Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 13 Aug 2012
Posts: 431
Concentration: Marketing, Finance
GPA: 3.23

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
16 Jan 2013, 04:04
vaivish1723 wrote: Is \(\sqrt{(x3)^2}=3x\)?
(1) \(x\neq{3}\) (2) \(xx >0\) \(\sqrt{(x3)^2} = 3x\) \(x3 = 3x\) \(3x >= 0\) \(3>=x\) x is less than or equal to 3
_________________
Impossible is nothing to God.



Director
Status: Tutor  BrushMyQuant
Joined: 05 Apr 2011
Posts: 610
Location: India
Concentration: Finance, Marketing
GPA: 3
WE: Information Technology (Computer Software)

Re: [square_root](X3)^2[/square_root][/m] = 3 X ?
[#permalink]
Show Tags
06 Mar 2013, 21:19
sujit2k7 wrote: This is a DS question ..
Is \(\sqrt{(X3)^2}\) = 3 X ?
1) X # 3 2) XX > 0 Only thing which the question is asking is 3X positive As Sqrt (X3)^2 = X3 if X3 is positive = 3X if 3X is positive STAT1 is INSUFFICIENT as X# 3 doesn't tell anything about whether 3X is positive or not. STAT2 XX > 0 since X is positive so X > 0 => X <0 and if X< 0 then 3X will be positive. So, Answer will be B Hope it helps!
_________________
Ankit
Check my Tutoring Site > Brush My Quant
GMAT Quant Tutor How to start GMAT preparations? How to Improve Quant Score? Gmatclub Topic Tags Check out my GMAT debrief
How to Solve : Statistics  Reflection of a line  Remainder Problems  Inequalities



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 613

Re: [square_root](X3)^2[/square_root][/m] = 3 X ?
[#permalink]
Show Tags
06 Mar 2013, 21:43
sujit2k7 wrote: This is a DS question ..
Is \(\sqrt{(X3)^2}\) = 3 X ?
1) X # 3 2) XX > 0 We know that \(\sqrt{X^2}\) = X. Thus, the question stem is asking whether X3 = 3X. This is possible only if (X3) is negative or X<3. From F.S 1, we have x is not equal to 3. Clearly Insufficient. From F.S 2, we have XX>0. Thus, as X is always positive, X has to be negative. Thus, if X is negative, it will always be less than 3. Sufficient. B.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Manager
Joined: 05 Nov 2012
Posts: 65
Concentration: International Business, Operations
GPA: 3.65

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
18 Apr 2013, 16:04
vaivish1723 wrote: Is \(\sqrt{(x3)^2}=3x\)?
(1) \(x\neq{3}\) (2) \(xx >0\) Here is how i solved it: 1) x [/s]=[/s] 3. Not sufficient 2) xx>0 => x<0 only then the given inequality holds so [/square_root](s3)^2[/square_root] => (x3) (as we know [/square_root]x^2[/square_root] =  (x) if x<0) and 3x = (x3) so sufficient. IMO B.
_________________
___________________________________________ Consider +1 Kudos if my post helped



Intern
Joined: 14 Jun 2014
Posts: 4

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
24 Dec 2014, 02:13
vaivish1723 wrote: Is \(\sqrt{(x3)^2}=3x\)?
(1) \(x\neq{3}\) (2) \(xx >0\) Hi Bunuel, Please When x \leq{3}, then LHS=x3=x+3=3x=RHS, hence in this case equation holds true. Should the part in red not just be "<"?



Math Expert
Joined: 02 Sep 2009
Posts: 49860

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
24 Dec 2014, 07:24



Intern
Joined: 02 Feb 2011
Posts: 38

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
07 Jan 2016, 01:29
HI understand the square root concept.
But I ended up squaring both sides of equation and got the question as x3=3x.
Can someone explain why cant we square both the sides of equation to eliminate square root on lefthand side?



Math Expert
Joined: 02 Sep 2009
Posts: 49860

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
10 Jan 2016, 07:01



Intern
Joined: 02 Feb 2011
Posts: 38

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
10 Jan 2016, 14:03
Thanks a lot Bunuel!! I got the concept, i forgot to apply the concept i.e not to square when not sure about the sign.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6367
GPA: 3.82

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
11 Jan 2016, 19:22
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. Is root{(x3)^2}=3x? (1) x≠3 (2) −xx>0 When you modify the original condition and the question, it becomes nth power root (A^n)=A when n=even, and A=A when A>=0, A=A when A<0. So, x3=3x=(x3)? becomes x3<0?, x<3?. There is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), x=/3> x=2 yes, x=4 no, which is not sufficient. For 2), xx>0 > x<0<3, which is yes and sufficient. Therefore, the answer is B. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Manager
Joined: 29 Oct 2016
Posts: 237
Concentration: Finance, Economics

Is root{(x3)^2}=3x?
[#permalink]
Show Tags
11 Feb 2017, 00:59
Let's paraphrase the question. \(\sqrt{(x3)^{2}}\) = (3x) ? is equal to is x3 < 0 ?
Apparently,stmt (1) is insufficient.
Consider stmt (2) : xx > 0 This inequality can be deduced to x > 0. Hence x < 0;we now know that x3 <0. Thus,it is sufficient.
Ans B



Intern
Joined: 29 Nov 2016
Posts: 9

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
25 Apr 2017, 09:19
VeritasPrepKarishma wrote: mrcrescentfresh wrote: I am having a hard time grasping why we cannot simplify the problem as:
((X3)^2)^1/2 = (3  X) to (X  3)^2 = (3  X)^2?
I know I have worked problems before where we have been able to solve it by squaring both sides, but when done in this scenario the answer is entirely different than the OA.
Please help. That is because if the question says: Is 5 = 5? And you do not know but you square both sides and get 25 = 25 Can you say then that 5 = 5? No! I understand that you would have successfully used the technique of squaring both sides before but that would be in conditions like these: Given equation: \(\sqrt{X} = 3\) Squaring both sides: X = 9 Here you already know that the equation holds so you can square it. It will still hold. This is like saying: It is given that 5 = 5. Squaring both sides, 25 = 25 which is true. This question is similar to the first case. It is asked whether \(\sqrt{((X3)^2)} = (3  X)\)? LHS is positive because \(\sqrt{((X3)^2)} = X3\) and by definition of mod, we know that X = X if X is positive or zero and X if X is negative (or zero). Since X3 =  (X  3), we can say that X  3 <= 0 or that X <= 3 So the question is: Is X <= 3? Stmnt 1 not sufficient. But stmnt 2 says XX > 0 This means XX is positive. Since X will be positive, X must be negative to get rid of the extra negative sign in front. So this statement tells us that X < 0. Then X must be definitely less than 3. Sufficient. How did you get this?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8374
Location: Pune, India

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
26 Apr 2017, 00:56
hannahkagalwala wrote: VeritasPrepKarishma wrote: mrcrescentfresh wrote: I am having a hard time grasping why we cannot simplify the problem as:
((X3)^2)^1/2 = (3  X) to (X  3)^2 = (3  X)^2?
I know I have worked problems before where we have been able to solve it by squaring both sides, but when done in this scenario the answer is entirely different than the OA.
Please help. That is because if the question says: Is 5 = 5? And you do not know but you square both sides and get 25 = 25 Can you say then that 5 = 5? No! I understand that you would have successfully used the technique of squaring both sides before but that would be in conditions like these: Given equation: \(\sqrt{X} = 3\) Squaring both sides: X = 9 Here you already know that the equation holds so you can square it. It will still hold. This is like saying: It is given that 5 = 5. Squaring both sides, 25 = 25 which is true. This question is similar to the first case. It is asked whether \(\sqrt{((X3)^2)} = (3  X)\)? LHS is positive because \(\sqrt{((X3)^2)} = X3\) and by definition of mod, we know that X = X if X is positive or zero and X if X is negative (or zero). Since X3 =  (X  3), we can say that X  3 <= 0 or that X <= 3 So the question is: Is X <= 3? Stmnt 1 not sufficient. But stmnt 2 says XX > 0 This means XX is positive. Since X will be positive, X must be negative to get rid of the extra negative sign in front. So this statement tells us that X < 0. Then X must be definitely less than 3. Sufficient. How did you get this? No, we are not establishing/using this. We are just simplifying the question. Since the question is: Is \(X3 =  (X  3)\) ? Is \((X  3) <= 0\)? Is \(X <= 3\)? And then we go on to evaluate each statement.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Senior Manager
Joined: 24 Oct 2016
Posts: 280
Location: India
Concentration: Finance, International Business
GPA: 3.96
WE: Human Resources (Retail Banking)

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
27 Apr 2017, 23:39
vaivish1723 wrote: Is \(\sqrt{(x3)^2}=3x\)?
(1) \(x\neq{3}\) (2) \(xx >0\) quite simple , as it is known that root could not have ve values so we are sure about the LHS now go through the statements statement 1. x is not equal to 3 so x can be anything except 3 , try plugging in say x=5 then LHS(2) not equal to RHS(2) so we get A No say x=5 then LHS(8) = RHS(8) so we get A yes . so not sufficient statement 2. it says that x must be ve so we get A yes so sufficient hence B



Intern
Joined: 02 Jan 2017
Posts: 44
Location: India
Concentration: Leadership, Marketing
WE: Engineering (Telecommunications)

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
05 May 2017, 00:55
(x3)^2}=3x==>> means should be always positive is 3x>0 or x<3 ? (1) x≠3 ,so x can>3 as well so INSUFF (2) −xx>0> TO BE GREATER THAN 0 X SHOULD BE VE ALWAYS Hence SUFF
_________________
KUDOS PLEASE, If my post Helped you. Thank you



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1208
Location: India
WE: Engineering (Other)

Is root{(x3)^2}=3x?
[#permalink]
Show Tags
30 Aug 2017, 07:01
Bunuelniks18 amanvermagmatQuote: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). With this understanding I proceeded a bit differently and want to know if my approach is correct: If I look closely at part inside sq root in LHS, then RHS = (LHS) With this thinking clearly i need term inside xto be negative since  (x3) = 3  x since x =\(\sqrt{x^2}\) Proceeding further for statement 2, x * x is a positive value, this is possible only when product is of two negative no so essentially x = x or in other words  (x3) = 3x which is our RHS Does this makes sense?
_________________
It's the journey that brings us happiness not the destination.



Intern
Joined: 31 May 2015
Posts: 2

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
02 Feb 2018, 13:32
Since the question doesnt say anything about x being an integer only, Why arent we testing the fraction use cases which comply with the DS statements ?
Please help me understand. Not sure if I am missing something here.



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
02 Feb 2018, 20:08
adkikani wrote: Bunuelniks18 amanvermagmatQuote: \(\sqrt{x^2}=x\), if \(x\geq{0}\); \(\sqrt{x^2}=x\), if \(x<0\). With this understanding I proceeded a bit differently and want to know if my approach is correct: If I look closely at part inside sq root in LHS, then RHS = (LHS) With this thinking clearly i need term inside xto be negative since  (x3) = 3  x since x =\(\sqrt{x^2}\) Proceeding further for statement 2, x * x is a positive value, this is possible only when product is of two negative noso essentially x = x or in other words  (x3) = 3x which is our RHS Does this makes sense? Hi adkikanii am a bit concerned about the above highlighted statement. product of two numbers can be positive when both are positive. we know x is always positive so for xx to be positive x>0 =>x<0 i.e x has to be negative now if LHS \(\sqrt{(x3)^2}\). we know that square root is always positive so LHS is positive RHS=3x where x is negative i.e. x is positive so RHS=positive+positive=positive. Hence LHS=RHS overall seems to be ok



PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82

Re: Is root{(x3)^2}=3x?
[#permalink]
Show Tags
02 Feb 2018, 20:10
akashyap2202 wrote: Since the question doesnt say anything about x being an integer only, Why arent we testing the fraction use cases which comply with the DS statements ?
Please help me understand. Not sure if I am missing something here. Hi akashyap2202In this question we simply need to know whether x<0. Now x can be an integer or a fraction. testing for fraction will not make any difference.




Re: Is root{(x3)^2}=3x? &nbs
[#permalink]
02 Feb 2018, 20:10



Go to page
Previous
1 2
[ 39 posts ]



