Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 May 2015, 12:23

# Today:

Free Access to GMAT Club Tests - May 25th for Memorial Day!!

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# R is a convex polygon. Does R have at least 8 sides?

Author Message
TAGS:
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 162 [1] , given: 0

R is a convex polygon. Does R have at least 8 sides? [#permalink]  13 Aug 2006, 14:44
1
KUDOS
3
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

28% (02:32) correct 72% (01:58) wrong based on 69 sessions
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.
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Apr 2014, 01:48, edited 1 time in total.
Edited the question and added the OA.
Senior Manager
Joined: 21 Jun 2006
Posts: 287
Followers: 1

Kudos [?]: 31 [0], given: 0

What is the sum of the interior angles for an octagon. I know it is 540 for a pentagon..
Senior Manager
Joined: 05 Mar 2006
Posts: 348
Followers: 1

Kudos [?]: 8 [0], given: 0

Sum of interior angles of any "regular" shape = (n-2)*180

n = number of sides
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 162 [0], given: 0

What do we know about interior angles of convex polygons?
Manager
Joined: 25 Apr 2006
Posts: 50
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: DS: Polygon [#permalink]  14 Aug 2006, 09:57
kevincan wrote:
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.

The sum of the interion angles of the polygon = 180(n-2) where n is the number of sides in the polygon.

From (1) 180(n-2) >240
n-2 > 4/3
n>10/3
therefore n should be atleast 4 but we cannot say it is atleast 8

From(2) 180(n-2) >=60n
n-2 >= n/3
2n/3 >= 2
n >=3
we cannot say n is atleast 8

Combining both, we can still say it is atleast 4 but not 8.

Senior Manager
Joined: 21 Jun 2006
Posts: 287
Followers: 1

Kudos [?]: 31 [0], given: 0

Thanks for the formula. I will have to remember that...

sum of interior angles = (n-2)*180
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 162 [0], given: 0

In a convex polygon, the maximum degree measure of an interior angle is....?
Manager
Joined: 25 Jul 2006
Posts: 100
Followers: 1

Kudos [?]: 4 [0], given: 0

kevincan wrote:
In a convex polygon, the maximum degree measure of an interior angle is....?

180.... thats the definitition of a convex polygn; all angles less than 180
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 127 [0], given: 0

Should be E.

St1: Could be 8 sided or any other.
8 sided = {80,80,80 and 168 each for other 5 angles}
4 sided = {90,90,110,70}: INSUFF

St2: Clearly INSUFF. True for all regular polygons of sides 4 or more.

Combined:
Same as statement 1.: INSUFF
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

Kudos [?]: 127 [0], given: 0

Re: DS: Polygon [#permalink]  15 Aug 2006, 06:06
kevincan wrote:
kevincan wrote:
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.

Yes, I got it. I always do silly mistakes in your questions.

Statement1 is SUFF. Lets assume this is a 8 sided polygon. Then 5 angles are 80 or less. Then other three angles are 1080 - 400 = 680. Because this is a convex polygon, sum of remaining three angles should not be greater than 540. So this is not an 8 sided polygon.
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

GMAT Instructor
Joined: 04 Jul 2006
Posts: 1269
Followers: 23

Kudos [?]: 162 [1] , given: 0

R is a convex polygon. Does R have at least 8 sides? (1) [#permalink]  23 Sep 2006, 08:56
1
KUDOS
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.
Intern
Joined: 01 Jan 2006
Posts: 28
Followers: 0

Kudos [?]: 1 [0], given: 0

1
This post was
BOOKMARKED
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.

What is convex polygon
A convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity:

* Every internal angle is at most 180 degrees.
* Every line segment between two vertices of the polygon does not go
exterior to the polygon

To have minimun 8 sides a polygon should have sum of angles 180(n-2)
180(8-2) = 1080

(1). Exactly 3 of the interior angles of R are greater than 80 degrees.
Lets take the greatest value for these angles- 180 and smallest for other 5 -80.
180*3+80*5= 940 < 1080 ..SUFFI

(2) None of the interior angles of R are less than 60 degrees.
Angles can have any value ..NOT SUFFI

Manager
Joined: 04 Jan 2014
Posts: 129
Followers: 1

Kudos [?]: 7 [0], given: 24

Re: R is a convex polygon. Does R have at least 8 sides? (1) [#permalink]  21 Apr 2014, 18:05
IMO is E.

A convex polygon with 4 sides can still have angles greater than 80 and less than 60. Experts advice on this?
Math Expert
Joined: 02 Sep 2009
Posts: 27494
Followers: 4312

Kudos [?]: 42300 [2] , given: 6012

Re: R is a convex polygon. Does R have at least 8 sides? (1) [#permalink]  22 Apr 2014, 02:45
2
KUDOS
Expert's post
pretzel wrote:
IMO is E.

A convex polygon with 4 sides can still have angles greater than 80 and less than 60. Experts advice on this?

No, the correct answer is A.

R is a convex polygon. Does R have at least 8 sides?

The Sum of Interior Angles of a polygon is $$180(n-2)$$ degrees, where $$n$$ is the number of sides (so is the number of angles). So, the greater the number of sides the greater is the sum of the angles.

For 8 sided polygon the sum of the angles is $$180(n-2)=180*6=1080$$ degrees. The question basically asks whether the sum of the angles of the polygon is more than or equal to 1080 degrees.

(1) Exactly 3 of the interior angles of R are greater than 80 degrees. This implies that each of the remaining angles must be less than or equal to 80 degrees.

Assume that the polygon IS 8-sided. In this case, the sum of those 3 angles would be $$3*80<(sum \ of \ the \ given \ 3 \ angles)<3*180$$ --> $$240<(sum \ of \ the \ given \ 3 \ angles)<540$$.

Thus the sum of the reaming 5 angles must be $$1080-540<(sum \ of \ the \ remaining \ 5 \ angles)<1080-240$$ --> $$540<(sum \ of \ the \ remaining \ 5 \ angles)<840$$. But the sum of the reaming 5 angles must be less than or equal to 5*80=400, and not greater than 540 degrees. Therefore the assumption that the polygon could be 8-sided was wrong.

If the polygon cannot be 8-sided, then it cannot be more sided too. So, R must have less than 8 sides. Sufficient.

(2) None of the interior angles of R are less than 60 degrees. Not sufficient: consider equilateral triangle (all angles 60 degrees) and regular octagon (all angles 1080/8=135 degrees).

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 4934
Followers: 297

Kudos [?]: 54 [0], given: 0

Re: R is a convex polygon. Does R have at least 8 sides? (1) [#permalink]  01 May 2015, 02:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: R is a convex polygon. Does R have at least 8 sides? (1)   [#permalink] 01 May 2015, 02:48
Similar topics Replies Last post
Similar
Topics:
R is a convex polygon. Does R have at least 8 sides? (1) 10 14 Aug 2008, 05:41
1 R is a convex polygon. Does R have at least 8 sides? (1) 4 11 Mar 2008, 11:29
R is a convex polygon. Does R have at least 8 sides? (1) 8 26 Jun 2007, 13:09
R is a convex polygon. Does R have at least 8 sides? (1) 3 26 Nov 2006, 06:43
R is a convex polygon. Does R have at least 8 sides? (1) 0 01 May 2015, 02:48
Display posts from previous: Sort by