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

It is currently 27 Nov 2014, 15:10

Happy Thanksgiving:

Free Access to GMAT Club Tests until 11 AM PST on Fri 11/28


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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
4 KUDOS received
Director
Director
avatar
Joined: 23 Sep 2007
Posts: 797
Followers: 5

Kudos [?]: 86 [4] , given: 0

Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 24 Apr 2008, 16:42
4
This post received
KUDOS
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:51) correct 46% (01:21) wrong based on 459 sessions
Is \sqrt{(x-3)^2} = 3-x?

(1) x\neq{3}

(2) -x|x| > 0
[Reveal] Spoiler: OA

Attachments

fasdfasdfasdfasdf.JPG
fasdfasdfasdfasdf.JPG [ 30.21 KiB | Viewed 9670 times ]

3 KUDOS received
Manager
Manager
User avatar
Joined: 24 Apr 2008
Posts: 162
Followers: 1

Kudos [?]: 37 [3] , given: 0

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 24 Apr 2008, 20:45
3
This post received
KUDOS
From the que: 3-x is always >0 --> x has to be less than 3.

Option 1: X can also be >3 when ans fails so insufficient
Option 2: -x|x|>0 implies x is always < 0 which means x is less than 3 hence sufficient.

Ans : B
2 KUDOS received
Director
Director
avatar
Joined: 14 Aug 2007
Posts: 735
Followers: 7

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

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 24 Apr 2008, 23:23
2
This post received
KUDOS
gmatnub wrote:
is sqrt ((x-3)^2) = 3-x?

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

The oa is B, but why is A alone not enough?


given |x-3| can be equal to 3-x for x < 3,

1) X can be greater than 3
2) X is less than 0, i.e x < 3, for all x.

so B
1 KUDOS received
Intern
Intern
avatar
Joined: 04 Dec 2009
Posts: 24
Followers: 0

Kudos [?]: 8 [1] , given: 13

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 13 Jun 2010, 01:57
1
This post received
KUDOS
I understand that 1) is insuff

But for 2) -x|x| > 0 means x cant be +ve => |x| = -x so that -x (-x) = x^2> 0

If x is -ve => (x-3)^2 = X^2+9-6x = (-ve)^2+9-6(-ve) = +ve+9-(-ve) = +ve +9 + (+ve) = +ve

=> sqrt ((x-3)^2) = +X-3

=> sqrt ( (x-3) ^2 ) is not equal to 3-x

=> Option B

Am I right In my logic.Please help
Expert Post
8 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24141
Followers: 3740

Kudos [?]: 31390 [8] , given: 3372

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 13 Jun 2010, 02:41
8
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
gautamsubrahmanyam wrote:
I understand that 1) is insuff

But for 2) -x|x| > 0 means x cant be +ve => |x| = -x so that -x (-x) = x^2> 0

If x is -ve => (x-3)^2 = X^2+9-6x = (-ve)^2+9-6(-ve) = +ve+9-(-ve) = +ve +9 + (+ve) = +ve

=> sqrt ((x-3)^2) = +X-3

=> sqrt ( (x-3) ^2 ) is not equal to 3-x

=> Option B

Am I right In my logic.Please help


Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!

CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 3291
Followers: 225

Kudos [?]: 44 [0], given: 0

Premium Member
Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 16 Sep 2013, 01:42
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 30 Jan 2012
Posts: 14
Location: United States
Concentration: Entrepreneurship, Strategy
GMAT 1: 640 Q47 V32
GPA: 3.6
Followers: 0

Kudos [?]: 8 [0], given: 19

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 23 Sep 2013, 07:09
Hello Bunuel,

Please help me understand where I am going wrong.

After this point..

|x-3|=3-x

Can this equation be written this way?

1)
x-3 = 3-x => x = 3

2)
-(x-3) = 3-x .. this leads to nothing

So I concluded that the question is whether x=3 and hence I chose A as answer.. but I am wrong.

What is that I doing wrong here?

Thanks
C23678


Bunuel wrote:
Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24141
Followers: 3740

Kudos [?]: 31390 [0], given: 3372

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 24 Sep 2013, 06:22
Expert's post
c23678 wrote:
Hello Bunuel,

Please help me understand where I am going wrong.

After this point..

|x-3|=3-x

Can this equation be written this way?

1)
x-3 = 3-x => x = 3

2)
-(x-3) = 3-x .. this leads to nothing

So I concluded that the question is whether x=3 and hence I chose A as answer.. but I am wrong.

What is that I doing wrong here?

Thanks
C23678


Bunuel wrote:
Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.


|x-3|=-(x-3) when x\leq{3}. In this case we'd have -(x-3)=3-x --> 3=3 --> true. This means that when x\leq{3}, then the equation holds true.

Try numbers less than or equal to 3 to check.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!

Intern
Intern
avatar
Joined: 07 May 2014
Posts: 15
Followers: 1

Kudos [?]: 2 [0], given: 6

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 27 Jul 2014, 09:29
Please clarify a doubt which i have in this question :

If we have a question, Is x<=5,
A. X<0
B. X<=0

What will be the answer?

In the original question, I am confused because 0, which satisfies the equation, doesn't appear in x|x| < 0. And hence the solution is incomplete.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24141
Followers: 3740

Kudos [?]: 31390 [0], given: 3372

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 27 Jul 2014, 13:50
Expert's post
vibsaxena wrote:
Please clarify a doubt which i have in this question :

If we have a question, Is x<=5,
A. X<0
B. X<=0

What will be the answer?

In the original question, I am confused because 0, which satisfies the equation, doesn't appear in x|x| < 0. And hence the solution is incomplete.


The answer would be D.

The original question asks whether x\leq{3}: the answer would be YES if x is 3 or less than 3. (2) says that x<0, so the answer is clearly YES.

Does this make sense?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!

Intern
Intern
avatar
Joined: 07 May 2014
Posts: 15
Followers: 1

Kudos [?]: 2 [0], given: 6

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 30 Jul 2014, 12:31
Thanks Bunnel,

I get it now. Actually, I didn't at first, then stumbled upon another question, a geometry one this time, and could draw the parallels. The question here doesn't ask if x<=0, it asks if x<3.

Got it, thanks. The geometry question I am referring to is this - a-circle-is-drawn-on-a-coordinate-plane-if-a-line-is-drawn-161692.html (the question asks if slope is less than 1, not zero, not anything else)!
MBA Blogger
avatar
Joined: 19 Apr 2014
Posts: 91
Location: India
Concentration: Strategy, Technology
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 21 [0], given: 43

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 01 Sep 2014, 23:24
Bunuel wrote:

Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.


Hi Bunuel,
Can't we rephrase the question like:
Is \sqrt{(x-3)^2}=3-x?
Or : (x-3)^2=(3-x)^2
Or : x-3=3-x
Or : x=3?

Please tell me where I am doing wrong?
Thanks.
_________________

KUDOS please!! If it helped. :)
Warm Regards.
Visit My Blog


Last edited by scofield1521 on 01 Sep 2014, 23:37, edited 1 time in total.
Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 716
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 20

Kudos [?]: 360 [0], given: 712

Premium Member CAT Tests
Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 01 Sep 2014, 23:33
scofield1521 wrote:
Hi Bunuel,
Can't we rephrase the question like:
Is \sqrt{(x-3)^2}=3-x?
Or : (x-3)^2=3-x
Or : x-3=3-x
Or : x=3?

Please tell me where I am doing wrong?
Thanks.


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

Squaring Both sides...

(x-3)^{2}=(3-x)^{2}
x^{2}+9-6x=9+x^{2}-6x=0

Now this expression will always be equal..for any value of x...so this approach leads you to no where
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

1 KUDOS received
Manager
Manager
User avatar
Joined: 03 Aug 2011
Posts: 224
Location: Bulgaria
GMAT 1: 640 Q44 V34
GMAT 2: 700 Q41 V44
GPA: 3.7
WE: Project Management (Energy and Utilities)
Followers: 8

Kudos [?]: 25 [1] , given: 340

GMAT ToolKit User
Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 02 Sep 2014, 06:08
1
This post received
KUDOS
Hi Bunuel,

Thanks for the great explanations and the GMAT Club Math Book as well! Great resource.

A question regarding the above question and square roots/absolute values in general. In the GMAT Club Math Book you write "That is, SQRT (25)=5 , NOT +5 or -5. In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only a positive value on the GMAT."

What you are basically saying here is that whenever we have an equation with a positive and even square root we shall utilize the absolute value. BUT when we have just a random figure, we shall use only the positive root. Right?

Thanks again!
_________________

Thank you very much for reading this post till the end! Kudos?

Intern
Intern
avatar
Joined: 07 May 2014
Posts: 15
Followers: 1

Kudos [?]: 2 [0], given: 6

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 03 Sep 2014, 04:20
Thanks Bunnel ! This was one brilliant explanation !


scofield1521 wrote:
Bunuel wrote:

Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.


Hi Bunuel,
Can't we rephrase the question like:
Is \sqrt{(x-3)^2}=3-x?
Or : (x-3)^2=(3-x)^2
Or : x-3=3-x
Or : x=3?

Please tell me where I am doing wrong?
Thanks.
Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 34
Followers: 0

Kudos [?]: 4 [0], given: 3

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 03 Sep 2014, 11:18
gmatnub wrote:
Is \sqrt{(x-3)^2} = 3-x?

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


mod(x-3)=3-x?

mod(y) = -y when y is -ve => mod(x-3) can be equal to -(x-3) only when x-3 is negative i.e x-3<0 => x<3

1) x not equal to 3=> which means x can be greater than 3 or less than 3
2) -x|x|>0=> this is possible only when x is -ve i.e x<0

statement 2 gives x<0, so statement 2 alone solves the problem.
Intern
Intern
avatar
Joined: 28 Sep 2012
Posts: 12
Followers: 0

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

CAT Tests
Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 30 Sep 2014, 10:25
Bunuel wrote:
gautamsubrahmanyam wrote:
I understand that 1) is insuff

But for 2) -x|x| > 0 means x cant be +ve => |x| = -x so that -x (-x) = x^2> 0

If x is -ve => (x-3)^2 = X^2+9-6x = (-ve)^2+9-6(-ve) = +ve+9-(-ve) = +ve +9 + (+ve) = +ve

=> sqrt ((x-3)^2) = +X-3

=> sqrt ( (x-3) ^2 ) is not equal to 3-x

=> Option B

Am I right In my logic.Please help


Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.


Hi Bunuel,

I am ok with X<=3 but statement B says x < 0 . Lets say X=2 in that case also the LHS = RHS but B says X<0 . I am confused where am i going wrong in my approach. Please help
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24141
Followers: 3740

Kudos [?]: 31390 [0], given: 3372

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 30 Sep 2014, 10:34
Expert's post
snehamd1309 wrote:
Bunuel wrote:
gautamsubrahmanyam wrote:
I understand that 1) is insuff

But for 2) -x|x| > 0 means x cant be +ve => |x| = -x so that -x (-x) = x^2> 0

If x is -ve => (x-3)^2 = X^2+9-6x = (-ve)^2+9-6(-ve) = +ve+9-(-ve) = +ve +9 + (+ve) = +ve

=> sqrt ((x-3)^2) = +X-3

=> sqrt ( (x-3) ^2 ) is not equal to 3-x

=> Option B

Am I right In my logic.Please help


Yes, the answer for this question is B.

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

Remember: \sqrt{x^2}=|x|. Why?

Couple of things:

The point here is that square root function can not give negative result: wich means that \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function! That is why \sqrt{x^2}=|x|

Back to the original question:

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

When x>3, then RHS (right hand side) 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\neq{3}. Clearly insufficient.

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

Answer: B.

Hope it helps.


Hi Bunuel,

I am ok with X<=3 but statement B says x < 0 . Lets say X=2 in that case also the LHS = RHS but B says X<0 . I am confused where am i going wrong in my approach. Please help


The question asks whether x\leq{3}?
The second statement says that x<0. So, the answer to the question is yes.

Also, if we know that x < 0, then HOW can x be 2?
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!

Intern
Intern
avatar
Joined: 01 Sep 2014
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 19

GMAT ToolKit User CAT Tests
Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 23 Oct 2014, 22:40
Hi Bunuel
I am still confused about this.Please help me out.
As a^2 = 25 has two solutions -------------------------> a=5 and a= -5
therefore a= sqrt 25 should also have two solutions-----> a=5 and a= -5

Then why do we say that square root of a positive no. is always positive?
Shouldn't sqrt 25 have two possible values +5 and -5. ?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24141
Followers: 3740

Kudos [?]: 31390 [1] , given: 3372

Re: Is sqrt ((x-3)^2) = 3-x? [#permalink] New post 24 Oct 2014, 02:21
1
This post received
KUDOS
Expert's post
arpitsharms wrote:
Hi Bunuel
I am still confused about this.Please help me out.
As a^2 = 25 has two solutions -------------------------> a=5 and a= -5
therefore a= sqrt 25 should also have two solutions-----> a=5 and a= -5

Then why do we say that square root of a positive no. is always positive?
Shouldn't sqrt 25 have two possible values +5 and -5. ?


NO!

When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the positive root.

That is:
\sqrt{9} = 3, NOT +3 or -3;
\sqrt[4]{16} = 2, NOT +2 or -2;

Notice that in contrast, the equation x^2 = 9 has TWO solutions, +3 and -3. Because x^2 = 9 means that x =-\sqrt{9}=-3 or x=\sqrt{9}=3.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Take a Survey about GMAT Prep - Win Prizes!

Re: Is sqrt ((x-3)^2) = 3-x?   [#permalink] 24 Oct 2014, 02:21
    Similar topics Author Replies Last post
Similar
Topics:
1 Is sqrt((x-3)^2) = 3-x dxx 1 15 May 2014, 12:44
Is x > sqrt(3)? (1) 3^(x) = sqrt(27) (2)x^3 + x^5 + x^7 spacelandprep 10 07 Mar 2011, 08:44
3 Experts publish their posts in the topic Is sqrt ((x-3)^2) = 3-x? rohitgoel15 5 22 Mar 2010, 21:37
is sqrt(x) odd ? (1) 3x^2 is even (2) x.sqrt(x) is divisble Mishari 2 10 Jun 2007, 11:32
is (sqrt. of (x-3)^2)= 3-x 1. x is not equal to 3 lan583 5 05 Oct 2006, 12:07
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 25 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| 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®.