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# If equation |x/2| + |y/2| = 5 enclose a certain region

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If equation |x/2| + |y/2| = 5 enclose a certain region [#permalink]  30 Sep 2010, 03:10
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Question Stats:

47% (01:55) correct 53% (01:14) wrong based on 299 sessions
If equation $$|\frac{x}{2}| + |\frac{y}{2}| = 5$$ 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

M25-19

[Reveal] Spoiler:
ME: well, since $$|x| + |y| = 10$$ ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks
[Reveal] Spoiler: OA
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Re: CMAT Club Test Question - m25 [#permalink]  30 Sep 2010, 03:22
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Barkatis wrote:
Hello,
Am new here. I just took the m25 GMAT CLub Test and I don't get the solution of a question. (Q19)

If equation $$|\frac{x}{2}| + |\frac{y}{2}| = 5$$ encloses a certain region on the coordinate plane, what is the area of this region?
20
50
100
200
400

OA: 200

ME: well, since $$|x| + |y| = 10$$ ; X can range from (-10) to (10) (when Y is 0) and the same for Y
So the length of the side of the square should be 20.
My Answer : 400

I think I am making a silly mistake some where but I just can't figure it out.

Thanks

Hi and welcome to the Gmat Club. Below is the solution for your problem. Hope it's clear.

$$|\frac{x}{2}| + |\frac{y}{2}| = 5$$

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.

Check similar problem at: graphs-modulus-help-86549.html?hilit=horizontal#p649401 it might help to get this one better.

Hope it helps.
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Re: CMAT Club Test Question - m25 [#permalink]  30 Sep 2010, 03:44
Thanks, the 20 was actually for the diagonals not the sides !
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Re: CMAT Club Test Question - m25 [#permalink]  30 Sep 2010, 16:41
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|X/2| + |Y/2| = 5
so when x = 0, y= |10|
when y=0 , x=|10|

so the sides of the enclosed area touches (0,10),(10,0),(0,-10) and (-10,0).
so its a square having the diagonal =20unit
So the area of the region = (20/1.414)^2 = 200
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Re: CMAT Club Test Question - m25 [#permalink]  12 Oct 2010, 07:45
i first didnt consider the mod value got the answer as 50.later i realised my mistake
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Re: GMAT club test m25 #19 [#permalink]  04 Nov 2010, 15:56
I think it is sometimes easy to solve a question by plotting it in graph. I to initially got the answer as 400 but plotting the same on the graph gave me the correct vertices and eventually I was able to solve the problem.

Thank you guyz.....
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Thanks,
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Re: CMAT Club Test Question - m25 [#permalink]  16 Nov 2010, 08:45
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|x|+||y|=10

put x=0

you get |y|=10 .....y=+-10

when you y=0

you get |x| = 10 ..... x=+-10

plot this on the co-ordinate plane.

you will get a rhombus
area of rhombus = 1/2 (d1 x d2)= 20X20/2= 200
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Re: If equation [m]|x/2| + |y/2| = 5 enclose a certain region [#permalink]  27 Sep 2013, 20:39
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Re: If equation |x/2| + |y/2| = 5 enclose a certain region [#permalink]  25 Oct 2014, 23:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If equation |x/2| + |y/2| = 5 enclose a certain region   [#permalink] 25 Oct 2014, 23:47
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# If equation |x/2| + |y/2| = 5 enclose a certain region

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