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.

Could you point me to any resources on how to draw the equations of the four lines without necessarily calculating the intersection points?