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Difficulty:
35%
(medium)
Question Stats:
65% (01:23) correct
35%
(01:46)
wrong
based on 58
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If P and Q are circular regions such that the area of one is 4 times the area of the other, what is the radius of the larger circle?
(1) The sum of the radii is 45.
(2) The sum of their areas is 1125π.
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(1) The sum of the radii is 45.
(2) The sum of their areas is 1125π.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Bunuel
Question: what is the radius of the larger circle?
Ratio of Area of two similar figures = Square of Ratio of corresponding sides
Ratio of Areas of two circles \(= (r_1/r_2)^2\)
i.e. \(4/1= (r_1/r_2)^2\)
i.e. \(2/1= (r_1/r_2)\)
Statement 1: The sum of the radii is 45.
i.e. \(45= (r_1+r_2)\)
one radius will be 15 and other will be 30
Two equations in two variables hence
SUFFICIENT
Statement 2: The sum of their areas is 1125π
i.e. \(π(r_1^2 + r_2^2) = 1125π\) where \(2/1= (r_1/r_2)\)
Two equations in two variables hence
SUFFICIENT
Answer: Option D
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