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# A bicycle wheel has spokes that go from a center point in the hub to

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Math Expert
Joined: 02 Sep 2009
Posts: 50572
A bicycle wheel has spokes that go from a center point in the hub to  [#permalink]

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23 Jul 2018, 19:37
00:00

Difficulty:

15% (low)

Question Stats:

77% (00:44) correct 23% (00:44) wrong based on 31 sessions

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A bicycle wheel has spokes that go from a center point in the hub to equally spaced points on the rim of the wheel. If there are fewer than six spokes, what is the smallest possible angle between any two spokes?

(A) 18°
(B) 30°
(C) 40°
(D) 60°
(E) 72°

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A bicycle wheel has spokes that go from a center point in the hub to  [#permalink]

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Updated on: 23 Jul 2018, 20:11
Bunuel wrote:
A bicycle wheel has spokes that go from a center point in the hub to equally spaced points on the rim of the wheel. If there are fewer than six spokes, what is the smallest possible angle between any two spokes?

(A) 18°
(B) 30°
(C) 40°
(D) 60°
(E) 72°

Given:
There are fewer than six spokes, so consider we have 5 spokes a,b,c,d,e

Angle between these 5 spokes should add up to 360
a+b+c+d+e = 360
Now we need to find the minimum possible angle. Since the spokes are equally spaced
360/5 = 72

Hence E
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Originally posted by Akash720 on 23 Jul 2018, 19:49.
Last edited by Akash720 on 23 Jul 2018, 20:11, edited 1 time in total.
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Re: A bicycle wheel has spokes that go from a center point in the hub to  [#permalink]

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23 Jul 2018, 20:07
There are fewer than six spokes

The angle between spokes is inversely proportional to the number of spokes

=> angle between spokes is least when the number of spokes is maximum

=> number of spokes is 5

Since the angle in a bicycle wheel which is a circle is 360

=> smallest possible angle between any two spokes is $$\frac{360}{5} = 72$$

Hence option E
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Re: A bicycle wheel has spokes that go from a center point in the hub to  [#permalink]

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23 Jul 2018, 20:10
Akash720 wrote:
Angle between these 5 spokes should add up to 360
a+b+c+d+e = 360

Hence C

Since spokes that go from a center point in the hub to equally spaced points on the rim of the wheel, all angles are equal => a = b = c = d = e = $$\frac{360}{5}$$ = 72
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Re: A bicycle wheel has spokes that go from a center point in the hub to &nbs [#permalink] 23 Jul 2018, 20:10
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