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# If O is the center of the circle above, what fraction of the

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If O is the center of the circle above, what fraction of the [#permalink]  11 Sep 2012, 03:33
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Circle.png [ 7.58 KiB | Viewed 6669 times ]
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Practice Questions
Question: 36
Page: 157
Difficulty: 550
[Reveal] Spoiler: OA

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Math Expert
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Re: If O is the center of the circle above, what fraction of the [#permalink]  11 Sep 2012, 03:34
Expert's post
SOLUTION

If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150°+150°=300° of the circle is not shaded, hence 360°-300°=60° of the circle is shaded, which is $$\frac{60}{360}=\frac{1}{6}$$ of the circular region.

Answer: C.
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Re: If O is the center of the circle above, what fraction of the [#permalink]  11 Sep 2012, 08:56
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Bunuel wrote:

Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Total angle in a circle = 360 degree
One of Non-shaded angle = 150 degree
Other Non-shaded angle = 150 degree (?) because it is opposite angle
Total Non-shaded angle = 150 + 150 = 300 degree
So, shaded angle = 360 - 300 = 60 degree

Shaded angle 60
--------------- = ------- = 1/6
Total angle 360

Hence, C
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Re: If O is the center of the circle above, what fraction of the [#permalink]  11 Sep 2012, 08:57
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I would say (C), but it seems such an easy answer. Anyways, here is the explanation: 360-2*150=60
60 degrees is the total of shaded regions, so 60/360 = 1/6.
So, please correct me if I went awry.

p.s.
where is trick here?
those shaded regions opposite to each other do not have equal angles?
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Re: If O is the center of the circle above, what fraction of the [#permalink]  12 Sep 2012, 03:37
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Bunuel wrote:

Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Since both Lines pass through centers they are alternate angles. Hence shaded degree measure is 360- (150x2)=60

So fraction of circle shaded = 60/360 = 1/6.

Hence Answer Choice C.
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Re: If O is the center of the circle above, what fraction of the [#permalink]  12 Sep 2012, 11:57
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Fraction of Shaded region = Angle made at the center by shaded region/ Angle at center of a circle
= (360-150*2)/360 = 60/360 = 1/6
Answer C
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Math Expert
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Posts: 27468
Followers: 4308

Kudos [?]: 42162 [0], given: 5957

Re: If O is the center of the circle above, what fraction of the [#permalink]  14 Sep 2012, 04:28
Expert's post
SOLUTION

If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

150°+150°=300° of the circle is not shaded, hence 360°-300°=60° of the circle is shaded, which is $$\frac{60}{360}=\frac{1}{6}$$ of the circular region.

Answer: C.

Kudos points given to everyone with correct solution. Let me know if I missed someone.
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Re: If O is the center of the circle above, what fraction of the [#permalink]  15 Sep 2012, 07:35
Part of circle not shaded=150+150=300. So, shaded part is 360-300=60.
Required fraction is :60/360=1/6
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Re: If O is the center of the circle above, what fraction of the [#permalink]  10 Sep 2014, 02:54
Bunuel wrote:
Attachment:
Circle.png
If O is the center of the circle above, what fraction of the circular region is shaded?

(A) 1/12
(B) 1/9
(C) 1/6
(D) 1/4
(E) 1/3

Practice Questions
Question: 36
Page: 157
Difficulty: 550

not shaded is 150+150 =300.

so shaded has to be 360-300= 60..

60/360 = 1/6.
Re: If O is the center of the circle above, what fraction of the   [#permalink] 10 Sep 2014, 02:54
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# If O is the center of the circle above, what fraction of the

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