Goemetry Q

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dev.gavande: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Tue Nov 27, 2007 2:35 am

by dev.gavande » Tue Oct 04, 2011 12:05 am

If equation encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

My answer is 100, its wrong. Need to know why.

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Source: Beat The GMAT — Problem Solving | Tue Oct 04, 2011 12:05 am

sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Tue Oct 04, 2011 12:06 am

Is this question in its entirety?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Oct 04, 2011 12:06 am

dev.gavande wrote:If equation encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

My answer is 100, its wrong. Need to know why.

What is the equation?

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dev.gavande: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Tue Nov 27, 2007 2:35 am

by dev.gavande » Tue Oct 04, 2011 12:11 am

Sorry did'nt see preview. here is the equation
If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Oct 04, 2011 12:16 am

dev.gavande wrote:Sorry did'nt see preview. here is the equation
If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?
"¢ 20
"¢ 50
"¢ 100
"¢ 200
"¢ 400

|x/2| + |y/2| = 5 implies |x| + |y| = 10

If you split this into the 4 possible values:

x + y = 10, x - y = 10, -x - y = 10, -x + y = 10
The above equations are lines with slopes -1, 1, -1, and 1 respectively.

If we graph this, it will be a rhombus with center at the origin.
Total Area = 1/2 (20 * 20) = 200

The correct answer is D.

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dev.gavande: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Tue Nov 27, 2007 2:35 am

by dev.gavande » Tue Oct 04, 2011 12:53 am

I am sorry i am not getting this... till the slopes its fine.
how did you figure it will be a rhombus?

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GmatKiss: Legendary Member; Posts: 2789; Joined: Tue Jul 26, 2011 12:19 amFollowed by: 43 members; Location: Chennai, India; Thanked: 206 times; GMAT Score:640

by GmatKiss » Tue Oct 04, 2011 5:49 am

Same doubt here! and how is it 1/2 (20 * 20)?!
Waiting for clarifications.

TIA,
GK

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Tue Oct 04, 2011 11:26 am

You get these 4 equations removing the modulus

x + y = 10, x - y = 10, -x - y = 10, -x + y = 10

Plot the lines in a graph, You get (0,10) (0.-10) (10,0) (-10,0) - A diamond shaped figure with center at origin. (Sub x=0 or y=0 in all the equations and plot the extreme values)

The 2 diagonals are 20 units and all 4 sides are equal, You could find the area of the rhombus.

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