Problem solving

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Newaz111: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Thu Apr 23, 2015 10:30 pm; Thanked: 1 times

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: Beat The GMAT — Data Sufficiency | Wed May 27, 2015 4:01 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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