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04 Sep 2018, 02:31
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D
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Both circles in the figure above have the same center, and the difference between their radii is 6. What is the outer circle’s radius?
(1) The outer circle’s area is 9 times the inner circle’s area.
(2) The inner circle’s circumference is \(\frac{1}{3}\) the outer circle’s circumference.
04 Sep 2018, 02:31
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Official Solution:
We’ll go for LOGICAL because that is our first choice in Data Sufficiency.
We have the gap between the radii but no other numbers; the outer circle’s radius is 6 more than inner circle’s radius. So, if we can calculate one, we’d know the other.
(1) Using the ratio between areas we can calculate the ratio between the radii (areas \(x^2:y^2\) --> radii \(x:y\)). With the ratio between the different radii we can express the small radii as a fraction of the large one, and together with the difference between them we can build an equation with one variable – sufficient! (B), (C) and (E) are eliminated.
(2) Again, using the given information, we can calculate the ratio between the radii. Now, just as in (1), we can create an equation with one variable to get the result we need. Sufficient. (A) is eliminated.
Answer: D
We’ll go for LOGICAL because that is our first choice in Data Sufficiency.
We have the gap between the radii but no other numbers; the outer circle’s radius is 6 more than inner circle’s radius. So, if we can calculate one, we’d know the other.
(1) Using the ratio between areas we can calculate the ratio between the radii (areas \(x^2:y^2\) --> radii \(x:y\)). With the ratio between the different radii we can express the small radii as a fraction of the large one, and together with the difference between them we can build an equation with one variable – sufficient! (B), (C) and (E) are eliminated.
(2) Again, using the given information, we can calculate the ratio between the radii. Now, just as in (1), we can create an equation with one variable to get the result we need. Sufficient. (A) is eliminated.
Answer: D
