GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Aug 2018, 06:27

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

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

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

Hide Tags

Manager
Manager
User avatar
Joined: 09 Jun 2009
Posts: 195
In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post Updated on: 26 Oct 2017, 06:46
10
67
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:26) correct 37% (01:33) wrong based on 1130 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

Originally posted by papillon86 on 08 Nov 2009, 14:11.
Last edited by Bunuel on 26 Oct 2017, 06:46, edited 3 times in total.
Edited the question and added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 14:34
14
17
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 19342 times ]


Answer: C
_________________

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

General Discussion
Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 271
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 15:27
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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 15:39
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: 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

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 271
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 16:58
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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 17:41
7
2
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: 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

Senior Manager
Senior Manager
User avatar
Affiliations: PMP
Joined: 13 Oct 2009
Posts: 271
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 08 Nov 2009, 20:23
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

Retired Moderator
avatar
B
Joined: 16 Nov 2010
Posts: 1458
Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 21 May 2011, 05:46
1
|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
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 22 May 2011, 07:21
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
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8195
Location: Pune, India
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 22 May 2011, 08:38
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

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 15 Feb 2012, 00:25
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: 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

Manager
Manager
User avatar
Joined: 25 Aug 2011
Posts: 174
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 27 Feb 2012, 23:33
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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 27 Feb 2012, 23:42
1
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 24253 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: 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

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 05 Dec 2012, 23:17
(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.

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 441
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 13 Dec 2012, 04:06
2
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.

VP
VP
User avatar
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1252
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
GMAT ToolKit User Premium Member
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 13 Dec 2012, 04:26
Bunuel wrote:
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).

Hope it's clear.


Hii Bunuel.
What is the best approach of finding the points of intersection in order to make the square.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 13 Dec 2012, 04:30
Marcab wrote:
Bunuel wrote:
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).

Hope it's clear.


Hii Bunuel.
What is the best approach of finding the points of intersection in order to make the square.


I'd say substituting x=0 and y=0 in the equations of lines and making a drawing.
_________________

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

Director
Director
User avatar
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 532
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 21 Aug 2013, 21:51
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.



The side of the square can't be 4, instead its sqrt(8)
_________________

Like my post Send me a Kudos :) It is a Good manner.
My Debrief: http://gmatclub.com/forum/how-to-score-750-and-750-i-moved-from-710-to-189016.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47983
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 22 Aug 2013, 03:21
honchos wrote:
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.



The side of the square can't be 4, instead its sqrt(8)


The side of the square IS 4:
Attachment:
MSP39361d6ehgde6ie87a8800003827f7f92a367c60.gif
MSP39361d6ehgde6ie87a8800003827f7f92a367c60.gif [ 1.86 KiB | Viewed 6987 times ]

_________________

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

Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: In the x-y plane, the area of the region bounded by the graph of |x +  [#permalink]

Show Tags

New post 27 Jan 2014, 03:00
Bunuel,

wouldn't it be sufficient to look at only two cases?

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

Which would give us 2*2 * 4 = 16?
Re: In the x-y plane, the area of the region bounded by the graph of |x + &nbs [#permalink] 27 Jan 2014, 03:00

Go to page    1   2    Next  [ 37 posts ] 

Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.