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

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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.
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