 2013
Posts: 9
Concentration: Accounting
GMAT Date: 05012013
GPA: 3.57

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
10 Mar 2013, 15:02
1
This post received KUDOS
1
This post was BOOKMARKED
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.



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
10 Mar 2013, 21:49
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 07 Feb 2013
Posts: 13
GMAT 1: 650 Q48 V32 GMAT 2: 730 Q49 V41
WE: Engineering (Other)

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
20 Jun 2013, 13:37
1
This post received KUDOS
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



Retired Moderator
Joined: 29 Oct 2013
Posts: 282
Concentration: Finance
GPA: 3.7
WE: Corporate Finance (Retail Banking)

If x is negative, is x < 3 ? [#permalink]
Show Tags
02 Dec 2015, 22:31
1
This post received KUDOS
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
_________________
Please contact me for super inexpensive quality private tutoring
My journey V46 and 750 > http://gmatclub.com/forum/myjourneyto46onverbal750overall171722.html#p1367876



Intern
Joined: 03 Jun 2017
Posts: 15

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
17 Jun 2017, 04:22
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



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
17 Jun 2017, 04:32



Senior Manager
Joined: 06 Jul 2016
Posts: 437
Location: Singapore
Concentration: Strategy, Finance

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
17 Jun 2017, 04:33
1
This post received KUDOS
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.
_________________
Put in the work, and that dream score is yours!



Intern
Joined: 03 Jun 2017
Posts: 15

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
18 Jun 2017, 03:38
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...



Intern
Joined: 08 Sep 2016
Posts: 32

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
11 Sep 2017, 18:10
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



Math Expert
Joined: 02 Sep 2009
Posts: 43804

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
11 Sep 2017, 19:50



Intern
Status: Don't watch the clock,Do what it does, Keep Going.
Joined: 10 Jan 2017
Posts: 46

If x is negative, is x < 3 ? [#permalink]
Show Tags
24 Sep 2017, 06:51
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



Intern
Joined: 14 Aug 2017
Posts: 33

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
05 Oct 2017, 00:06
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



Math Expert
Joined: 02 Sep 2009
Posts: 43804

If x is negative, is x < 3 ? [#permalink]
Show Tags
05 Oct 2017, 00:20
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 14 Aug 2017
Posts: 33

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
05 Oct 2017, 00:29
Thanks Bunuel. Doubt is cleared.



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2179
Location: United States (CA)

Re: If x is negative, is x < 3 ? [#permalink]
Show Tags
05 Dec 2017, 18:32
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.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: If x is negative, is x < 3 ?
[#permalink]
05 Dec 2017, 18:32






