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

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Joined: 21 Feb 2010
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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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Difficulty:

65% (hard)

Question Stats:

51% (01:48) correct 49% (01:41) wrong based on 154 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-equation- ... 01963.html
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Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordi  [#permalink]

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27 Nov 2017, 20:56
5
2
tt11234 wrote:
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

|x| + |y| = 10.
Take the first quadrant => x + y = 10
Draw a line with (10,0) and (0,10) .. Area of this quadrant will be = 0.5 * 10 * 10 = 50
As this is mod it will be same in all quadrant = 50 * 4 = 200
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Joined: 02 Sep 2009
Posts: 53066
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
1
1
$$|\frac{x}{2}| + |\frac{y}{2}| = 5$$

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]

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27 Nov 2017, 20:31
1
drawing each line by finding coordinates would take more than 2 minutes in actual gmat test. Is there any other way for dealing such questions? Or I need to increase my speed for such questions?
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Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordi  [#permalink]

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05 Dec 2017, 09:55
Hi Bunuel and other experts,
Can someone help me draw the diagram because with diagram i am getting 40 not 20.
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Posts: 53066
Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordi  [#permalink]

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05 Dec 2017, 10:08
sananoor wrote:
Hi Bunuel and other experts,
Can someone help me draw the diagram because with diagram i am getting 40 not 20.

Here it is:

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/if-equation- ... 01963.html
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Re: If equation |x/2| + |y/2| = 5 encloses a certain region on the coordi   [#permalink] 05 Dec 2017, 10:08
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