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If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi

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If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi [#permalink]

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New post 03 Sep 2010, 14:45
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If equation |x/2| + |y/2| + 5 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

(C) 2008 GMAT Club - m25#19
[Reveal] Spoiler: OA
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Re: If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi [#permalink]

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New post 03 Sep 2010, 15:18
Expert's post
\(|\frac{x}{2}| + |\frac{y}{2}| = 5\)

You will have 4 case:

\(x<0\) and \(y<0\) --> \(-\frac{x}{2}-\frac{y}{2}=5\) --> \(y=-10-x\);

\(x<0\) and \(y\geq{0}\) --> \(-\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10+x\);

\(x\geq{0}\) and \(y<0\) --> \(\frac{x}{2}-\frac{y}{2}=5\) --> \(y=x-10\);

\(x\geq{0}\) and \(y\geq{0}\) --> \(\frac{x}{2}+\frac{y}{2}=5\) --> \(y=10-x\);

So we have equations of 4 lines. If you draw these four lines you'll see that the figure which is bounded by them is square which is turned by 90 degrees and has a center at the origin. This square will have a diagonal equal to 20, so the \(Area_{square}=\frac{d^2}{2}=\frac{20*20}{2}=200\).

Or the \(Side= \sqrt{200}\) --> \(area=side^2=200\).

Answer: D.

Similar problem: graphs-modulus-help-86549.html?hilit=horizontal#p649401

Hope it's clear.
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Re: If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi   [#permalink] 03 Sep 2010, 15:18
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