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11 Mar 2008, 12:29
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R is a convex polygon. Does R have at least 8 sides?
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
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14 Mar 2008, 12:13
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R is a convex polygon. Does R have at least 8 sides?
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
(1) Exactly 3 of the interior angles of R are greater than 80 degrees.
(2) None of the interior angles of R are less than 60 degrees.
15 Mar 2008, 19:11
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think it's A
1: sufficient
since it's convex all angles are less then 180
3 are greaterthan 80 - so let's check for a boundary condition - all three of them being 180 (180 shouldn't alter the outcome because techicaly 179.99 should also work. moreover 180 is easy to deal with)
3 angles total to 3*180 = 460
that leaves 1080 (=(8-2)*180) - 460 = 620 degress for other 5 corners
the average angle of the remaining 5 crners is 620/5=120 which is greaterthan 80 - which doesn't agree with what condition says.
so the polygon cannot be an octagon.
2: tells that the polygon can not be a triangle, that's it. so insufficient.
1: sufficient
since it's convex all angles are less then 180
3 are greaterthan 80 - so let's check for a boundary condition - all three of them being 180 (180 shouldn't alter the outcome because techicaly 179.99 should also work. moreover 180 is easy to deal with)
3 angles total to 3*180 = 460
that leaves 1080 (=(8-2)*180) - 460 = 620 degress for other 5 corners
the average angle of the remaining 5 crners is 620/5=120 which is greaterthan 80 - which doesn't agree with what condition says.
so the polygon cannot be an octagon.
2: tells that the polygon can not be a triangle, that's it. so insufficient.
