Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 14:17

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is root{(x-3)^2}=3-x?

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23
Followers: 26

Kudos [?]: 466 [0], given: 11

### Show Tags

16 Jan 2013, 04:04
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

$$\sqrt{(x-3)^2} = 3-x$$
$$|x-3| = 3-x$$
$$3-x >= 0$$
$$3>=x$$ x is less than or equal to 3
_________________

Impossible is nothing to God.

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 614
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 570 Q49 V19
GMAT 2: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Followers: 108

Kudos [?]: 650 [1] , given: 57

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

### Show Tags

06 Mar 2013, 21:19
1
KUDOS
sujit2k7 wrote:
This is a DS question ..

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

1) X # 3
2) -X|X| > 0

Only thing which the question is asking is 3-X positive
As Sqrt (X-3)^2
= X-3 if X-3 is positive
= 3-X if 3-X is positive

STAT1
is INSUFFICIENT as X# 3 doesn't tell anything about whether 3-X is positive or not.

STAT2
-X|X| > 0
since |X| is positive so
-X > 0
=> X <0
and if X< 0 then 3-X will be positive.
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: 629
Followers: 83

Kudos [?]: 1192 [0], given: 136

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

### Show Tags

06 Mar 2013, 21:43
2
This post was
BOOKMARKED
sujit2k7 wrote:
This is a DS question ..

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

1) X # 3
2) -X|X| > 0

We know that $$\sqrt{X^2}$$ = |X|. Thus, the question stem is asking whether |X-3| = 3-X. This is possible only if (X-3) 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 -X|X|>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.
_________________
Manager
Joined: 05 Nov 2012
Posts: 71
Schools: Foster '15 (S)
GPA: 3.65
Followers: 1

Kudos [?]: 135 [0], given: 8

### Show Tags

18 Apr 2013, 16:04
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Here is how i solved it:

1) x [/s]=[/s] 3. Not sufficient
2) -x|x|>0 => x<0 only then the given inequality holds

so [/square_root](s-3)^2[/square_root] => -(x-3) (as we know [/square_root]x^2[/square_root] = - (x) if x<0) and 3-x = -(x-3) so sufficient.

IMO B.
_________________

___________________________________________
Consider +1 Kudos if my post helped

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15431
Followers: 649

Kudos [?]: 207 [0], given: 0

### Show Tags

16 May 2014, 01:01
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 14 Jun 2014
Posts: 4
Followers: 0

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

### Show Tags

24 Dec 2014, 02:13
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Hi Bunuel,

When x\leq{3}, then LHS=|x-3|=-x+3=3-x=RHS, hence in this case equation holds true. Should the part in red not just be "<"?
Math Expert
Joined: 02 Sep 2009
Posts: 38858
Followers: 7727

Kudos [?]: 106044 [0], given: 11607

### Show Tags

24 Dec 2014, 07:24
dmgmat2014 wrote:
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

Hi Bunuel,

When x\leq{3}, then LHS=|x-3|=-x+3=3-x=RHS, hence in this case equation holds true. Should the part in red not just be "<"?

No, because x=3 also satisfies $$\sqrt{(x-3)^2}=3-x$$.
_________________
Intern
Joined: 02 Feb 2011
Posts: 42
Followers: 0

Kudos [?]: 2 [0], given: 108

### 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 |x-3|=|3-x|.

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: 38858
Followers: 7727

Kudos [?]: 106044 [0], given: 11607

### Show Tags

10 Jan 2016, 07:01
seemachandran wrote:
HI understand the square root concept.

But I ended up squaring both sides of equation and got the question as |x-3|=|3-x|.

Can someone explain why cant we square both the sides of equation to eliminate square root on lefthand side?

Hope it helps.
_________________
Intern
Joined: 02 Feb 2011
Posts: 42
Followers: 0

Kudos [?]: 2 [0], given: 108

### 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: 3288
GPA: 3.82
Followers: 239

Kudos [?]: 2021 [0], given: 0

### 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{(x-3)^2}=3-x?

(1) x≠3
(2) −x|x|>0

When you modify the original condition and the question, it becomes n-th power root (A^n)=|A| when n=even, and |A|=A when A>=0, |A|=-A when A<0. So, |x-3|=3-x=-(x-3)? becomes x-3<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), -x|x|>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 one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15431
Followers: 649

Kudos [?]: 207 [0], given: 0

### Show Tags

06 Feb 2017, 03:35
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 29 Oct 2016
Posts: 269
Concentration: Finance, Economics
GMAT 1: 620 Q50 V24
GRE 1: 314 Q167 V147
Followers: 1

Kudos [?]: 24 [0], given: 906

### Show Tags

11 Feb 2017, 00:59
Let's paraphrase the question.
$$\sqrt{(x-3)^{2}}$$ = (3-x) ? is equal to is x-3 < 0 ?

Apparently,stmt (1) is insufficient.

Consider stmt (2) : -x|x| > 0
This inequality can be deduced to -x > 0.
Hence x < 0;we now know that x-3 <0.
Thus,it is sufficient.

Ans B
Intern
Joined: 29 Nov 2016
Posts: 11
Followers: 0

Kudos [?]: 0 [0], given: 141

### 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:

((X-3)^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.

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 $$\sqrt{((X-3)^2)} = (3 - X)$$?

LHS is positive because $$\sqrt{((X-3)^2)} = |X-3|$$
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 |X-3| = - (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 -X|X| > 0
This means -X|X| 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: 7372
Location: Pune, India
Followers: 2287

Kudos [?]: 15099 [1] , given: 224

### Show Tags

26 Apr 2017, 00:56
1
KUDOS
Expert's post
hannahkagalwala wrote:
VeritasPrepKarishma wrote:
mrcrescentfresh wrote:
I am having a hard time grasping why we cannot simplify the problem as:

((X-3)^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.

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 $$\sqrt{((X-3)^2)} = (3 - X)$$?

LHS is positive because $$\sqrt{((X-3)^2)} = |X-3|$$
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 |X-3| = - (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 -X|X| > 0
This means -X|X| 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 $$|X-3| = - (X - 3)$$ ?
Is $$(X - 3) <= 0$$?
Is $$X <= 3$$?

And then we go on to evaluate each statement.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Senior Manager
Joined: 24 Oct 2016
Posts: 298
Followers: 1

Kudos [?]: 12 [0], given: 84

### Show Tags

27 Apr 2017, 23:39
vaivish1723 wrote:
Is $$\sqrt{(x-3)^2}=3-x$$?

(1) $$x\neq{3}$$
(2) $$-x|x| >0$$

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: 15
Followers: 0

Kudos [?]: 2 [0], given: 9

### Show Tags

05 May 2017, 00:55
(x-3)^2}=3-x==>> means should be always positive

is 3-x>0 or x<3 ?

(1) x≠3 ,so x can>3 as well so INSUFF

(2) −x|x|>0-->

TO BE GREATER THAN 0 X SHOULD BE -VE ALWAYS
Hence SUFF
Re: Is root{(x-3)^2}=3-x?   [#permalink] 05 May 2017, 00:55

Go to page   Previous    1   2   [ 37 posts ]

Display posts from previous: Sort by