The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?
A) 8
B) 9
C) 10
D) 11
E) 13
There you go ...
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
How many sides?
This topic has expert replies
-
ronaldramlan
- Senior | Next Rank: 100 Posts
- Posts: 87
- Joined: Mon Jun 30, 2008 5:44 am
- Thanked: 14 times
- Followed by:2 members
GMAT/MBA Expert
-
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
Say, the number of sides of the polygon is n.ronaldramlan wrote:The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?
A) 8
B) 9
C) 10
D) 11
E) 13
Hence, sum of the interior angles of the polygon = (n - 2)*180 degrees
Smallest angle is 136 degrees and all the interior angles are consecutive integers. Hence, the measures of the interior angles of the polygon in degrees are 136, (136 + 1), (136 + 2), ..., and (136 + n - 1).
Hence, sum of the angles = [136 + (136 + 1) + (136 + 2) + ... + (136 + n - 1)] = 136n + n(n - 1)/2
Thus, 136n + n(n - 1)/2 = (n - 2)*180
----> 272n + n² - n = 360n - 720
----> n² -89n + 720 = 0
----> (n - 9)(n - 80) = 0
Now, if n is equal to 80, then some of the interior angles of the polygon will be greater than 180. Hence, only possible value of n is 9.
The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
-
Ozlemg
- Master | Next Rank: 500 Posts
- Posts: 407
- Joined: Tue Jan 25, 2011 9:19 am
- Thanked: 25 times
- Followed by:7 members
Woow!!! Thank you indeed!
Mentality of the problem is simple; and the explanation of the answer is easy to follow but construstion of the equations is hell hard! I think this can be sharpen by practice and somehow, developing an ability to see the big picture...
Thank you again.
Ozlem
Mentality of the problem is simple; and the explanation of the answer is easy to follow but construstion of the equations is hell hard! I think this can be sharpen by practice and somehow, developing an ability to see the big picture...
Thank you again.
Ozlem
The more you suffer before the test, the less you will do so in the test! 
-
goalevan
- Master | Next Rank: 500 Posts
- Posts: 111
- Joined: Tue Dec 30, 2008 1:25 pm
- Location: USA
- Thanked: 28 times
- GMAT Score:770
I avoided the quadratic and approximated by taking [(n-2)*180]/n] = 140
180n - 360 = 140n
40n = 360
n = 360/40
n = 9
Then listed the numbers to ensure it worked with 136 as the smallest integer:
136, 137, 138, 139, 140, 141, 142, 143, 144
B
180n - 360 = 140n
40n = 360
n = 360/40
n = 9
Then listed the numbers to ensure it worked with 136 as the smallest integer:
136, 137, 138, 139, 140, 141, 142, 143, 144
B
-
mk101
- Senior | Next Rank: 100 Posts
- Posts: 58
- Joined: Fri Oct 22, 2010 1:05 am
- Location: Bhopal
- Thanked: 1 times
- GMAT Score:710
Another approach to this question -ronaldramlan wrote:The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?
A) 8
B) 9
C) 10
D) 11
E) 13
There you go ...
sum of interior angles of a polygon = (n-2)180 - this must have "0" at its unit's place
the smallest angle is 136, which has 6 at the units place - Now you have to add the units place of consecutive digits i.e. - 6 + 7 + 8 + 9 + 0 +1 +2 +3 +4 = gives a 0 at the units place.
check the options if 9 sides exist as one of the answers. Ans b
