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# If equation |x| + |y| = 5 encloses a certain region on the

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Manager
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If equation |x| + |y| = 5 encloses a certain region on the [#permalink]  18 Jan 2008, 00:38
If equation |x| + |y| = 5 encloses a certain region on the graph, what is the area of that region?

* 5
* 10
* 25
* 50
* 100

i don't even know how to evaluate a statement like that...
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Re: absolute value problem [#permalink]  18 Jan 2008, 00:46
1
KUDOS
D

Just draw it.
we have a square with diagonal=5*2=10

Area=a^2=\frac{(\sqrt2*a)^2}{2}=\frac{(diagonal)^2}{2}=\frac{(10)^2}{2}=50
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PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only $0.99 (read more) Math: GMAT Math Book ||| General: GMATTimer ||| Chicago Booth: Slide Presentation The People Who Are Crazy Enough to Think They Can Change the World, Are the Ones Who Do. Manager Joined: 15 Nov 2007 Posts: 137 Followers: 1 Kudos [?]: 23 [0], given: 2 Re: absolute value problem [#permalink] 18 Jan 2008, 01:06 walker wrote: D Just draw it. we have a square with diagonal=5*2=10 Area=a^2=\frac{(\sqrt2*a)^2}{2}=\frac{(diagonal)^2}{2}=\frac{(10)^2}{2}=50 sweet... kudos +1... check back on the exponent question i had for me. Director Joined: 01 Jan 2008 Posts: 635 Followers: 3 Kudos [?]: 114 [0], given: 1 Re: absolute value problem [#permalink] 18 Jan 2008, 07:55 my approach was similar to walker's - it's important to draw it to visualize, then obviously the area of each triangle is 5*5/2 = 25/2 and there are 4 triangles. the answer is 50. SVP Joined: 04 May 2006 Posts: 1946 Schools: CBS, Kellogg Followers: 10 Kudos [?]: 168 [0], given: 1 Re: absolute value problem [#permalink] 19 Jan 2008, 02:41 walker wrote: D Just draw it. we have a square with diagonal=5*2=10 Area=a^2=\frac{(\sqrt2*a)^2}{2}=\frac{(diagonal)^2}{2}=\frac{(10)^2}{2}=50 At first, I dont know how to solve this problem, but when I see your drawing, I read it as: Keep x=0, you had y = + - 5, and vice versa, keep y=0, you had x = +-5. Do you have any tips for absolute value problem? When problem involves x and y, I am in block. _________________ CEO Joined: 17 Nov 2007 Posts: 3597 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 232 Kudos [?]: 1301 [0], given: 346 Re: absolute value problem [#permalink] 19 Jan 2008, 03:05 sondenso wrote: Do you have any tips for absolute value problem? When problem involves x and y, I am in block. The right but long approach is: |x| + |y| = 5 is equal: x+y=5\text{ if x\ge0;y\ge0} x-y=5\text{ if x\ge0;y<0} -x+y=5\text{ if x<0;y\ge0} -x-y=5\text{ if x<0;y<0} shortcut: your drawing have to be symmetric for x and y. Therefore you can draw only x+y=5 (I quadrant) and use mirror symmetry _________________ iOS/Android: GMAT ToolKit - The bestselling GMAT prep app | GMAT Club (free) | PrepGame | GRE ToolKit | LSAT ToolKit PROMO: Are you an exiting GMAT ToolKit (iOS) user? Get GMAT ToolKit 2 (iOS) for only$0.99 (read more)
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Manager
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Re: absolute value problem [#permalink]  07 Feb 2008, 01:19
can we take 3,2 or 4,1 as points?
Since the absolute value will always be "5".

-Jack
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Re: absolute value problem [#permalink]  07 Feb 2008, 01:54
jackychamp wrote:
can we take 3,2 or 4,1 as points?
Since the absolute value will always be "5".

-Jack

we can but these points are not vertexs of the square and therefore, the points cannot help us to find area.
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Re: absolute value problem   [#permalink] 07 Feb 2008, 01:54
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