What is the area of the circle above with center O?

Statement 1: b = h = radius of circle
thus
1/2*b*h = 18
r^2 = 36 => r = 6

Sufficient

Statement 2 : (90/360 )* 2pi r = 3 pi
r=6

Sufficient

Ans: D

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 above with center O?

(1) The area of ∆ AOC is 18.
(2) The length of arc ABC is 3π.


This type of question is currently frequently given in the gmat test. When you modify the original condition and the question, it is AO=CO=r, which becomes AC=root(2)r. That is, there is 1 variable(r), which should match with the number of equations. For 1) 1 question, for 2) 1 queation, which is likely to make D the answer.
In 1), r=6 is derived from (1/2)r^2=18, which is unique and sufficient.
In 2), r=6 is derived from 2πr(90/360)=3π, which is unique and sufficient. Therefore, 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.

For Statement One...how do you know that AO and OC have the same length? How do you know that the lengths are not different?

Thank you.

It's given that O is the center of the circle, so OA = OC = radius.