Find all School-related info fast with the new School-Specific MBA Forum

It is currently 29 Jul 2016, 11:34
GMAT Club Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is (x-3)^2 =3-x ? (1) x not = 3 (2) -x|x| > 3

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Intern
Intern
avatar
Joined: 03 Dec 2009
Posts: 7
Followers: 0

Kudos [?]: 6 [2] , given: 1

Is (x-3)^2 =3-x ? (1) x not = 3 (2) -x|x| > 3 [#permalink]

Show Tags

New post 20 Dec 2009, 07:50
2
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

56% (02:06) correct 44% (01:15) wrong based on 390 sessions

HideShow timer Statistics

Is \(\sqrt{(x-3)^2}=3-x\)?

(1) \(x\neq{3}\)

(2) -x|x| > 3
[Reveal] Spoiler: OA
Manager
Manager
avatar
Joined: 05 Dec 2009
Posts: 127
Followers: 2

Kudos [?]: 86 [0], given: 0

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 20 Dec 2009, 18:25
Ans: E.

First statement is not sufficient because if x=4, it may or may not be true. LHS = +1 or -1 while RHS = -1.

Second statement leads us to -3^1/2 < x < 0. For all the values between 0 and -3^1/2, which leads to |LHS| = RHS.
Expert Post
9 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34112
Followers: 6106

Kudos [?]: 76860 [9] , given: 9992

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 21 Dec 2009, 02:47
9
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
jan4dday wrote:
Is \(\sqrt{(x-3)^2}=3-x\)?

(1) x not = 3

(2) -x|x| > 3

will give OA as soon as 1st few replies come in


Remember: \(\sqrt{x^2}=|x|\).

\(\sqrt{(x-3)^2}=|x-3|\). So the question becomes is \(|x-3|=3-x\).

When \(x>3\), then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When \(x\leq{3}\), then \(LHS=|x-3|=-x+3=3-x=RHS\), hence in this case equation holds true.

Basically question asks is \(x\leq{3}\)?

(1) x is not equal to 3. Clearly insufficient.

(2) \(-x|x| > 3\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient.

Answer: B.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 26 May 2005
Posts: 209
Followers: 2

Kudos [?]: 109 [0], given: 1

Re: How to solve this Question...I have no clue... [#permalink]

Show Tags

New post 27 Feb 2010, 21:47
is \sqrt{(x-3)^2} = 3-x?
square root of a number is positive.
if x<=3 .. 3-x is always positive
if x>3 ... 3-x is negative

st 1) x!=3 .
not sufficient as we dont know if x>3 or x<3
st 2) -x |x| > 0
|x| is always greater than 0, so x has to be negative for the expression to be > 0

if x is negative, then \sqrt{(x-3)^2} = 3-x

B
Manager
Manager
avatar
Joined: 04 Apr 2009
Posts: 68
Location: United Kingdom
Schools: Cornell
Followers: 1

Kudos [?]: 32 [0], given: 6

Re: How to solve this Question...I have no clue... [#permalink]

Show Tags

New post 17 Mar 2011, 03:58
Just a slight correction I think...
St2 is saying x<-sqrt of 3 which is still a sufficient condition.
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 308 [0], given: 123

Reviews Badge
Re: TOUGH DS Q! [#permalink]

Show Tags

New post 17 Mar 2011, 04:27
I got x<-1.732 from statement 2

This satisfies the x<3 requisite
Hence B

Posted from my mobile device Image
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 465 [0], given: 36

Premium Member Reviews Badge
Re: How to solve this Question...I have no clue... [#permalink]

Show Tags

New post 17 Mar 2011, 23:07
sqrt((x-3)^2) = |x-3| = x-3 if x > 3 or 3-x if x < 3

(1) is not enough

(2) -x|x| is positive then

So -x is also +ve and hence x is -ve

so x < 3, hence answer is B
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
User avatar
Joined: 19 Dec 2010
Posts: 145
Followers: 2

Kudos [?]: 25 [0], given: 12

Re: How to solve this Question...I have no clue... [#permalink]

Show Tags

New post 18 Mar 2011, 20:49
I'm a bit confused by this problem
Why can I not square both sides of the statement to get rid of the radical?
I will then have (x-3)^2=(3-x)^2
Statement 1 and 2 both will not apply in this case and the answer is then E.

However if I choose Bunuels method of doing it, I still dont get how B is the answer.
Statement 2 basically says that x=-2,-3....and so on and so forth will satisfy the statement. So basically all negative numbers equal to or less than 2 will satisfy the condition...
Senior Manager
Senior Manager
avatar
Joined: 29 Jan 2011
Posts: 367
Followers: 0

Kudos [?]: 157 [0], given: 87

Is (x - 3) ^2 = 3 - x 1) x not equal to 3 2) -x|x| [#permalink]

Show Tags

New post 24 Jul 2011, 22:55
1
This post was
BOOKMARKED
Is \(\sqrt{(x - 3)}^2\) = 3 - x

1) x not equal to 3

2) -x|x| > 0
Intern
Intern
avatar
Joined: 15 Mar 2010
Posts: 10
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Is [m][square_root](x - 3)[/square_root]^2[/m] = 3 - x [#permalink]

Show Tags

New post 24 Jul 2011, 23:17
s = 3 - x

1) x not equal to 3

2) -x|x| > 0


Ans: Q can be repharsed as is 3-x>0 ?

Stmt1: x<>3 --> x can take on any values other that x such as x = -9 and 3-(-9) = 12

or x = 10 and 3-(10) = -7 Insuff

Stmt 2 : x has to be negative and any negative value of x will render 3 - x positive. Suff

(B)
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 943
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 107

Kudos [?]: 466 [0], given: 18

Re: Is [m][square_root](x - 3)[/square_root]^2[/m] = 3 - x [#permalink]

Show Tags

New post 24 Jul 2011, 23:47
Lets disect the question stem first.

sqrt((x-3)^2) = 3 - x

Carrying out the squaring and then the square root operation, we get:

|(x-3)| = 3 - x

To solve the modulus sign, we will have two cases -
Case 1: (x-3)>=0
=> x = 3

Case 2: (x-3) < 0
=> Every value of x less than 3 satisfies the equation

Therefore sqrt((x-3)^2) = 3 - x
for all values of x<=3, but this equation is not satisfied for values of x>3

Now consider the statements of the DS.

Statement (1): x is not equal to 3
If x is not equal to 3, it could be greater than 3 or less than 3. If x is less than 3, the equation is satisfied. If x is greater than 3, the equation is not satisfied. Therefore we cannot say if the equation will be satisfied if x is not equal to 3.
Statement (1) alone is therefore insufficient to answer the question.

Next lets consider statement (2):
Statement (2): -x|x|>0
Again to remove the modulus sign make two cases.
Case 1: x>=0 => -x(x) >0 => -(x^2) > 0, which is impossible because x^2 is always >=0, so -(x^2) cannot be >0 for any values of x. Therefore to satisfy this inequality, x cannot be >0
Case 2: x<0 => -x (-x) > 0
=> x^2 > 0 , which is true for all values of x except 0.
Therefore the inequality is satisfied for all values of x<0

Therefore from statement (2) we know that x<0. And from the stem of the question (after we solved it), we know that the equation given in the stem is satisfied for all values of x<=3. Therefore the equation will hold for all values of x specified by statement (2). Therefore statement (2) alone is enough to solve the question.

The answer is therefore (B).
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager
Manager
User avatar
Joined: 16 Jan 2011
Posts: 103
Followers: 11

Kudos [?]: 130 [0], given: 13

Re: Is [m][square_root](x - 3)[/square_root]^2[/m] = 3 - x [#permalink]

Show Tags

New post 28 Jul 2011, 10:26
could you explain me please why do you use inequality signs? in question stem there is just equal sign
Director
Director
User avatar
Status:
Joined: 24 Jul 2011
Posts: 943
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 107

Kudos [?]: 466 [0], given: 18

Re: Is [m][square_root](x - 3)[/square_root]^2[/m] = 3 - x [#permalink]

Show Tags

New post 28 Jul 2011, 22:48
The inequality sign is needed to work with the modulus. When we remove the square root sign, we must take the modulus of the answer because the answer could be positive or negative.

To know more about working with modulus operators, please search for 'Absolute value (Modulus'
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Top MBA Admissions Consulting | Top MiM Admissions Consulting

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1712
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 88

Kudos [?]: 763 [0], given: 109

Is square_root of (x-3)^2 = 3 - x ? [#permalink]

Show Tags

New post 27 Jun 2012, 12:08
Is \(\sqrt{(x-3)^2} = 3 - x\) ?

(1) x is not equal to 3
(2) \(-x |x| > 0\)

According to my reasoning:
\(\sqrt{(x-3)^2}\)\(= |x-3|\)
So, the question is:
Is \(|x-3| = 3 -x\)?
In other words:
Is \(x - 3 < 0\) ?
Is \(x < 3\)?

So, let's see the clues:
(1) x is not equal to 3
INSUFFICIENT.

(2) \(-x |x| > 0\)
Based on this info we know that x is not zero.
So,
\(-x > 0\)
\(x < 0\)
SUFFICIENT.

IMO, the OA is :
[Reveal] Spoiler:
B

Please, confirm whether I am Ok.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34112
Followers: 6106

Kudos [?]: 76860 [0], given: 9992

Re: Is square_root of (x-3)^2 = 3 - x ? [#permalink]

Show Tags

New post 27 Jun 2012, 12:15
Expert's post
Merging similar topics.

metallicafan wrote:
Is \(\sqrt{(x-3)^2} = 3 - x\) ?

(1) x is not equal to 3
(2) \(-x |x| > 0\)

According to my reasoning:
\(\sqrt{(x-3)^2}\)\(= |x-3|\)
So, the question is:
Is \(|x-3| = 3 -x\)?
In other words:
Is \(x - 3 < 0\) ?
Is \(x < 3\)?

So, let's see the clues:
(1) x is not equal to 3
INSUFFICIENT.

(2) \(-x |x| > 0\)
Based on this info we know that x is not zero.
So,
\(-x > 0\)
\(x < 0\)
SUFFICIENT.

IMO, the OA is :
[Reveal] Spoiler:
B

Please, confirm whether I am Ok.


You are right OA is B.
_________________

New to the Math Forum?
Please read this: 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?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 02 Jun 2011
Posts: 159
Followers: 1

Kudos [?]: 65 [0], given: 11

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 28 Jun 2012, 14:53
Bunuel wrote:
jan4dday wrote:
Is \(\sqrt{(x-3)^2}=3-x\)?

(1) x not = 3

(2) -x|x| > 3

will give OA as soon as 1st few replies come in


Remember: \(\sqrt{x^2}=|x|\).

\(\sqrt{(x-3)^2}=|x-3|\). So the question becomes is \(|x-3|=3-x\).

When \(x>3\), then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When \(x\leq{3}\), then \(LHS=|x-3|=-x+3=3-x=RHS\), hence in this case equation holds true.

Basically question asks is \(x\leq{3}\)?

(1) x is not equal to 3. Clearly insufficient.

(2) \(-x|x| > 3\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient.

Answer: B.


Dear Bunuel,
is it possible in this question to solve by taking conditions x>0 and x<0 for |x-3| = 3-x instead of x>3 ?
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1230
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 107

Kudos [?]: 1226 [0], given: 116

Premium Member
Re: DS Question: Is ((x-3)^2)^(1/2) = 3-x? (1) x<>3 (2) -x|x|>0 [#permalink]

Show Tags

New post 21 Nov 2012, 22:02
arvindbhat1887 wrote:
I have no idea how to solve this. Aren't the two of them always equal? I thought LHS = RHS without (1) and (2). VERY confused. Please help


The question is

Is \(\sqrt{(x-3)^2}= 3-x\)?

(1) x<>3

(2) -x|x|>0

\(\sqrt{y}\) can only be positive or 0.

So,The question is basically asking whether 3-x >= 0

1) Insufficient. If x=1, true, If x=10, false.

2) From this we get that x is negative. So -x is postivie. So, 3 + (-x) will always be a positive number. Sufficient.

Answer is hence B.

Kudos Please... If my post helped.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Current Student
avatar
Joined: 02 Jan 2013
Posts: 57
GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 43 [0], given: 2

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 09 Jan 2013, 19:14
Bunuel wrote:
jan4dday wrote:
Is \(\sqrt{(x-3)^2}=3-x\)?

(1) x not = 3

(2) -x|x| > 3

will give OA as soon as 1st few replies come in


Remember: \(\sqrt{x^2}=|x|\).

\(\sqrt{(x-3)^2}=|x-3|\). So the question becomes is \(|x-3|=3-x\).

When \(x>3\), then RHS is negative, but LHS (absolute value) is never negative, hence in this case equations doesn't hold true.

When \(x\leq{3}\), then \(LHS=|x-3|=-x+3=3-x=RHS\), hence in this case equation holds true.

Basically question asks is \(x\leq{3}\)?

(1) x is not equal to 3. Clearly insufficient.

(2) \(-x|x| > 3\), basically this inequality implies that \(x<0\), hence \(x<3\). Sufficient.

Answer: B.




(2) Actually \(-x|x| > 3\), implies that \(x<-sqrt(3)\), but still, as you mentioned, consequently implies that \(x<3\). Sufficient.
Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 154
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 1

Kudos [?]: 62 [0], given: 39

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 31 Mar 2014, 12:55
Hi Bunuel,

In the solution provided by you, why not choosing two conditions x>=0 and x<0? Also how did you come to this conclusion that Basically question is asking x\leq{3}?

Please help me understand this concept.

Regards,
Ravi
Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 154
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 1

Kudos [?]: 62 [0], given: 39

Re: TOUGH DS Q! [#permalink]

Show Tags

New post 31 Mar 2014, 13:22
email2vm wrote:
Hi Bunuel,

In the solution provided by you, why not choosing two conditions x>=0 and x<0? Also how did you come to this conclusion that Basically question is asking x\leq{3}?

Please help me understand this concept.

Regards,
Ravi


I got it now!

|x-3| = (3-x) ===> |3-x| = (3-x) ===>which is only possible when (3-x) >=0 (i.e +ve)

(like |x| =x only when x>=0)

so we have 3-x >=0 ====> x<=3


Also for option B

-x|x| > 3
==> x|x| < 3
so |x| is always positive but so make it less than 3 , x must be negative. i.e. x<0
Re: TOUGH DS Q!   [#permalink] 31 Mar 2014, 13:22

Go to page    1   2    Next  [ 22 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Is 1+x+x^2+x^3+x^4<1/(1-x)? 1) x>0 2) x<1 * A solution will be post MathRevolution 6 21 Mar 2016, 04:31
Experts publish their posts in the topic (x-x_1)*(x-x_2)*(x-x_3)........(x-x_n) MacFauz 6 04 Dec 2012, 01:11
2 Experts publish their posts in the topic Is 3^(x+2)/9 > 1 ? metallicafan 8 26 Jun 2012, 12:25
Experts publish their posts in the topic Is x > sqrt(3)? (1) 3^(x) = sqrt(27) (2)x^3 + x^5 + x^7 spacelandprep 10 07 Mar 2011, 09:44
13 Experts publish their posts in the topic Is 1+x+x^2+x^3+....+x^10 positive? gmatpapa 15 02 Jan 2011, 02:34
Display posts from previous: Sort by

Is (x-3)^2 =3-x ? (1) x not = 3 (2) -x|x| > 3

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.