GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Oct 2019, 06:50

### 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

# The 8 spokes of a custom circular bicycle wheel radiate from the centr

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58332
The 8 spokes of a custom circular bicycle wheel radiate from the centr  [#permalink]

### Show Tags

14 Sep 2015, 23:06
1
9
00:00

Difficulty:

35% (medium)

Question Stats:

70% (02:26) correct 30% (02:23) wrong based on 144 sessions

### HideShow timer Statistics

The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?

A. 1/72
B. 1/36
C. 1/18
D. 1/12
E. 1/9

Kudos for a correct solution.

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2974
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: The 8 spokes of a custom circular bicycle wheel radiate from the centr  [#permalink]

### Show Tags

14 Sep 2015, 23:43
3
Bunuel wrote:
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?

A. 1/72
B. 1/36
C. 1/18
D. 1/12
E. 1/9

Kudos for a correct solution.

Largest angle = 80
Let, Difference between any two angles in A.P. = d

i.e. Sum of all angles will be
80 + (80-d) + (80-2d) + (80-3d) + (80-4d) + (80-5d) + (80-6d) + (80-7d) = 640 - 28d

But sum of all central angles in a circle = 360

i.e. 640 - 28d = 360
i.e. d = 280/28 = 10

Smallest Sector = (80-7d) = 80-7*10 = 10
Smallest sector as Fraction of entire circle = 10/360 = 1/36

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 30 Aug 2015
Posts: 30
Concentration: Marketing, Finance
WE: Brand Management (Manufacturing)
Re: The 8 spokes of a custom circular bicycle wheel radiate from the centr  [#permalink]

### Show Tags

15 Sep 2015, 02:41
3
1
Bunuel wrote:
The 8 spokes of a custom circular bicycle wheel radiate from the central axle of the wheel and are arranged such that the sectors formed by adjacent spokes all have different central angles, which constitute an arithmetic series of numbers (that is, the difference between any angle and the next largest angle is constant). If the largest sector so formed has a central angle of 80°, what fraction of the wheel’s area is represented by the smallest sector?

A. 1/72
B. 1/36
C. 1/18
D. 1/12
E. 1/9

Kudos for a correct solution.

8 spokes, then the circle is broken up into 8 sectors. The central angles of these sectors are 8 different numbers: call them a, b, c, d, e, f, g, and h, with a as the smallest number and h as the biggest number.

All of these angles add up to 360°, the total central angle in a circle.

Since there are 8 angles, the average of all the angles must be 360/8 = 45°.

Since the angle measures are evenly spaced as a series, the average of all the angles must also be the average of the smallest & the largest angles. That is, (a + h)/2 = 45.

Finally, since h = 80, we can figure out a, which equals 10.

A 10° angle is 10/360 = 1/36 of the circle. The sector with this angle occupies just 1/36 of the wheel’s area.

OA must be B.
_________________
Please award kudos if you like my explanation.
Thanks
Intern
Joined: 03 Feb 2014
Posts: 38
Location: United States
Concentration: Entrepreneurship, General Management
WE: General Management (Other)
Re: The 8 spokes of a custom circular bicycle wheel radiate from the centr  [#permalink]

### Show Tags

15 Sep 2015, 07:13
2
Total of all the central angles = 360
Since, there are 8 sectors, average angle = 360/8 = 45
largest angle = 80, smallest angle = x → (80+x)/2 = 45 → x = 10
sector angle & the sector area are in the same proportion → fraction of the total area occupied by the smallest sector = 10/360 = 1/36
_________________
--Shailendra
Intern
Joined: 09 Sep 2018
Posts: 16
Re: The 8 spokes of a custom circular bicycle wheel radiate from the centr  [#permalink]

### Show Tags

24 Sep 2018, 13:51
Smallest Angle: A1= A
Second Angle: A2= A+i
Third Angle: A3= A+2i
N Angle: AN= A+(N-1)i
Data:
8 angle (a) 80= A+7i
All angles(b) 360= 8A + 28i
multiply (a).-4 and add to (b)
40=4A
A=10

10/360 = 1/36
Re: The 8 spokes of a custom circular bicycle wheel radiate from the centr   [#permalink] 24 Sep 2018, 13:51
Display posts from previous: Sort by