by tommywallach Tue Dec 31, 2013 6:28 pm
Hey MD,
The answer will be 12. Where did you find this question? It seems a little hard for the GRE.
Basically, coordinate graph questions are always about either line equations or right triangles. This question is pretending it's about circles, but it isn't really. Think of it this way.
4 of the points will simply be the points you get when you go up 5, left 5, right 5, or down 5 from the center point.
The other 8 are a little more complex. Remember that the distance between any two points in a coordinate graph can always be expressed as a right triangle (try drawing a line between any two points). Then you can build a right triangle with the difference between the X values and the Y values of the two points as the length of the two perpendicular sides.
Because this circle has a radius of 5, it will create triangles of 3-4-5 and 4-3-5 (in one case, the side that is parallel to the x-axis is 3 and the side that is parallel to the y-axis is 4; in the other case, the side that is parallel to the x-axis is 4 and the side that is parallel to the y-axis is 3). It will do this in each of the four "quadrants" of the circle, making for 8 more right triangles with integer side values.
Hope that helps!
-t