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Senior Manager
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Equation |x/2| +|y/2|=5 encloses a certain region on the [#permalink]
 09 Sep 2007, 15:26
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 read the explanation
I have no idea how we know the above region encloses a square
I am totally lost on this
Can anyone help me out?
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Director
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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 read the explanation
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
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Senior Manager
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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?
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Manager
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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)
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Senior Manager
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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 read the explanation
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...?
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Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
Schools: Wharton'11 HBS'12
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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 read the explanation
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 |
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Manager
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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.
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VP
Joined: 18 May 2008
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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.
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Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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?
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GMAT Instructor
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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
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Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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?
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Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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
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CEO
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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?
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Current Student
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Re: Geometry Question-Not sure where they got the theory [#permalink]
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
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Re: Geometry Question-Not sure where they got the theory
[#permalink]
03 Jun 2008, 08:12
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