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26 Nov 2006, 07:43
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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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27 Nov 2006, 15:21
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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) assume 7 sides assume 3 angles 80 each = 240
sum of int angle of polygon = (n-2)*180
5*180=240+rest of 4 sides* angle= each other angle=(900-240)/4=640/4
= 160 this contradics (1) so not 7 sides
assume 10 sides (10-2)*180=240+ 7*angle==> angle 171
insuff
(2) assume each angle be 60
(n-2)*180=n*60
3n-6=n
2n=6 n=3;
suff
(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) assume 7 sides assume 3 angles 80 each = 240
sum of int angle of polygon = (n-2)*180
5*180=240+rest of 4 sides* angle= each other angle=(900-240)/4=640/4
= 160 this contradics (1) so not 7 sides
assume 10 sides (10-2)*180=240+ 7*angle==> angle 171
insuff
(2) assume each angle be 60
(n-2)*180=n*60
3n-6=n
2n=6 n=3;
suff
28 Nov 2006, 17:36
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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 ;
it means 5 of the interior angles are <=80 degrees each.
Lets say 80 deg each. Total of these = 5*80 = 400
Sum of interior angles of R = (8-2)*180
= 6* 180 = 1080
So sum of 3 interior angles(> 80) will be = 1080 - 400 = 680
Each of thes needs be = 680/3 = 226.6 deg min
As R is a convex polygon; any interior angle should not be >180
we say that R can not have at least 8 sides
but if it had 7 sides
((7-2)*180 - 4*80)/3= 192.33 >180 ; can't have atleast 7 too
if it had 6
((6-2)*180 - 3*80)/3= 160 so R can have max 6 sides ..
so (1) is suff
(2) None of the interior angles of R are less than 60 degrees
(7-2)*180/7 = 128 deg each when R has 7 sides
(8-2)* 180/8 = 135.deg each when R has 8 sides
can't say R has at least 8 sides.
so (2) is insuff
Ans is (A)..Whats the OA?
(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 ;
it means 5 of the interior angles are <=80 degrees each.
Lets say 80 deg each. Total of these = 5*80 = 400
Sum of interior angles of R = (8-2)*180
= 6* 180 = 1080
So sum of 3 interior angles(> 80) will be = 1080 - 400 = 680
Each of thes needs be = 680/3 = 226.6 deg min
As R is a convex polygon; any interior angle should not be >180
we say that R can not have at least 8 sides
but if it had 7 sides
((7-2)*180 - 4*80)/3= 192.33 >180 ; can't have atleast 7 too
if it had 6
((6-2)*180 - 3*80)/3= 160 so R can have max 6 sides ..
so (1) is suff
(2) None of the interior angles of R are less than 60 degrees
(7-2)*180/7 = 128 deg each when R has 7 sides
(8-2)* 180/8 = 135.deg each when R has 8 sides
can't say R has at least 8 sides.
so (2) is insuff
Ans is (A)..Whats the OA?
