GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jun 2020, 10:52

### 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

# In a 12-sided regular polygon shown above, O is the center ...........

Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3394
In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

05 Dec 2018, 00:13
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:34) correct 25% (01:26) wrong based on 104 sessions

### HideShow timer Statistics

NUS School Moderator
Joined: 18 Jul 2018
Posts: 1121
Location: India
Concentration: Operations, General Management
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE: Engineering (Energy and Utilities)
In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

05 Dec 2018, 00:31
1
Angle b = 360/12 = 30 degrees.
Then a/b = 150/30 = 5.

Attachments

PS!.JPG [ 18.42 KiB | Viewed 1343 times ]

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 6305
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

05 Dec 2018, 00:46
1
1
EgmatQuantExpert wrote:

In a 12-sided regular polygon shown above, O is the center of the polygon. What is the value of $$\frac{a}{b}$$?

A. 2
B. 3
C. 4
D. 5
E. 6

each interior angle 'a' = 180-360/n = 180-360/12= 180-30=150

and center angle would b = 360/12= 30

so ratio a/b = 150/30 = 5 IMO D
Intern
Joined: 05 Dec 2018
Posts: 1
Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

05 Dec 2018, 01:31
1
Sum of interior angle of polygon = n-2*180 = 1800
So sum of each angle = 1800/12 = 150 = a
Sum of all angles at the centre shall be 360 so b = 360/12 = 30
so a/b = 150/30 = 5
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3394
In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

10 Dec 2018, 01:03

Solution

Given:
• We are given a 12-sided regular polygon, and O is the center of the polygon

To find:
• We are asked to find the value of $$\frac{a}{b}$$

Approach and Working:
From the given figure, we can see that ‘a’ is the interior angle of the regular polygon,
• We know that, interior angle of an n-sided regular polygon = $$180 * \frac{(n – 2)}{n}$$,
o From this, we get, $$a = 180 * \frac{(12 - 2)}{12} = 150^o$$

We can also infer that $$b = \frac{360}{n}$$, where n is the number of sides of the polygon
• Since, there can be ‘n’ such triangles formed inside the polygon, and sum of all the angles at the center = $$360^o$$
• Thus, $$b = \frac{360}{12} = 30^o$$

Therefore, the value of $$\frac{a}{b} = \frac{150}{30} = 5$$

Hence the correct answer is Option D.

_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 15039
Re: In a 12-sided regular polygon shown above, O is the center ...........  [#permalink]

### Show Tags

02 Apr 2020, 08:44
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: In a 12-sided regular polygon shown above, O is the center ...........   [#permalink] 02 Apr 2020, 08:44