It is currently 21 Oct 2017, 02:20

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

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y

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

Hide Tags

2 KUDOS received
Director
Director
avatar
Joined: 01 Aug 2008
Posts: 728

Kudos [?]: 844 [2], given: 99

If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 09 Jan 2010, 14:17
2
This post received
KUDOS
15
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

48% (01:00) correct 52% (01:33) wrong based on 434 sessions

HideShow timer Statistics

If \(y\geq{0}\), what is the value of x?

(1) \(|x - 3|\geq{y}\)

(2) \(|x - 3|\leq{-y}\)
[Reveal] Spoiler: OA

Kudos [?]: 844 [2], given: 99

Expert Post
5 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129072 [5], given: 12194

Re: what is the value of x? [#permalink]

Show Tags

New post 09 Jan 2010, 14:45
5
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
If \(y\geq{0}\), what is the value of x?

(1) \(|x - 3|\geq{y}\)

(2) \(|x - 3|\leq{-y}\)

(1) Given \(y\) is non negative value and \(|x - 3|\geq{y}\), so \(|x - 3|\) is more than some non negative value, (we could say the same ourselves as absolute value in our case (\(|x - 3|\)) is never negative). So we can not determine single numerical value of \(x\). Not sufficient.

Or another way: to check \(|x - 3|\geq{y}\geq{0}\) is sufficient or not just plug numbers:
A. \(x=5\), \(y=1>0\), and B. \(x=8\), \(y=2>0\): you'll see that both fits in \(|x - 3|>=y\), \(y\geq{0}\).

Or another way:
\(|x - 3|\geq{y}\) means that:

\(x - 3\geq{y}\geq{0}\) when \(x-3>0\) --> \(x>3\)

OR (not and)
\(-x+3\geq{y}\geq{0}\) when \(x-3<0\) --> \(x<3\)

Generally speaking \(|x - 3|\geq{y}\geq{0}\) means that \(|x - 3|\), an absolute value, is not negative. So, there's no way you'll get a unique value for \(x\). INSUFFICIENT.

(2) \(|x-3|\leq{-y}\), \(y\geq{0}\) --> \(0\leq{-y}\), equation says that \(|x-3|\) less or equals to zero, but \(|x-3|\) never negative (\(|x-3|\geq{0}\)), so only solution is if \(|x-3|=0=y\) --> \(x-3=0\) --> \(x=3\). SUFFICIENT

In other words:
\(-y\) is zero or less, and the absolute value (\(|x-3|\)) must be at zero or below this value. But absolute value (in this case \(|x-3|\)) can not be less than zero, so it must be \(0\).

Answer: B.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129072 [5], given: 12194

1 KUDOS received
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2761

Kudos [?]: 1886 [1], given: 235

Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: value of x? [#permalink]

Show Tags

New post 08 May 2010, 10:35
1
This post received
KUDOS
neoreaves wrote:
If y > = 0, what is the value of x?
1. |x - 3| >= y
2. |x - 3| <= - y


IMO B

Statement 1). |x - 3| >= y >=0
|x - 3| >= 0 , for different values of x, this is true.

Statement 2). |x - 3| <= - y since |x - 3| is always >=0 , and y>=0

|x - 3| <= - y will hold true only when y is 0

=> |x - 3| = 0 , only solution is x=3 hence sufficient.

Thus B
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Kudos [?]: 1886 [1], given: 235

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129072 [1], given: 12194

Re: Simple inequality [#permalink]

Show Tags

New post 19 Jun 2010, 00:37
1
This post received
KUDOS
Expert's post
gmatbull wrote:
If y >= 0, what is the value of x ?

(1) |x - 3| >= y
(2) |x - 3| <= -y

I know that the value of an abs expression cannot be less than 0. so does that imply
that x is 0 units from 3?


As \(y\) is some non-negative value (0, 7, 1.4, ...) then \(-y\) is some non-positive value (0, -9, -5.6, ...). Statement 2 says that \(|x-3|\leq{-y}\) (\(|x-3|\leq{non-positive}\)) - absolute value is less than or equal to some non-positive value, BUT absolute value can not be negative, least value of it is zero, thus \(|x-3|={0}=y\) --> \(x=3\).

Refer for the full solution to my previous post.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129072 [1], given: 12194

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 13 Jan 2011
Posts: 380

Kudos [?]: 37 [1], given: 29

Concentration: Entrepreneurship, International Business
Re: what is the value of x? [#permalink]

Show Tags

New post 19 Jun 2011, 09:15
1
This post received
KUDOS
Ahhhhh i hate absolute value questions. Gets me every time!
_________________

*******************************************************************
~ PickyTooth - Eat Like a Local Foodie // http://www.pickytooth.com ~
*******************************************************************

Kudos [?]: 37 [1], given: 29

1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16610

Kudos [?]: 273 [1], given: 0

Premium Member
Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 12 Jan 2014, 07:38
1
This post received
KUDOS
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

Kudos [?]: 273 [1], given: 0

Senior Manager
Senior Manager
avatar
Joined: 30 Aug 2009
Posts: 283

Kudos [?]: 188 [0], given: 5

Location: India
Concentration: General Management
Re: Gmat Prep DS value question ! [#permalink]

Show Tags

New post 21 Mar 2010, 00:54
nsp007 wrote:
If \(y >= 0\) , what is the value of x ?

1. \(|x-3| >= y\)
2. \(|x-3| <= -y\)


Can anyone pls. explain how to approach such a problem?



B

stmnt1 - |x-3| >= y >=0

let y = 0 then we have |x-3| >= 0 .... x can be 0,1,2,3. hence insuff

stmnt2 - |x-3| <= -y

we know that |x-3| will always be +ve,so only value of y can be 0. we have |x-3| = 0 or x = 3. hence suff

Kudos [?]: 188 [0], given: 5

Manager
Manager
User avatar
Joined: 13 Dec 2009
Posts: 248

Kudos [?]: 250 [0], given: 13

Reviews Badge
Re: Gmat Prep DS value question ! [#permalink]

Show Tags

New post 21 Mar 2010, 23:11
nsp007 wrote:
If \(y >= 0\) , what is the value of x ?

1. \(|x-3| >= y\)
2. \(|x-3| <= -y\)


Can anyone pls. explain how to approach such a problem?

OA
[Reveal] Spoiler:
B


stmt1: |x-3| >= y
in case y>= 0 if we consider y = 0, |x-3| >= 0
but y can be 0, 1,2,3 anything so insufficient.

stmt2: |x-3| <= -y since y >= 0 => -y <= 0
so we can say |x-3| <= -y <= 0
but |x-3| has to be positive which is only possible if y = 0 and |x-3| = 0
only one condition suffice this if x=3, hence sufficient.
so B is the answer
_________________

My debrief: done-and-dusted-730-q49-v40

Kudos [?]: 250 [0], given: 13

Director
Director
avatar
Joined: 21 Dec 2009
Posts: 582

Kudos [?]: 832 [0], given: 20

Concentration: Entrepreneurship, Finance
Re: Simple inequality [#permalink]

Show Tags

New post 19 Jun 2010, 01:17
Bunuel wrote:
gmatbull wrote:
If y >= 0, what is the value of x ?

(1) |x - 3| >= y
(2) |x - 3| <= -y

I know that the value of an abs expression cannot be less than 0. so does that imply
that x is 0 units from 3?


As \(y\) is some non-negative value (0, 7, 1.4, ...) then \(-y\) is some non-positive value (0, -9, -5.6, ...). Statement 2 says that \(|x-3|\leq{-y}\) (\(|x-3|\leq{non-positive}\)) - absolute value is less than or equal to some non-positive value, BUT absolute value can not be negative, least value of it is zero, thus \(|x-3|={0}=y\) --> \(x=3\).

Refer for the full solution to my previous post.

Hope it's clear.


I trust your explanations - very clear. Thanks
_________________

KUDOS me if you feel my contribution has helped you.

Kudos [?]: 832 [0], given: 20

Retired Moderator
User avatar
Joined: 02 Sep 2010
Posts: 793

Kudos [?]: 1186 [0], given: 25

Location: London
GMAT ToolKit User Reviews Badge
Re: what is the value of x? [#permalink]

Show Tags

New post 08 Oct 2010, 16:00
Graphical Solution

We know y>=0. We need to know x.

(1) y<=|x-3|

Image

The inequality represents the regino between the x-axis and the blue line. Knowing y>=0 is not enough to know x

(2)-y>=|x-3| OR y<=-|x-3|

Image

The inequality represents the region below the blue line. We know y>=0, this can only represent the point where, the blue line meets the x-axis or x=3. Sufficient

Answer is (B)
_________________

Math write-ups
1) Algebra-101 2) Sequences 3) Set combinatorics 4) 3-D geometry

My GMAT story

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 1186 [0], given: 25

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129072 [0], given: 12194

Re: what is the value of x? [#permalink]

Show Tags

New post 14 Mar 2011, 03:57
vjsharma25 wrote:
Bunuel wrote:
(2) \(|x-3|\leq{-y}\), \(y\geq{0}\) --> [highlight]\(0\leq{-y}\)[/highlight], equation says that \(|x-3|\) less or equals to zero, but \(|x-3|\) never negative (\(|x-3|\geq{0}\)), so only solution is if \(|x-3|=0=y\) --> \(x-3=0\) --> \(x=3\). SUFFICIENT
It should be [highlight]\(0\geq{-y}\)[/highlight] in my opinion


No, it should be as it is.

(2) \(|x-3|\leq{-y}\) --> now, as LHS is absolute value, which is always non-negative, then we have that \(-y\) is more than or equal to some non-negative value: \(0\leq{-y}\) --> \(y\leq{0}\). As also is given that \(y\geq{0}\) then \(y=0\) --> \(|x-3|\leq{0}\) --> absolute value can not be negative, so \(|x-3|=0\) --> \(x=3\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129072 [0], given: 12194

Manager
Manager
User avatar
Joined: 10 Nov 2010
Posts: 158

Kudos [?]: 334 [0], given: 6

Re: what is the value of x? [#permalink]

Show Tags

New post 14 Mar 2011, 04:05
Bunuel wrote:
vjsharma25 wrote:
Bunuel wrote:
(2) \(|x-3|\leq{-y}\), \(y\geq{0}\) -->[highlight]\(0\leq{-y}\)[/highlight], equation says that \(|x-3|\) less or equals to zero, but \(|x-3|\) never negative (\(|x-3|\geq{0}\)), so only solution is if \(|x-3|=0=y\) --> \(x-3=0\) --> \(x=3\). SUFFICIENT
It should be [highlight]\(0\geq{-y}\)[/highlight] in my opinion


No, it should be as it is.

(2) \(|x-3|\leq{-y}\) --> now, as LHS is absolute value, which is always non-negative, then we have that \(-y\) is more than or equal to some non-negative value: \(0\leq{-y}\) --> \(y\leq{0}\). As also is given that \(y\geq{0}\) then \(y=0\) --> \(|x-3|\leq{0}\) --> absolute value can not be negative, so \(|x-3|=0\) --> \(x=3\).


Does this symbol ---> means "implies that"?. Because I interpreted it that way in the statement.
Rest of the explanation is clear to me.

Kudos [?]: 334 [0], given: 6

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129072 [0], given: 12194

Re: what is the value of x? [#permalink]

Show Tags

New post 14 Mar 2011, 04:16

Kudos [?]: 129072 [0], given: 12194

Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 1964

Kudos [?]: 2051 [0], given: 376

Re: what is the value of x? [#permalink]

Show Tags

New post 14 Mar 2011, 04:42
If y>=0, what is the value of x?

(1) |x-3| >= y

x-3>=y
x>=y+3
or
x-3<=-y
x<=3-y
N.S.

(2)
-(-y)<=x-3<=-y
+y<=x-3<=-y

A positive y can never be less than a -ve y. It can be equal only when y=0
so; +y=x-3=-y=0
x-3=0
x=3
Sufficient.

Ans: "B"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 2051 [0], given: 376

VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1285

Kudos [?]: 283 [0], given: 10

Re: what is the value of x? [#permalink]

Show Tags

New post 20 May 2011, 00:56
absolute value can never give negative results.
B is possible for x = 3
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Kudos [?]: 283 [0], given: 10

SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1597

Kudos [?]: 592 [0], given: 36

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: what is the value of x? [#permalink]

Show Tags

New post 20 May 2011, 08:38
(1)

x - 3 >= 0 as y is >= 0

=> x >= 3

InSufficient

(2)

|x-3| <= 0 as -y <= 0

but |x-3| can't be negative

=> x-3 = 0

=> x = 3

Sufficient

Answer - B
_________________

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

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 592 [0], given: 36

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16610

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 29 Jun 2015, 05:13
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

Kudos [?]: 273 [0], given: 0

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16610

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 17 Sep 2016, 23:08
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

Kudos [?]: 273 [0], given: 0

Intern
Intern
avatar
Joined: 27 Oct 2013
Posts: 39

Kudos [?]: 4 [0], given: 61

Schools: Erasmus '17
Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 16 Oct 2016, 19:49
Bunuel wrote:
If \(y\geq{0}\), what is the value of x?

(1) \(|x - 3|\geq{y}\)

(2) \(|x - 3|\leq{-y}\)

(1) Given \(y\) is non negative value and \(|x - 3|\geq{y}\), so \(|x - 3|\) is more than some non negative value, (we could say the same ourselves as absolute value in our case (\(|x - 3|\)) is never negative). So we can not determine single numerical value of \(x\). Not sufficient.

Or another way: to check \(|x - 3|\geq{y}\geq{0}\) is sufficient or not just plug numbers:
A. \(x=5\), \(y=1>0\), and B. \(x=8\), \(y=2>0\): you'll see that both fits in \(|x - 3|>=y\), \(y\geq{0}\).

Or another way:
\(|x - 3|\geq{y}\) means that:

\(x - 3\geq{y}\geq{0}\) when \(x-3>0\) --> \(x>3\)

OR (not and)
\(-x+3\geq{y}\geq{0}\) when \(x-3<0\) --> \(x<3\)

Generally speaking \(|x - 3|\geq{y}\geq{0}\) means that \(|x - 3|\), an absolute value, is not negative. So, there's no way you'll get a unique value for \(x\). INSUFFICIENT.

(2) \(|x-3|\leq{-y}\), \(y\geq{0}\) --> \(0\leq{-y}\), equation says that \(|x-3|\) less or equals to zero, but \(|x-3|\) never negative (\(|x-3|\geq{0}\)), so only solution is if \(|x-3|=0=y\) --> \(x-3=0\) --> \(x=3\). SUFFICIENT

In other words:
\(-y\) is zero or less, and the absolute value (\(|x-3|\)) must be at zero or below this value. But absolute value (in this case \(|x-3|\)) can not be less than zero, so it must be \(0\).

Answer: B.

Bunuel

For A. u removed euqlity sign from the equestion.

equation results in x>=3 or x<=3, Hence x could be 3. Hence A sufficies, the condition.
Please tell me, where i understood it wrong.

Kudos [?]: 4 [0], given: 61

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129072 [0], given: 12194

Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y [#permalink]

Show Tags

New post 17 Oct 2016, 03:10
rahul202 wrote:
Bunuel wrote:
If \(y\geq{0}\), what is the value of x?

(1) \(|x - 3|\geq{y}\)

(2) \(|x - 3|\leq{-y}\)

(1) Given \(y\) is non negative value and \(|x - 3|\geq{y}\), so \(|x - 3|\) is more than some non negative value, (we could say the same ourselves as absolute value in our case (\(|x - 3|\)) is never negative). So we can not determine single numerical value of \(x\). Not sufficient.

Or another way: to check \(|x - 3|\geq{y}\geq{0}\) is sufficient or not just plug numbers:
A. \(x=5\), \(y=1>0\), and B. \(x=8\), \(y=2>0\): you'll see that both fits in \(|x - 3|>=y\), \(y\geq{0}\).

Or another way:
\(|x - 3|\geq{y}\) means that:

\(x - 3\geq{y}\geq{0}\) when \(x-3>0\) --> \(x>3\)

OR (not and)
\(-x+3\geq{y}\geq{0}\) when \(x-3<0\) --> \(x<3\)

Generally speaking \(|x - 3|\geq{y}\geq{0}\) means that \(|x - 3|\), an absolute value, is not negative. So, there's no way you'll get a unique value for \(x\). INSUFFICIENT.

(2) \(|x-3|\leq{-y}\), \(y\geq{0}\) --> \(0\leq{-y}\), equation says that \(|x-3|\) less or equals to zero, but \(|x-3|\) never negative (\(|x-3|\geq{0}\)), so only solution is if \(|x-3|=0=y\) --> \(x-3=0\) --> \(x=3\). SUFFICIENT

In other words:
\(-y\) is zero or less, and the absolute value (\(|x-3|\)) must be at zero or below this value. But absolute value (in this case \(|x-3|\)) can not be less than zero, so it must be \(0\).

Answer: B.

Bunuel

For A. u removed euqlity sign from the equestion.

equation results in x>=3 or x<=3, Hence x could be 3. Hence A sufficies, the condition.
Please tell me, where i understood it wrong.


Yes, x can be 3 but how does this help to get the exact value of x? Cannot x be any other value?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Kudos [?]: 129072 [0], given: 12194

Re: If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y   [#permalink] 17 Oct 2016, 03:10

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

If y>=0, What is the value of x? (1) |x-3|>=y (2) |x-3|<=-y

  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 | Emoji artwork provided by EmojiOne

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®.