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# Equation |x/2| +|y/2|=5 encloses a certain region on the

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Senior Manager
Joined: 02 May 2004
Posts: 311
Equation |x/2| +|y/2|=5 encloses a certain region on the [#permalink]

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09 Sep 2007, 15:26
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane..
What is the area of the region?

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

I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?
Director
Joined: 03 May 2007
Posts: 872
Schools: University of Chicago, Wharton School
Re: Geometry Question-Not sure where they got the theory [#permalink]

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09 Sep 2007, 15:44
jamesrwrightiii wrote:
Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region?

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

I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200
Senior Manager
Joined: 02 May 2004
Posts: 311

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09 Sep 2007, 15:56
I am still confused though...actually the answer is C

I am still confused how you know it's a square..

If you multiply everything by 2, then you have X + Y=10

Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?
Manager
Joined: 16 Feb 2007
Posts: 71

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09 Sep 2007, 16:04
jamesrwrightiii wrote:
I am still confused though...actually the answer is C

I am still confused how you know it's a square..

If you multiply everything by 2, then you have X + Y=10

Why can't you have numbers such as 6 and 4..or 8 and 2..or 9 and 1?

no fistail is right... it is 200 (choice D)

just draw it into a plan and you notice that it is a square with side of 10*sqrt(2)
Senior Manager
Joined: 02 May 2004
Posts: 311
Re: Geometry Question-Not sure where they got the theory [#permalink]

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09 Sep 2007, 16:17
Fistail wrote:
jamesrwrightiii wrote:
Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region?

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

I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200

Ok here is what I am confused about..
All the equation says is that |x|+|y|=10

I am just not sure how we know to go 10 over for each side when all the equation says is that X and Y need to equal 10...?
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: Geometry Question-Not sure where they got the theory [#permalink]

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09 Sep 2007, 16:38
well to be more specific..its the x^2-y^2 plane

if x^2=0 then y^2=-10

if x^2=10 then y^2=0

now remember this |x| and |y| so -y^2=10 when -x^2=0 etc..

you will realize that the region is a square..and that the side of the square is sqrt(2)10.

area of the square=200

Fistail wrote:
jamesrwrightiii wrote:
Equation |x/2| +|y/2|=5 encloses a certain region on the coordinate plane. What is the area of the region?

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

I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?

draw xy plane. go for 10 left, right, up and down. then you get a square with a side of 10sqrt2.

so the ares = (10sqrt^2)^2 = 200
Manager
Joined: 10 Dec 2006
Posts: 90
Re: Geometry Question-Not sure where they got the theory [#permalink]

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02 Jun 2008, 19:49
If I consider the following points (-5,5), (5,5), (-5,-5) and (5,-5), the figure enclosed is a square with an area of 100 sq units.

Should the question be what is the max area of the region?

Thanks.
VP
Joined: 18 May 2008
Posts: 1260
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 03:45
I agree with rakesh22.It should be a square of each side 10. so area is 100 i.e. C
rakesh22 wrote:
If I consider the following points (-5,5), (5,5), (-5,-5) and (5,-5), the figure enclosed is a square with an area of 100 sq units.

Should the question be what is the max area of the region?

Thanks.
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 07:34
you know what i agree with 100..cause we only focus on half of the square...

walker..what do u think?
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1262
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 07:40
Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 07:42
kevincan wrote:
Look at the first quadrant (x >0, y > 0) : x + y = 10, so we get a line segment with endpoints (0,10) and (10,0). We will get a square that can be broken up into 4 right triangles, each with area (10)(10)/2 = 50

but arent we only looking for the triangles in region 1 and 2?
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 07:49
never mind..

i got confused by the other posters..grrrrrrr

this is 200..

|x|+|y|=10

condition1
x>0 y>0

x+y=10...you get a triangle with slope 10sqrt(2)

condition 2
x<0 y<0

-x-y=10
-y=10+x..

condition 3
x>0 y<0
x-y=10
-y=10-x

and condition 4
x<0 y>0
-x+y=10
y=10+x
CEO
Joined: 29 Mar 2007
Posts: 2560
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 08:07
fresinha12 wrote:
never mind..

i got confused by the other posters..grrrrrrr

this is 200..

|x|+|y|=10

condition1
x>0 y>0

x+y=10...you get a triangle with slope 10sqrt(2)

condition 2
x<0 y<0

-x-y=10
-y=10+x..

condition 3
x>0 y<0
x-y=10
-y=10-x

and condition 4
x<0 y>0
-x+y=10
y=10+x

I really dont see how ur getting sides of 10sqrt2.

You plug in for x or y in the original and you get 5,-5,5,-5 etc...

This is square w/ sides of 10.

What am I missing here?
Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12
Re: Geometry Question-Not sure where they got the theory [#permalink]

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03 Jun 2008, 08:12
GMATBLACKBELT wrote:
fresinha12 wrote:

I really dont see how ur getting sides of 10sqrt2.

You plug in for x or y in the original and you get 5,-5,5,-5 etc...

This is square w/ sides of 10.

What am I missing here?

ok lets see..

|x/2|+|y/2|=5

=> |x|+|y|=10

suppose x=0 and y is positive..y/2=5 y=10..

get it? the question is asking about the area occupied by the region given by the equation |x|+|y|=10..

the |x/2|+|y/2| is just to throw you off..the actual equation is |x|+|y|=10
Re: Geometry Question-Not sure where they got the theory   [#permalink] 03 Jun 2008, 08:12
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