NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 05:44 It is currently 26 Apr 2024, 05:44
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Mary divides a circle into 12 sectors. The central angles of these sec

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92933
Own Kudos [?]: 619155 [2]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
Mary divides a circle into 12 sectors. The central angles of these sec [#permalink] New post   18 Apr 2019, 00:25
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

56% (02:31) correct 44% (02:17) wrong based on 45 sessions
Hide Show timer Statistics
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?

(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
ShowHide Answer
Official Answer
C
User avatar
S
MofeBhatia
Manager
Manager
Joined: 29 Nov 2018
Posts: 60
Own Kudos [?]: 122 [0]
Given Kudos: 33
Location: India
GPA: 4
WE:Information Technology (Consulting)
Send PM
GMAT ToolKit User
Re: Mary divides a circle into 12 sectors. The central angles of these sec [#permalink] New post   18 Apr 2019, 07:42
Since the central angles form a A.P , whose sum will be 360 ( sum of all central angles of a circle)
Number of central angles/sectors = 12 = n
common difference = d

So, 360 = n/2 { 2a + (n-1)d}
substitutingn = 12

360 = 6{ 2a + 11d }
60 - 2a = 11d
substituting option values ( trial method)
option C , a = 8 then 60 - 16 = 11d , d = 44/11 = 4
d has to be a integer and only option C satisfy that condition.
avatar
B
Albs
Intern
Intern
Joined: 16 Nov 2015
Posts: 44
Own Kudos [?]: 30 [0]
Given Kudos: 74
Location: United Kingdom
Concentration: Social Entrepreneurship, Other
Schools: Instead Sept 20 Intake (D) Imperial '22 (A) Oxford "21 (D) Cass '21 (A$) Cambridge "21
GMAT 1: 610 Q39 V35
Send PM
Re: Mary divides a circle into 12 sectors. The central angles of these sec [#permalink] New post   20 Apr 2019, 12:19
Is there another explanation? I don't understand the question.
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6296 [1]
Given Kudos: 704
Location: India
Send PM
Re: Mary divides a circle into 12 sectors. The central angles of these sec [#permalink] New post   20 Apr 2019, 22:23
1
Kudos
As 12 angles are in AP, we can assume their values
a-11d,a-9d, a-7d,a-5d,a-3d,a-d,a+d,a+3d,a+5d,a+7d,a+9d,a+11d
Their sum is equal to 360
a-11d+a-9d+a-7d+a-5d+a-3d+a-d+a+d+a+3d+a+5d+a+7d+a+9d+a+11d=360
12a=360
a=30
Let smallest angle is x
x=a-11d
a-x=11d
30-x should be multiple of 11
Only option C gives value of '30-x' a multiple of 11
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22055 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Mary divides a circle into 12 sectors. The central angles of these sec [#permalink] New post   23 Apr 2019, 19:47
Expert Reply
Bunuel wrote:
Mary divides a circle into 12 sectors. The central angles of these sectors, measured in degrees, are all integers and they form an arithmetic sequence. What is the degree measure of the smallest possible sector angle?

(A) 5
(B) 6
(C) 8
(D) 10
(E) 12



Let x = the angle measure of the smallest sector and d = the common difference, so we have:

x + (x + d) + (x + 2d) + … + (x + 11d) = 360

12x + (1 + 2 + .. + 11)d = 360

12x + 66d = 360

2x + 11d = 60

2x = 60 - 11d

x = (60 - 11d)/2

We see that d is at most 4 since x is a positive integer, and if d is 4, then x is the smallest positive integer it can be. So x = (60 - 44)/2 = 8.

Answer: C
GMAT Club Bot
gmatclubot
Re: Mary divides a circle into 12 sectors. The central angles of these sec [#permalink]
23 Apr 2019, 19:47
Moderators:
Bunuel
Math Expert
92931 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions