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Problem solving

by Newaz111 » Wed May 27, 2015 4:01 pm
In the xy-plane, the point (-2, -3) is the center of a circle. The point (-2, 1) lies inside the circle and the point (4, -3) lies outside the circle. If the radius r of the circle is an integer, then r =

A. 6
B. 5
C. 4
D. 3
E. 2

Please help me...
Thank you.
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Source: — Data Sufficiency |

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by Ian Stewart » Wed May 27, 2015 5:36 pm
If a point is inside the circle, its distance from the circle's center is less than the radius. The point (-2, 1) is exactly 4 units above the center (-2, -3), so if that point is inside the circle, the radius must be greater than 4.

Similarly, if a point is outside a circle, its distance from the circle's center is greater than the radius. The point (4, -3) is exactly 6 units to the right of (-2, -3), so if that point is outside the circle, the radius must be less than 6.

So if the radius must be an integer, the answer is 5.
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