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, 04:33

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

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Circle.png [ 7.58 KiB | Viewed 1508 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

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Re: If O is the center of the circle above, what fraction of the [#permalink]

11 Sep 2012, 04:34

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, 09:56

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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, 09:57

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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, 04:37

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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, 12:57

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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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Re: If O is the center of the circle above, what fraction of the [#permalink]

14 Sep 2012, 05:28

SOLUTION

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Re: If O is the center of the circle above, what fraction of the [#permalink]

15 Sep 2012, 08:35

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] 15 Sep 2012, 08:35

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

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