In the x-y plane the area of the region bounded by the : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 10 Dec 2016, 05:41
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

In the x-y plane the area of the region bounded by the

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

Hide Tags

5 KUDOS received
Manager
Manager
User avatar
Joined: 09 Jun 2009
Posts: 226
Followers: 2

Kudos [?]: 234 [5] , given: 6

In the x-y plane the area of the region bounded by the [#permalink]

Show Tags

New post 08 Nov 2009, 13:11
5
This post received
KUDOS
48
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (02:26) correct 38% (01:33) wrong based on 979 sessions

HideShow timer Statistics

In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 4 is

A. 8
B 12
C. 16
D. 20
E. 24

Need help in solving equations involving Mod......
help?
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Feb 2012, 23:29, edited 2 times in total.
Edited the question and added the OA
Expert Post
11 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35950
Followers: 6862

Kudos [?]: 90110 [11] , given: 10417

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 13:34
11
This post received
KUDOS
Expert's post
14
This post was
BOOKMARKED
papillon86 wrote:
In x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 4 is

a) 8
b) 12
c) 16
d) 20

Need help in solving equations involving Mod......
help?


OK, there can be 4 cases:

|x+y| + |x-y| = 4

A. x+y+x-y = 4 --> x=2
B. x+y-x+y = 4 --> y=2
C. -x-y +x-y= 4 --> y=-2
D. -x-y-x+y=4 --> x=-2

The area bounded by 4 graphs x=2, x=-2, y=2, y=-2 will be square with the side of 4 so the area will be 4*4=16.
Attachment:
MSP17971c13h40gd024h6g10000466ge1e9df941i96.gif
MSP17971c13h40gd024h6g10000466ge1e9df941i96.gif [ 1.86 KiB | Viewed 9770 times ]


Answer: C
_________________

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

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 158 [0], given: 37

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 14:27
Bunuel wrote:
papillon86 wrote:
In x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 4 is

a) 8
b) 12
c) 16
d) 20

Need help in solving equations involving Mod......
help?


I've never seen such kind of question in GMAT before.

OK there can be 4 cases:

|x+y| + |x-y| = 4

A. x+y+x-y = 4 --> x=2
B. x+y-x+y = 4 --> y=2
C. -x-y +x-y= 4 --> y=-2
D. -x-y-x+y=4 --> x=-2

The area bounded by 4 graphs x=2, x=-2, y=2, y=-2 will be square with the side of 4 so the area will be 4*4=16.

Answer: C


Why cant we consider (4,0) and (0,4) as points on graph ? then area would be different... , right?
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35950
Followers: 6862

Kudos [?]: 90110 [0], given: 10417

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 14:39
srini123 wrote:
Why cant we consider (4,0) and (0,4) as points on graph ? then area would be different... , right?


First of all we are not considering points separately, as we have X-Y plane and roots of equation will represent lines, we'll get the figure bounded by this 4 lines. The equations for the lines are:

x=2
x=-2
y=2
y=-2

This lines will make a square with the side 4, hence area 4*4=16.

Second: points (4,0) or (0,4) doesn't work for |x+y| + |x-y| = 4.
_________________

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

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 158 [0], given: 37

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 15:58
Bunuel wrote:
srini123 wrote:
Why cant we consider (4,0) and (0,4) as points on graph ? then area would be different... , right?


First of all we are not considering points separately, as we have X-Y plane and roots of equation will represent lines, we'll get the figure bounded by this 4 lines. The equations for the lines are:

x=2
x=-2
y=2
y=-2

This lines will make a square with the side 4, hence area 4*4=16.

Second: points (4,0) or (0,4) doesn't work for |x+y| + |x-y| = 4.


Thanks Bunuel, I used similar method for a similar question and I got wrong answer
the question was



what is the area bounded by graph\(|x/2| + |y/2| = 5\)?

I got hunderd since
x=10
x=-10
y=10
y=-10

isnt the area 400 ? the answer given was 200, please explain
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35950
Followers: 6862

Kudos [?]: 90110 [3] , given: 10417

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 16:41
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
srini123 wrote:
Thanks Bunuel, I used similar method for a similar question and I got wrong answer
the question was

what is the area bounded by graph\(|x/2| + |y/2| = 5\)?

I got hunderd since
x=10
x=-10
y=10
y=-10


isnt the area 400 ? the answer given was 200, please explain


I think this one is different.

\(|\frac{x}{2}| + |\frac{y}{2}| = 5\)

After solving you'll get equation of four lines:

\(y=-10-x\)
\(y=10+x\)
\(y=10-x\)
\(y=x-10\)

These four lines will also make a square, BUT in this case the diagonal will be 20 so the \(Area=\frac{20*20}{2}=200\). Or the \(Side= \sqrt{200}\), area=200.

If you draw these four lines you'll see that the figure (square) which is bounded by them is turned by 90 degrees and has a center at the origin. So the side will not be 20.

Also you made a mistake in solving equation. The red part is not correct. You should have the equations written above.

In our original question when we were solving the equation |x+y| + |x-y| = 4 each time x or y were cancelling out so we get equations of a type x=some value twice and y=some value twice. And these equations give the lines which are parallel to the Y or X axis respectively so the figure bounded by them is a "horizontal" square (in your question it's "diagonal" square).
Image

Hope it's clear.
_________________

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

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 312
Followers: 4

Kudos [?]: 158 [0], given: 37

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 08 Nov 2009, 19:23
Thanks Bunuel , once again wonderful explanation +1 Kudos..

have a good day...
_________________

Thanks, Sri
-------------------------------
keep uppp...ing the tempo...

Press +1 Kudos, if you think my post gave u a tiny tip

Senior Manager
Senior Manager
avatar
Joined: 24 Mar 2011
Posts: 457
Location: Texas
Followers: 5

Kudos [?]: 154 [0], given: 20

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 20 May 2011, 11:39
Bunuel wrote:
x=2
x=-2
y=2
y=-2

This lines will make a square with the side 4, hence area 4*4=16.


i am still now able to follow if the area that is formed with these lines is as per fig 1 or fig 2
Attachments

Doc2.docx [11.23 KiB]
Downloaded 132 times

To download please login or register as a user

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

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

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 20 May 2011, 16:31
Thats same as what you see in fig 2 .

agdimple333 wrote:
Bunuel wrote:
x=2
x=-2
y=2
y=-2

This lines will make a square with the side 4, hence area 4*4=16.


i am still now able to follow if the area that is formed with these lines is as per fig 1 or fig 2
Director
Director
avatar
Joined: 01 Feb 2011
Posts: 757
Followers: 14

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

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 20 May 2011, 16:33
solving the inequality we have the following as solutions

x=2
y=2
y=-2
x=-2


drawing this in a graph, we can observe that it forms a square with side length of 4.

Hence the area is 4*4 = 16

Answer is C.
VP
VP
avatar
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 236 [0], given: 10

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 20 May 2011, 20:50
so check for ++, +-, -+ and --

giving x=2|-2 and y=2|-2

hence a square with 4*4 area = 16
_________________

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

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

Kudos [?]: 507 [1] , given: 36

Premium Member Reviews Badge
Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 21 May 2011, 04:46
1
This post received
KUDOS
|x-y| = x-y if x-y > 0

|x-y| = -(x-y) if x-y < 0

x+y > 0 => x > -y then x !> y


x+y + x - y = 4

x = 2

-x - y + x - y = 4 (if x < -y, then x !< y)

y = -2


x + y -x + y = 4

=> y = 2

-x-y + x - y = 4

=> y = -2


Answer - C
_________________

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

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 22 May 2011
Posts: 1
Followers: 0

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

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 22 May 2011, 06:21
Given |x-y| + |x+y| = 4

I don't understand why can't |x-y| and |x+y| be 1 and 3 instead of 2 and 2! (which again equals 4)

Can any one please explain this to me?

Thanks & Regards,
Vinu
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 7076
Location: Pune, India
Followers: 2091

Kudos [?]: 13309 [0], given: 222

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 22 May 2011, 07:38
VinuPriyaN wrote:
Given |x-y| + |x+y| = 4

I don't understand why can't |x-y| and |x+y| be 1 and 3 instead of 2 and 2! (which again equals 4)

Can any one please explain this to me?

Thanks & Regards,
Vinu


Look at the solution given by Bunuel above. When you solve it, you get four equations.
One of them is x = 2 which means that x = 2 and y can take any value. If y = 1, |x-y| = 1 and |x+y| = 3.
For different values of y, |x-y| and |x+y| will get different values. We are not discounting any of them.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35950
Followers: 6862

Kudos [?]: 90110 [0], given: 10417

Re: Absolute Values [#permalink]

Show Tags

New post 14 Feb 2012, 23:25
Expert's post
1
This post was
BOOKMARKED
prashantbacchewar wrote:
In the X-Y plane, the area of the region bounded by the graph of |x + y| + |x – y| = 4 is
(1) 8
(2) 12
(3) 16
(4) 20
(5) 24


Merging similar topics. Please ask if anything remains unclear.

Some questions on the same subject to practice:
m06-5-absolute-value-108191.html
graphs-modulus-help-86549.html
m06-q5-72817.html
if-equation-encloses-a-certain-region-110053.html

Hope it helps.
_________________

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
User avatar
Joined: 25 Aug 2011
Posts: 193
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Followers: 1

Kudos [?]: 278 [0], given: 11

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 27 Feb 2012, 22:33
Hi,
Can this be solved by graphing. If yes .. how do we graph the equation with 2 mod parts

VeritasPrepKarishma wrote:
VinuPriyaN wrote:
Given |x-y| + |x+y| = 4

I don't understand why can't |x-y| and |x+y| be 1 and 3 instead of 2 and 2! (which again equals 4)

Can any one please explain this to me?

Thanks & Regards,
Vinu


Look at the solution given by Bunuel above. When you solve it, you get four equations.
One of them is x = 2 which means that x = 2 and y can take any value. If y = 1, |x-y| = 1 and |x+y| = 3.
For different values of y, |x-y| and |x+y| will get different values. We are not discounting any of them.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 35950
Followers: 6862

Kudos [?]: 90110 [1] , given: 10417

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 27 Feb 2012, 22:42
1
This post received
KUDOS
Expert's post
devinawilliam83 wrote:
Hi,
Can this be solved by graphing. If yes .. how do we graph the equation with 2 mod parts

VeritasPrepKarishma wrote:
VinuPriyaN wrote:
Given |x-y| + |x+y| = 4

I don't understand why can't |x-y| and |x+y| be 1 and 3 instead of 2 and 2! (which again equals 4)

Can any one please explain this to me?

Thanks & Regards,
Vinu


Look at the solution given by Bunuel above. When you solve it, you get four equations.
One of them is x = 2 which means that x = 2 and y can take any value. If y = 1, |x-y| = 1 and |x+y| = 3.
For different values of y, |x-y| and |x+y| will get different values. We are not discounting any of them.


Yes, it can be done by graphing. |x+y| + |x-y| = 4 can expand in four different wasy:

A. x+y+x-y = 4 --> x=2
B. x+y-x+y = 4 --> y=2
C. -x-y +x-y= 4 --> y=-2
D. -x-y-x+y=4 --> x=-2

So you can draw all these four lines x=2, x=-2, y=2, y=-2 to get a square with the side of 4:
Attachment:
Square.gif
Square.gif [ 1.86 KiB | Viewed 14776 times ]
See more examples here:
m06-5-absolute-value-108191.html
graphs-modulus-help-86549.html
m06-q5-72817.html
if-equation-encloses-a-certain-region-110053.html

Hope it helps.
_________________

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

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 417 [0], given: 11

GMAT ToolKit User
Re: In the x-y plane the area of the region bounded by the [#permalink]

Show Tags

New post 05 Dec 2012, 22:17
(1) derive all equations from |x+y| + |x-y| = 4

x+y+x-y =4 ==> x=2
x+y-x+y =4 ==> y=2
-x-y+x-y =4 ==> y=-2
-x-y-x+y =4 ==> x=-2

(2) Plot your four lines
(3) Notice you have formed a square region bounded by x=2, y=2, y=-2 and x=-2 lines
(4) Area = 4*4 = 16

Answer: C

For more detailed solutions for similar question types: Image
_________________

Impossible is nothing to God.

Manager
Manager
User avatar
Joined: 24 Mar 2010
Posts: 81
Followers: 1

Kudos [?]: 54 [0], given: 134

Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 12 Dec 2012, 08:06
Quote:

OK there can be 4 cases:

|x+y| + |x-y| = 4

A. x+y+x-y = 4 --> x=2
B. x+y-x+y = 4 --> y=2
C. -x-y +x-y= 4 --> y=-2
D. -x-y-x+y=4 --> x=-2


Bunuel,

Would appreciate it, if you could thoroughly explain the above.

Thanks.
_________________

- Stay Hungry, stay Foolish -

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 417 [2] , given: 11

GMAT ToolKit User
Re: graphs_Modulus....Help [#permalink]

Show Tags

New post 13 Dec 2012, 03:06
2
This post received
KUDOS
eaakbari wrote:
Quote:

OK there can be 4 cases:

|x+y| + |x-y| = 4

A. x+y+x-y = 4 --> x=2
B. x+y-x+y = 4 --> y=2
C. -x-y +x-y= 4 --> y=-2
D. -x-y-x+y=4 --> x=-2


Any absolute values such as |x| = 5 could mean that x = 5 or x = -5.

Derive both (-) and (+) possibilities.

For the problem: |x+y| + |x-y| = 4

We could derive two possibilities for |x+y| could be -(x+y) and (x+y)
We could derive two possibilities for |x-y| could be -(x-y) and (x-y)

This is the reason why we have 4 derived equations.

(x+y) + (x-y) = 4
(x+y) - (x-y) = 4
-(x+y) + (x-y) = 4
-(x+y) - (x-y) = 4

Just simplify those...

If you want more practice on this question type: http://burnoutorbreathe.blogspot.com/2012/12/absolute-values-solving-for-area-of.html
_________________

Impossible is nothing to God.

Re: graphs_Modulus....Help   [#permalink] 13 Dec 2012, 03:06

Go to page    1   2   3    Next  [ 53 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic In the xy-plane, triangular region S is bounded by the lines x=0,y=0, Bunuel 1 30 Nov 2016, 02:05
10 Experts publish their posts in the topic In the rectangular coordinate system above, the shaded region is bound Bunuel 6 04 Dec 2014, 06:46
27 Experts publish their posts in the topic What is the area of the region enclosed by lines y=x, x=−y, Rock750 16 06 Apr 2013, 10:17
19 Experts publish their posts in the topic Region R is a square in the x-y plane with vertices mikemcgarry 10 08 Feb 2013, 10:45
3 Experts publish their posts in the topic In the x-y plane, the square region bound by (0,0), (10, 0) mikemcgarry 20 21 Nov 2012, 15:34
Display posts from previous: Sort by

In the x-y plane the area of the region bounded by the

  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®.