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Each side of a given polygon is parallel to either the X or [#permalink]
16 Apr 2010, 05:12

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Difficulty:

75% (hard)

Question Stats:

52% (03:01) correct
48% (01:49) wrong based on 85 sessions

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

Re: Polygon with concave and convex corners [#permalink]
19 Apr 2010, 14:04

I had to visualize this one. In a polygon with sides parallel to the x or y axis, the smallest number of sides would be four, making a rectangle (4 concave corners, 0 convex corners). As you "add" corners, you can do it one of two ways: either by taking a "bite" out of a corner taking away one concave corner, and replacing it with one convex corner and two concave corners, or taking a bite out of a side adding two concave and two convex corners. Either way, you are still add a 1:1 ratio of corners with each addition, plus the four corners you had at the beginning.So you will always have four more concave corners than convex corners.

If there is a mathmatical way to figure this out I would love to hear it, but visuallizing it in this way is the fastest way I can think of.

Re: Polygon with concave and convex corners [#permalink]
19 Apr 2010, 14:16

mmphf wrote:

I had to visualize this one. In a polygon with sides parallel to the x or y axis, the smallest number of sides would be four, making a rectangle (4 concave corners, 0 convex corners). As you "add" corners, you can do it one of two ways: either by taking a "bite" out of a corner taking away one concave corner, and replacing it with one convex corner and two concave corners, or taking a bite out of a side adding two concave and two convex corners. Either way, you are still add a 1:1 ratio of corners with each addition, plus the four corners you had at the beginning.So you will always have four more concave corners than convex corners.

If there is a mathmatical way to figure this out I would love to hear it, but visuallizing it in this way is the fastest way I can think of.

visualizing is the best way.

pls check the bolded text above, it should be vice versa _________________

Each side of a given polygon is parallel to either the X or [#permalink]
29 Apr 2010, 04:10

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Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90o or concave if the internal angle is 270o. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90o or concave if the internal angle is 270o. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(1)20 (2)0 (3)21 (4)22 (5)23

Sum of all the angles is 180(n-2). Let the total no of 90 deg angle be x Let the total no of 270 deg angle be y

Re: Each side of a given polygon is parallel to either the X or [#permalink]
18 May 2015, 21:59

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