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concept? equation encloses a certain region - find the area?

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concept? equation encloses a certain region - find the area?

by kaps786 » Sat Aug 13, 2011 9:40 am
Experts and everyone,

How should you approach questions like equation encloses a certain region? - find the area.

I am trying to understand the underlying concept and what is tested on the GMAT, so key takeaways for examining such questions will be really appreciated. Basically, I am clueless on this, so some detail fro scratch would be really appreciated.

I dont find a whole lot on these types of questions in the forums or guides as well, so would really appreciate any experts who could answer this.

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

50

20

400

100

200

OA BELOW



OA - 200


There are few others that I saw as follows-

Equation |x| + |y| = 10 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

OA D

Please solve any, but kindly explain way to approach and concept if possible.

Thank you in advance,

kaps
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by gmatboost » Mon Aug 15, 2011 9:28 am
Those two questions are the same question. Multiply the first one by 2 and you get the second one.

This is a pretty hard question, I would be a little surprised to see it but it's not unreasonable.

I would start by finding the "Extreme points" of the shape. In this case, looking at |x| + |y| = 10, the extreme points are (10, 0), (0,10), (-10, 0), (0, -10).
Them, think about some other easy to plot points: (5, 5), (5, -5), (-5, 5), (-5, -5).

When you do this, you start to see the shape emerge, a square that is rotated 45 degrees (looks like a diamond). It is a square with side length 10*root(2), so the area is[10*root(2)]^2 = 200.
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by kaps786 » Mon Aug 15, 2011 10:45 pm
Thanks Greg - your posts, on this and others are very helpful.
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by gmatboost » Mon Aug 15, 2011 11:57 pm
Glad to hear that they are helpful.
Don't hesitate to let me know if any of them aren't clear enough, etc.
Greg Michnikov, Founder of GMAT Boost

GMAT Boost offers 250+ challenging GMAT Math practice questions, each with a thorough video explanation, and 100+ GMAT Math video tips, each 90 seconds or less.
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