If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi : GMAT Problem Solving (PS)
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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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03 Sep 2010, 13:45
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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
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Re: If equation |x/2| + |y/2| + 5 encloses a certain region on the coordi [#permalink]

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03 Sep 2010, 14:18
$$|\frac{x}{2}| + |\frac{y}{2}| = 5$$

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 $$Side= \sqrt{200}$$ --> $$area=side^2=200$$.

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, 14:18
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