xy plane

mariah wrote:20.In a xy-plane, eight points are given. If a point is selected at random, what is the probability that x+2y>10?
please explain

It helps to begin by sketching the line x+2y=10 on a piece of paper.
Every point on this line satisfies the equation x+2y=10
You will also see that this line divides the coordinate plane into two regions. In the region below the line, the coordinates of every point satisfy the inequality x+2y<10. In the region above the line the coordinates of every point satisfy the inequality x+2y>10.

So the question could be reworded as "In a xy-plane, eight points are given. If a point is selected at random, what is the probability that the point lies in the region above the line?"

Now that we've reworded the question, we can see that this question cannot be answered, unless we know the location of each of the 8 points. For example, if all 8 points are above the line x+2y=10, then the probability of selecting a point that is above the line will be 1. If all 8 points are below the line x+2y=10, then the probability of selecting a point that is above the line will be 0. And there are plenty of other scenarios in between.

So, as it stands, this question cannot be answered. I'm quite certain that it isn't an official GMAT question.