Is root(x-5)^2 = 5 - x ? : GMAT Data Sufficiency (DS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 09 Dec 2016, 16:35
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.

Close

Request Expert Reply

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is root(x-5)^2 = 5 - x ?

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

Hide Tags

1 KUDOS received
Manager
Manager
avatar
Joined: 01 Apr 2006
Posts: 183
Location: Toronto, Canada
Followers: 1

Kudos [?]: 95 [1] , given: 0

Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 13 Jan 2007, 10:52
1
This post received
KUDOS
19
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

61% (02:23) correct 39% (01:27) wrong based on 800 sessions

HideShow timer Statistics

Is \(\sqrt{(x-5)^2} = 5 - x\)?

(1) -x|x| > 0
(2) 5 - x > 0
[Reveal] Spoiler: OA
2 KUDOS received
SVP
SVP
User avatar
Joined: 01 May 2006
Posts: 1797
Followers: 9

Kudos [?]: 146 [2] , given: 0

 [#permalink]

Show Tags

New post 13 Jan 2007, 11:11
2
This post received
KUDOS
2
This post was
BOOKMARKED
For me (D) :)

sqrt( (x-5)^2) = 5 - x ?
<=> |x-5| = 5-x ?
<=> |5-x| = 5-x ?

This is true if 5-x >= 0 <=> x =< 5

So we end up with checking if x =< 5 ?

Stat 1
-x |x| > 0
<=> x < 0 < 5

SUFF.

Stat 2
5 - x > 0
<=> x < 5

SUFF.
Intern
Intern
avatar
Joined: 10 Jun 2009
Posts: 31
Location: Stockholm, Sweden
Followers: 0

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

Re: DS: Sqrt inequality [#permalink]

Show Tags

New post 15 Jun 2009, 11:25
My line of thinking is that the only time you can answer "no" to the question is when x>=5. For all values below 5 the answer is "yes"

1) tells us that x is negative - sufficient
2) tells us that x is <5 - sufficient
Intern
Intern
avatar
Joined: 30 Jul 2009
Posts: 21
Followers: 0

Kudos [?]: 10 [0], given: 18

Re: DS: Sqrt inequality [#permalink]

Show Tags

New post 09 Sep 2009, 11:01
Just want to make sure that my line of thinking is right. I got D as well.

sqrt(x-5)^2 = 5-x
==> |x-5| = 5-x

which means that if

x-5<0, -(x-5) = 5-x = no solution, therefore x<5

x-5>0, x-5 = 5-x, which means that x>5 and x = 5

from (1) -x|x| > 0, we know that x has to be negative -(-x)|-x| is the only way to get a number greater than 0. Therefore, this means that of the three possible solutions for x, only this x<5 hold true.

from (2) 5-x>0, therefore x<5.

Can someone please point out if there is something wrong with my reasoning.
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90100 [5] , given: 10413

Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 09 Sep 2009, 14:41
5
This post received
KUDOS
Expert's post
8
This post was
BOOKMARKED
dhushan wrote:
Just want to make sure that my line of thinking is right. I got D as well.

sqrt(x-5)^2 = 5-x
==> |x-5| = 5-x

which means that if

x-5<0, -(x-5) = 5-x = no solution, therefore x<5

x-5>0, x-5 = 5-x, which means that x>5 and x = 5

from (1) -x|x| > 0, we know that x has to be negative -(-x)|-x| is the only way to get a number greater than 0. Therefore, this means that of the three possible solutions for x, only this x<5 hold true.

from (2) 5-x>0, therefore x<5.

Can someone please point out if there is something wrong with my reasoning.


Is \(\sqrt{(x-5)^2}=5-x\)?

First of all, recall that \(\sqrt{x^2}=|x|\).

Is \(\sqrt{(x-5)^2}=5-x\)? --> is \(|x-5|=5-x\)? --> is \(x-5\leq{0}\)? --> is \(x\leq{5}\)?

(1) \(-x|x| > 0\) --> \(|x|\) is never negative (positive or zero), so for \(-x|x|\) to be positive, \(-x\) must be positive \(-x>0\) --> \(x<0\). Sufficient.

(2) \(5-x>0\) --> \(x<5\). Sufficient.

Answer: D.
_________________

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: 08 Jul 2009
Posts: 171
Followers: 0

Kudos [?]: 25 [0], given: 26

Re: Square root. [#permalink]

Show Tags

New post 29 Dec 2009, 11:27
For the question to be true. the right side of the equation has to be positive, (hence x has to be smaller than 5) because the left side of the equation is always positive.

s1 tells us that x is a negative number. So, it's sufficient
s2 tells us that x is less than 5, so it sufficient.

Therefore, answer D
Manager
Manager
User avatar
Joined: 25 Aug 2009
Posts: 175
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years
Followers: 12

Kudos [?]: 175 [0], given: 3

Re: Square root. [#permalink]

Show Tags

New post 31 Dec 2009, 08:40
The question basically wants to know if x<=5 else RHS will be x-5

Statement 1
-x|x|>0
or
x|x|<0 (multiply by -1 both sides and reverse the sign)
either x<0 or |x|<0
since |x| is always positive or 0 x<0 is true.
if x<0 then x<5 hence sufficient

Statement 2
5-x>0
5>x
This is what we are looking for hence sufficient

Answer is D.
_________________

Rock On

Manager
Manager
avatar
Joined: 18 Jul 2009
Posts: 53
Followers: 3

Kudos [?]: 103 [0], given: 7

Re: Square root. [#permalink]

Show Tags

New post 31 Dec 2009, 08:49
Since L.H.S is a square it will be always positive.and R.H.S 5-x will only be positive when x is less than or equal to 5. so in other words the question can be rephrase as is x<=5


stmt1: -x|x|>0

divide both side by |x| we get -x>0 it means x < 0 sufficient


stmt 2: 5-x>0

add x both side
we get 5>x means x<5 sufficient.


hope this helps
Intern
Intern
User avatar
Joined: 25 Apr 2009
Posts: 10
Followers: 0

Kudos [?]: 1 [0], given: 2

Re: Square root. [#permalink]

Show Tags

New post 31 Dec 2009, 21:25
Simplify the question:
|x-5|=5-x

statement 1:
x<0

statement 2:
5>x

plug in any numbers for each statement.
Hence, D
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 7076
Location: Pune, India
Followers: 2089

Kudos [?]: 13304 [0], given: 222

Re: Square root. [#permalink]

Show Tags

New post 19 Mar 2011, 19:20
Expert's post
2
This post was
BOOKMARKED
arjunrampal wrote:
Please explain the approach to solve the problem and point to any relevant material available in the GMAT club.

Attachment:
square_root_D.JPG


[Reveal] Spoiler:
AO=D


Let me point out something here: You cannot square both sides to get
Is \((\sqrt{(x-5)^2})^2 = (5-x)^2\) ?

People sometimes get confused here. Why can you not square it?
It is a question similar to 'Is x = 5?' Can you square both sides here and change the question to 'Is \(x^2 = 25\)?' Please remember, they are not the same. x^2 can be 25 even if x is not 5 ( when x = -5, even then x^2 = 25).
Only if it is given to you that x = 5, then you can say that x^2 = 25.

You can rephrase the question in the following manner (and many more ways)

Is \((\sqrt{(x-5)^2}) = (5-x)\) ?
Is \(|x-5| = (5-x)\) ?
or Is \(|5-x| = (5-x)\)?
We know that |x| = x only when x >= 0
So \(|5-x| = (5-x)\) only when 5 - x >= 0 or when x <= 5

Stmnt 1: -x|x| > 0
Since |x| is always positive (or zero), -x must be positive too. So x must be negative.
If x < 0, then x is obviously less than 5. Sufficient.

Stmnt 2: 5 - x> 0
x < 5. Sufficient

Answer D
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 507 [0], given: 36

Premium Member Reviews Badge
Re: Square root. [#permalink]

Show Tags

New post 20 Mar 2011, 01:39
sqrt((x-5)^2) = |x-5|

If (x-5) < 0 then |x-5| = 5 -x

So the question is if x < 5

From (1), -x|x| > 0 => -x is +ve, so x is -ve hence sufficient.

From (2), 5-x > 0, so x-5 < 0, which is what the question is asking, so answer is D.
_________________

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

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 114 [0], given: 42

Re: Square root. [#permalink]

Show Tags

New post 20 Mar 2011, 12:39
sqrt(x^2) = |x|

|x-5| will only be equal to 5-x when x-5<0 => x has to be less than 5. so we have to see if x<5?

1. Sufficient

-x|x| <0
|x| is always +ve => x is -ve i.e x<0<5 = >x<5

2. Sufficient
x<5

Answer D
Manager
Manager
User avatar
Joined: 27 Apr 2014
Posts: 53
GMAT 1: 710 Q47 V40
Followers: 0

Kudos [?]: 5 [0], given: 20

GMAT ToolKit User
Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 26 Jul 2014, 11:51
you need to prove that
x<= 5 so x = 5 & x<5

Statement 2 doesnt prove x<5

Something I'm missing?
_________________

Kudos my back and I Kudos your back

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90100 [0], given: 10413

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 26 Jul 2014, 12:00
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 55 [0], given: 185

Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 11 Jul 2015, 01:04
I simplified the equation up to the point where it states:
Is \((x-4)*(x-5) = 0\) or is x1 = 4 / x2 = 5 ?

I then was not able to use statement 1 properly, but would that theoretically be possible?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90100 [0], given: 10413

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 11 Jul 2015, 01:29
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 55 [0], given: 185

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 11 Jul 2015, 04:06
Bunuel wrote:
noTh1ng wrote:
I simplified the equation up to the point where it states:
Is \((x-4)*(x-5) = 0\) or is x1 = 4 / x2 = 5 ?

I then was not able to use statement 1 properly, but would that theoretically be possible?


It's not clear HOW you get the above. Please elaborate.


I think i miscalculated. Now did it again, simplifying the equation \(\sqrt{(x-5)^2} = 5 - x\)?

should result in 25=25, correct?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35932
Followers: 6860

Kudos [?]: 90100 [0], given: 10413

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 11 Jul 2015, 07:40
noTh1ng wrote:
Bunuel wrote:
noTh1ng wrote:
I simplified the equation up to the point where it states:
Is \((x-4)*(x-5) = 0\) or is x1 = 4 / x2 = 5 ?

I then was not able to use statement 1 properly, but would that theoretically be possible?


It's not clear HOW you get the above. Please elaborate.


I think i miscalculated. Now did it again, simplifying the equation \(\sqrt{(x-5)^2} = 5 - x\)?

should result in 25=25, correct?


No. The above equation holds for ANY value of x less than or equal to 5.
_________________

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

Intern
Intern
avatar
Joined: 09 Feb 2013
Posts: 18
Followers: 0

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

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 12 Jul 2015, 05:49
Bunuel wrote:
dhushan wrote:
Just want to make sure that my line of thinking is right. I got D as well.

sqrt(x-5)^2 = 5-x
==> |x-5| = 5-x

which means that if

x-5<0, -(x-5) = 5-x = no solution, therefore x<5

x-5>0, x-5 = 5-x, which means that x>5 and x = 5

from (1) -x|x| > 0, we know that x has to be negative -(-x)|-x| is the only way to get a number greater than 0. Therefore, this means that of the three possible solutions for x, only this x<5 hold true.

from (2) 5-x>0, therefore x<5.

Can someone please point out if there is something wrong with my reasoning.


Is \(\sqrt{(x-5)^2}=5-x\)?

First of all, recall that \(\sqrt{x^2}=|x|\).

Is \(\sqrt{(x-5)^2}=5-x\)? --> is \(|x-5|=5-x\)? --> is \(x-5\leq{0}\)? --> is \(x\leq{5}\)?

(1) \(-x|x| > 0\) --> \(|x|\) is never negative (positive or zero), so for \(-x|x|\) to be positive, \(-x\) must be positive \(-x>0\) --> \(x<0\). Sufficient.

(2) \(5-x>0\) --> \(x<5\). Sufficient.

Answer: D.



Hi Bunuel,

I didn't understand from here : is |x−5|=5−x? --> is x−5≤0? --> is x≤5?.

Can you please explain further ?

Regards
Kshitij
1 KUDOS received
Intern
Intern
avatar
Joined: 04 Jan 2015
Posts: 7
Followers: 0

Kudos [?]: 8 [1] , given: 2

Re: Is root(x-5)^2 = 5 - x ? [#permalink]

Show Tags

New post 12 Jul 2015, 07:32
1
This post received
KUDOS
kshitij89

Modulus always results in an positive value.
If x-5>0 then |x−5| should be equal to x-5
However, If x-5<0 then modulus would result the positive value of it i.e. -(x-5)=5-x

Thus, is |x−5|=5−x? --> is x−5<0? --> is x<5?

Solving as Bunuel ,you'll get D. :)
Re: Is root(x-5)^2 = 5 - x ?   [#permalink] 12 Jul 2015, 07:32

Go to page    1   2    Next  [ 23 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
3 Experts publish their posts in the topic Is 1/(5 - X) > X/5? Bunuel 6 24 Jun 2016, 02:08
5 Experts publish their posts in the topic If 5-√5<x<5+√5, x=? MathRevolution 7 01 Apr 2016, 07:07
10 Experts publish their posts in the topic Is sqrt(x-5)^2 = 5-x? metallicafan 8 06 Sep 2010, 11:20
5 If |x| > 5, is |x - 5| = 5 - x ezhilkumarank 8 07 Aug 2010, 16:57
7 Experts publish their posts in the topic Is root(5-x)^2=5-x? burnttwinky 11 02 May 2010, 14:51
Display posts from previous: Sort by

Is root(x-5)^2 = 5 - x ?

  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®.