=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
Since we have 1 variable, the radius r for the sphere, and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1)
Since the circumference of the sphere is 2Ï€r = 6Ï€, we must have r = 3.
The volume of the sphere is (4/3)Ï€r^2 = (4/3)Ï€(3)^2 = 12Ï€.
Condition 1) is sufficient since it yields a unique answer,
Condition 2)
Since the surface area of the sphere is 4Ï€r^2 = 36Ï€, we must have r = 3.
The volume of the sphere is (4/3)Ï€r^2 = (4/3)Ï€3^2 = 12Ï€.
Condition 2) is sufficient since it yields a unique answer,
Therefore, D is the answer.
Answer: D
Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
