region on the coordinate plane

[nahid078]

If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?

1) 20
2) 50
3) 100
4) 200
5) 400

[GMATGuruNY]

If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?

1) 20
2) 50
3) 100
4) 200
5) 400

Determine the y-intercepts by plugging in x=0:
|0/2| + |y/2| = 5
|y/2| = 5
y = ±10.
Thus, the y-intercepts are (0, 10) and (0, -10).

Determine the x-intercepts by plugging in y=0:
|x/2| + |0/2| = 5
|x/2| = 5
x = ±10.
Thus, the x-intercepts are (-10, 0) and (10, 0).

Link together (-10, 0), (0, 10), (10, 0) and (0, -10).
The following graph is yielded:


The resulting graph is a square with a diagonal of length 20.
For any square with side s, the length of the diagonal = s√2.
Since s√2 = 20, we get:
s = 20/√2
A = s² = (20/√2)² = 400/2 = 200.

The correct answer is D.

[Max@Math Revolution]

Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


If equation |x/2|+|y/2|=5 encloses a certain region on the coordinate plane, what is the area of this region?

1) 20
2) 50
3) 100
4) 200
5) 400

when y=0, |x/2|=5, |x|=10, x=-10,10 and when x=0 |y/2|=5, |y|=10, y=-10,10. Therefore there are 4 points (-10,-10),(-10,10),(10,-10),(10,10) and we have parallelogram. The area is =(1/2)20*20=200, therefore the answer is D.


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Hi nahid078,

Mitchell's approach is spot-on, so I won't rehash any of that here. Instead, I'll offer some general advice about co-ordinate geometry (re: graphing) on Test Day. Graphing is a relatively rare subject in the Quant section (you'll likely see just 1-2 questions on it on Test Day) - so it's not a bit point-gainer or point-loser. That having been said, most graphing questions are based on a handful of 'rules' that you probably already know (graphing points and lines, slope, etc.), so it's often really helpful to physically draw a picture of what you're dealing with. The process of graphing is essentially just about TESTing VALUES, do you shouldn't be afraid to think about what the possible co-ordinates COULD be, then draw a picture and use all of that information to answer the question.

GMAT assassins aren't born, they're made,
Rich