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# Suppose the areas of the two sectors shown are equal, what is the rati

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Math Expert
Joined: 02 Sep 2009
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Suppose the areas of the two sectors shown are equal, what is the rati  [#permalink]

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11 Sep 2018, 03:10
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Difficulty:

25% (medium)

Question Stats:

83% (01:00) correct 17% (00:50) wrong based on 14 sessions

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Suppose the areas of the two sectors shown are equal, what is the ratio of angle a to angle b?

(1) The ratio of the radius of circle A to that of circle B is 3 : 1.

(2) The ratio of the area of circle A to that of circle B is 9 : 1.

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Re: Suppose the areas of the two sectors shown are equal, what is the rati  [#permalink]

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11 Sep 2018, 04:17
Bunuel wrote:

Suppose the areas of the two sectors shown are equal, what is the ratio of angle a to angle b?

(1) The ratio of the radius of circle A to that of circle B is 3 : 1.

(2) The ratio of the area of circle A to that of circle B is 9 : 1.

Attachment:
image011.jpg

Attachment:
image012.jpg

Ratio of areas = $$angle_1 * r_1^2 / angle_2 * r_2^2$$

now we know that $$angle_1 * r_1^2 = angle_2 * r_2^2$$ because ratio of area is 1 as bopth are equal

hence, $$angle_1 / angle_2 = r_2^2 / r_1^2$$

So we need to know only the ratio of the radius

Question : FInd ratio of angles of the two sectors?

Statement 1: The ratio of the radius of circle A to that of circle B is 3 : 1.

SUFFICIENT as per the above reasoning mentioned

Statement 2: The ratio of the area of circle A to that of circle B is 9 : 1.

Ratio of area is same as square of ratio of radius which is needed to answer the question hence

SUFFICIENT

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Re: Suppose the areas of the two sectors shown are equal, what is the rati   [#permalink] 11 Sep 2018, 04:17
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