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Difficulty:
25%
(medium)
Question Stats:
71% (01:30) correct
29%
(01:33)
wrong
based on 26
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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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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
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Bunuel
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
Answer: option D
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