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quantskillsgmat: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Fri Apr 23, 2010 1:14 am; Thanked: 1 times; Followed by:1 members

how to do it fast,

by quantskillsgmat » Wed Jan 25, 2012 4:03 am

Each side of a polygon is parallol to X axis or Y axis.A corner of this polygon is convex if internal angle is 90 and concave if interior angle is 270 degrees. If the number of convex corners are 25 in this polygon,then concave must be
a)20 b)0 c)21 d)22

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Source: Beat The GMAT — Problem Solving | Wed Jan 25, 2012 4:03 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jan 25, 2012 4:10 am

quantskillsgmat wrote:Each side of a polygon is parallol to X axis or Y axis.A corner of this polygon is convex if internal angle is 90 and concave if interior angle is 270 degrees. If the number of convex corners are 25 in this polygon,then concave must be

This can be easily solved without going into much detailed mathematics.

Just note that any polygon such that each of its sides are parallel to parallol to either X axis or Y axis (i.e. all internal angles are either 90 degrees or 270 degrees) will have even number of sides. And hence, even number of corners.

As number of convex corner is ODD, number of concave corners must be EVEN.

Only option C is feasible.

The correct answer is C.

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mankey: Legendary Member; Posts: 627; Joined: Thu Jun 23, 2011 9:12 am; Thanked: 4 times; Followed by:1 members

by mankey » Wed Jan 25, 2012 9:09 am

Dear Anurag

Please explain this theorem further, it is still not clear.

Thanks.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jan 25, 2012 9:21 am

mankey wrote:Please explain this theorem further...

This is no theorem, just try drawing few polygons for yourself. You'll see that no polygon can be drawn with odd number of sides which will have all the sides parallel to either of the axis.

Refer to the attached figure for better understanding.