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Re: What is the area of the circle?
[#permalink]
21 Feb 2016, 23:02
Expert Reply
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
What is the area of the circle?
I: The radius of the circle is "a" unit.
II: The area of another circle whose radius is double the radius of this circle is (4a)^2, square units.
In the original condition, there is a circle, which means you need to know the radius. So, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), you cannot figure out a, which is not sufficient. For 2), you cannot figure out a, which is not sufficient. When 1) & 2), you also cannot figure out a, which is not sufficient. The answer is E. However, if you can figure out the value of a, the answer is D.
For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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