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

It is currently 20 Sep 2018, 19:25

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

If equation |x/2| + |y/2| = 5 enclose a certain region

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

Hide Tags

Intern
Intern
avatar
Joined: 19 Sep 2010
Posts: 25
If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 30 Sep 2010, 04:10
10
50
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

52% (01:04) correct 48% (01:15) wrong based on 1389 sessions

HideShow timer Statistics

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?

A. 20
B. 50
C. 100
D. 200
E. 400

M25-19

ME: well, since \(|x| + |y| = 10\) ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: CMAT Club Test Question - m25  [#permalink]

Show Tags

New post 30 Sep 2010, 04:22
5
17
Barkatis wrote:
Hello,
Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200

ME: well, since \(|x| + |y| = 10\) ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks


Hi and welcome to the Gmat Club. Below is the solution for your problem. Hope it's clear.

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

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-\frac{x}{2}-\frac{y}{2}=5\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(\frac{x}{2}-\frac{y}{2}=5\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Check similar problem at: graphs-modulus-help-86549.html?hilit=horizontal#p649401 it might help to get this one better.

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

Most Helpful Community Reply
Manager
Manager
avatar
Joined: 22 Aug 2008
Posts: 156
Re: CMAT Club Test Question - m25  [#permalink]

Show Tags

New post 30 Sep 2010, 17:41
8
|X/2| + |Y/2| = 5
so when x = 0, y= |10|
when y=0 , x=|10|

so the sides of the enclosed area touches (0,10),(10,0),(0,-10) and (-10,0).
so its a square having the diagonal =20unit
So the area of the region = (20/1.414)^2 = 200
General Discussion
Manager
Manager
avatar
Joined: 07 Feb 2010
Posts: 135
Re: CMAT Club Test Question - m25  [#permalink]

Show Tags

New post 16 Nov 2010, 09:45
3
1
|x|+||y|=10

put x=0

you get |y|=10 .....y=+-10

when you y=0

you get |x| = 10 ..... x=+-10

plot this on the co-ordinate plane.

you will get a rhombus
area of rhombus = 1/2 (d1 x d2)= 20X20/2= 200
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 15 Jan 2012, 10:26
3
8
Apex231 wrote:
If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A 20
B 50
C 100
D 200
E 400


First of all to simplify the given expression a little bit let's multiply it be 2: \(|\frac{x}{2}|+|\frac{y}{2}|=5\) --> \(|x|+|y|=10\).

Now, find x and y intercepts of the region (x-intercept is a value(s) of x for y=0 and similarly y-intercept is a value(s) of y for x=0):
\(y=0\) --> \(|x|=10\) --> \(x=10\) and \(x=-10\);
\(x=0\) --> \(|y|=10\) --> \(y=10\) and \(y=-10\).

So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

When you join them you'll get the region enclosed by \(|x|+|y|=10\):

Image

You can see that it's a square. Why a square? Because diagonals of the rectangle are equal (20 and 20), and also are perpendicular bisectors of each other (as they are on X and Y axis), so it must be a square. As this square has a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Similar questions:
http://gmatclub.com/forum/m06-5-absolut ... 08191.html
http://gmatclub.com/forum/graphs-modulu ... 86549.html

Hope it's clear.

Attachment:
Enclosed region.gif
Enclosed region.gif [ 2.04 KiB | Viewed 24850 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: 03 Oct 2009
Posts: 52
Re: Area of region  [#permalink]

Show Tags

New post 15 Jan 2012, 10:58
I had solved till this point - So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

But instead of joining these points i did this - 4 * (10 * 10) = 400 , which is wrong of course.

So when we join these points, how |x|+|y| = 10 stays satisfied , what's the maths behind it?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: Area of region  [#permalink]

Show Tags

New post 15 Jan 2012, 11:07
2
Apex231 wrote:
I had solved till this point - So we have 4 points: (10, 0), (-10, 0), (0, 10) and (-10, 0).

But instead of joining these points i did this - 4 * (10 * 10) = 400 , which is wrong of course.

So when we join these points, how |x|+|y| = 10 stays satisfied , what's the maths behind it?


Given: \(|x|+|y|=20\)

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-x-y=10\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-x+y=10\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(x-y=10\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(x+y=10\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll get the figure shown in 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

Senior Manager
Senior Manager
avatar
B
Joined: 24 Aug 2009
Posts: 476
Schools: Harvard, Columbia, Stern, Booth, LSB,
If equation |x/2|+|y/2| = 5 encloses a certain region  [#permalink]

Show Tags

New post 10 Sep 2012, 12:25
CMcAboy wrote:
Can someone help me with this question:

If equation |x/2| + |y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A) 20
B) 50
C) 100
D) 200
E) 400



I believe this is the simplest & the quickest solution
|x/2| + |y/2| = 5
Put x = 0 in the above equation we get |y/2| = 5, which means y= 10, - 10
Put y = 0 in the above equation we get |y/2| = 5, which means x= 10, - 10

If you see plot these four points you get a square with two equal diagonals of length 20 units
Thus area = 1/2 * (Diagonal)^2 -----> 1/2 * 400 = 200

I hope this will help many.
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS.
Kudos always maximizes GMATCLUB worth
-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 436
Concentration: Marketing, Finance
GPA: 3.23
GMAT ToolKit User
Re: If equation |x/2|+|y/2| = 5 encloses a certain region  [#permalink]

Show Tags

New post 05 Dec 2012, 23:30
(1) derive all equations
x+y = 10
x-y = 10
x+y=-10
-x+y=10

(2) Get your x and y intercepts

(0,10), (10,0)
(0,-10),(10,0)
(0,-10),(-10,0)
(0,10),(-10,0)

(3) You will have a square with a diagonal of 20
(4) Calculate area = \((10 * \sqrt{2})\sqrt{^2}\) = 200

Answer : D
_________________

Impossible is nothing to God.

Intern
Intern
User avatar
Joined: 13 Jul 2014
Posts: 10
Location: India
Concentration: Operations, Technology
GMAT Date: 11-06-2014
GRE 1: Q159 V144
If equation |x/2|+|y/2| = 5 encloses a certain region  [#permalink]

Show Tags

New post 15 Oct 2014, 19:17
Apex231 wrote:
If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A. 20
B. 50
C. 100
D. 200
E. 400



Hello There,
Equation of a straight line whose x and y intercepts are a and b resp. is (x/a) + (y/b) = 1 i.e., coordinates of two ends of the line are (a,0) and (0,b).
Now, from the given question,
|x/2|+|y/2| = 5, reducing this to intercept form we get,
|x/10|+|y/10| = 1
Considering the equation without modulus, coordinates are (10,0) and (0,10). Since there is modulus, other two coordinates are (-10,0) and (0,-10).
Now coordinates (10,0), (0,10), (-10,0) and (0,-10) form a square with diagonal length = 20.
Here diagonal length can be obtained by calculating the distance between (10,0) and (-10,0) or (0,10) and (0,-10).
In a square,
Diagonal = Side * sqrt(2)
Side = 10 * sqrt(2)
Area = Side * Side = 200.

Ans : D

Hope this helps!
Thanks!
_________________

Regards,
Bharat Bhushan Sunkara.


"You need to sacrifice what you are TODAY, for what you want to be TOMORROW!!"

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49271
Re: If equation |x/2|+|y/2| = 5 encloses a certain region  [#permalink]

Show Tags

New post 16 Oct 2014, 00:48
Apex231 wrote:
If equation |x/2|+|y/2| = 5 encloses a certain region on the coordinate plane, what is the area of this region?

A. 20
B. 50
C. 100
D. 200
E. 400


Similar questions to practice:
the-area-bounded-by-the-curves-x-y-1-and-x-y-1-is-93103.html
in-the-x-y-plane-the-area-of-the-region-bounded-by-the-86549.html
if-equation-x-2-y-2-5-enclose-a-certain-region-101963.html
what-is-the-area-of-the-region-enclosed-by-lines-y-x-x-y-150487.html
new-set-of-mixed-questions-150204-100.html#p1208441
the-area-bounded-by-the-three-curves-x-y-1-x-1-and-y-186595.html
if-equation-x-2-y-2-5-encloses-a-certain-region-126117.html

Hope this 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

Intern
Intern
avatar
Joined: 25 Jan 2014
Posts: 16
Concentration: Technology, General Management
Premium Member
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 10 Jun 2015, 09:21
Bunuel wrote:
Barkatis wrote:
Hello,
Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200

ME: well, since \(|x| + |y| = 10\) ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks


Hi and welcome to the Gmat Club. Below is the solution for your problem. Hope it's clear.

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

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-\frac{x}{2}-\frac{y}{2}=5\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(\frac{x}{2}-\frac{y}{2}=5\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Check similar problem at: graphs-modulus-help-86549.html?hilit=horizontal#p649401 it might help to get this one better.

Hope it helps.


hey Bunuel,

I had another way of solving. The answer is wrong but i wanted to know what is wrong in the method.

We can re-write the question as below

\(x^2/4 +y^2/4 = 5\) (since \(|x| = x^2\))

\(x^2 + y^2 = 20\)

This is the equation is a circle having the centre at (0,0) (general form is \(x^2 + y^2= r^2\))

area =\(3.14 * R^2\) = \(3.14 * 20\) = 62.8

What am i assuming wrong here?? Thanks!
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 10 Jun 2015, 09:50
arshu27 wrote:
Bunuel wrote:

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200


I had another way of solving. The answer is wrong but i wanted to know what is wrong in the method.

We can re-write the question as below

\(x^2/4 +y^2/4 = 5\) (since \(|x| = x^2\))


\(x^2 + y^2 = 20\)

This is the equation is a circle having the centre at (0,0) (general form is \(x^2 + y^2= r^2\))

area =\(3.14 * R^2\) = \(3.14 * 20\) = 62.8

What am i assuming wrong here?? Thanks!


The part that I have highlighted above is WRONG which the first step in your solution

|x| is NOT equal to x^2 for all values of x[/highlight]

The Function "Modulus" only keeps the final sign Positive but that doesn't mean what you mentioned in the quoted Highlighted section.

Alternatively you can solve this question in this way

Step 1: Substitute y=0, \(|\frac{x}{2}| + |\frac{0}{2}| = 5\) i.e. \(|\frac{x}{2}| = 5\) i.e. \(|x| = 10\) i.e. \(x = +10\)

So on the X-Y plane you get two Point (+10,0) and (-10,0)

Step 2:Substitute x=0, \(|\frac{0}{2}| + |\frac{y}{2}| = 5\) i.e. \(|\frac{y}{2}| = 5\) i.e. \(|y| = 10\) i.e. \(y = +10\)

So on the X-Y plane you get two lines parallel to X-Axis passing through Y=+10 and Y=-10

So on the X-Y plane you get two Point (0, +10) and (0, -10)

Join all the four points, It's a Square with Side \(10\sqrt{2}\)

i.e. Area =\((10\sqrt{2})^2\) = 200
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 10 Jun 2015, 10:02
arshu27 wrote:
Bunuel wrote:
Barkatis wrote:
Hello,
Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200

ME: well, since \(|x| + |y| = 10\) ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks


Hi and welcome to the Gmat Club. Below is the solution for your problem. Hope it's clear.

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

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-\frac{x}{2}-\frac{y}{2}=5\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(\frac{x}{2}-\frac{y}{2}=5\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Check similar problem at: graphs-modulus-help-86549.html?hilit=horizontal#p649401 it might help to get this one better.

Hope it helps.


hey Bunuel,

I had another way of solving. The answer is wrong but i wanted to know what is wrong in the method.

We can re-write the question as below

\(x^2/4 +y^2/4 = 5\) (since \(|x| = x^2\))

\(x^2 + y^2 = 20\)

This is the equation is a circle having the centre at (0,0) (general form is \(x^2 + y^2= r^2\))

area =\(3.14 * R^2\) = \(3.14 * 20\) = 62.8

What am i assuming wrong here?? Thanks!



One More Clarification

( \(|x| is NOT equal to x^2\))

Instead, \(|x| = \sqrt{(x^2)}\)
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Manager
Manager
avatar
B
Joined: 20 Apr 2014
Posts: 95
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 12 Jun 2015, 14:43
why should I suppose that x or y equals +- 10 & zeros ? what about +- 5 as following :
|+ 5 |+ |-5| = 10
|-5|+|+5| = 10
|-5|+|-5|= 10
|+5|+|+5|=10
S0 we have Square with side of 10 length
Its area is 100
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 12 Jun 2015, 23:02
hatemnag wrote:
why should I suppose that x or y equals +- 10 & zeros ? what about +- 5 as following :
|+ 5 |+ |-5| = 10
|-5|+|+5| = 10
|-5|+|-5|= 10
|+5|+|+5|=10
S0 we have Square with side of 10 length
Its area is 100


Hi Hatemnag,

The given equation is basically representing FOUR linear equations which are representing 4 lines on the plane

One Linear equation when x is +ve and y is +ve i.e. X+Y = 10
Second Linear equation when x is +ve and y is -ve i.e. X-Y = 10
Third Linear equation when x is -ve and y is +ve i.e. -X+Y = 10
Forth Linear equation when x is -ve and y is -ve i.e. -X-Y = 10

So you need to plot these equation and then take the area of Quadrilateral formed

Also, Please Note that Four Vertices of Quadrilateral are obtained where two lines Intersect, and The intersections of the lines are obtained at points (10,0), (-10,0), (0,10) and (0,-10)


Whereas, what you have done is taking any FOUR RANDOM POINTS on those four lines as per your convenience and then have assumed that these points form the Square


I hope this clears your doubt!
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Current Student
avatar
Joined: 29 May 2013
Posts: 108
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 20 Jun 2015, 01:15
Bunuel wrote:
Barkatis wrote:
Hello,
Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)

If equation \(|\frac{x}{2}| + |\frac{y}{2}| = 5\) encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200

ME: well, since \(|x| + |y| = 10\) ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks


Hi and welcome to the Gmat Club. Below is the solution for your problem. Hope it's clear.

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

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-\frac{x}{2}-\frac{y}{2}=5\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(\frac{x}{2}-\frac{y}{2}=5\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Check similar problem at: graphs-modulus-help-86549.html?hilit=horizontal#p649401 it might help to get this one better.

Hope it helps.


Sorry, i dont know what i am missing, how do i get the diagonal to be 20?...from the square i got, i have all the sides equal to 20, hence the area=400.
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 20 Jun 2015, 01:53
2
2
jayanthjanardhan wrote:

Sorry, i dont know what i am missing, how do i get the diagonal to be 20?...from the square i got, i have all the sides equal to 20, hence the area=400.


Hi Jayanthjanardan,

The given equation is basically representing FOUR linear equations which are representing 4 lines on the plane

One Linear equation when x is +ve and y is +ve i.e. X+Y = 10
Second Linear equation when x is +ve and y is -ve i.e. X-Y = 10
Third Linear equation when x is -ve and y is +ve i.e. -X+Y = 10
Forth Linear equation when x is -ve and y is -ve i.e. -X-Y = 10

NOTE: PLEASE PLOT THE LINES TO UNDERSTAND THE FIGURE (REFER THE FIGURE) and see that Diagonal of Square is 10

So you need to plot these equation and then take the area of Quadrilateral formed

Also, Please Note that Four Vertices of Quadrilateral are obtained where two lines Intersect, and The intersections of the lines are obtained at points (10,0), (-10,0), (0,10) and (0,-10)

Whereas, what you have done is taking any FOUR RANDOM POINTS on those four lines as per your convenience and then have assumed that these points form the Square


I hope this clears your doubt!
Attachments

File comment: www.GMATinsight.com
figure.jpg
figure.jpg [ 88.87 KiB | Viewed 5595 times ]


_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Current Student
avatar
Joined: 29 May 2013
Posts: 108
Location: India
Concentration: Technology, Marketing
WE: Information Technology (Consulting)
Re: If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 20 Jun 2015, 03:01
Hi GMATInight,

thanks a lot for the expalnantion. I get the logic now.

However, kindly refer to this link below.

in-the-x-y-plane-the-area-of-the-region-bounded-by-the-86549-40.html#p1540033

Its a similar problem, but the diagram we end getting is a square and not a rhombus...what am i missing here?
SVP
SVP
User avatar
P
Joined: 08 Jul 2010
Posts: 2314
Location: India
GMAT: INSIGHT
WE: Education (Education)
Reviews Badge
If equation |x/2| + |y/2| = 5 enclose a certain region  [#permalink]

Show Tags

New post 20 Jun 2015, 03:10
jayanthjanardhan wrote:
Hi GMATInight,

thanks a lot for the expalnantion. I get the logic now.

However, kindly refer to this link below.

in-the-x-y-plane-the-area-of-the-region-bounded-by-the-86549-40.html#p1540033

Its a similar problem, but the diagram we end getting is a square and not a rhombus...what am i missing here?


Even that is a square but never forget that a Square is a specific type of Rhombus only

I hope, You can understand that the Product of the slopes of the adjacent sides is -1 in that fugure which proves the angle between the adjacent sides as 90 degree

a Square is a "Rhombus with all angles 90 degrees". So calling it a Rhombus won;t be wrong either but you are right about the figure being a Square.
_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

If equation |x/2| + |y/2| = 5 enclose a certain region &nbs [#permalink] 20 Jun 2015, 03:10

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

If equation |x/2| + |y/2| = 5 enclose a certain region

  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®.