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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.

Re: CMAT Club Test Question - m25 [#permalink]
30 Sep 2010, 03:22

4

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Expert's post

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.

Re: CMAT Club Test Question - m25 [#permalink]
30 Sep 2010, 16:41

2

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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

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.

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]
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