Data Sufficiency

[Math Revolution GMAT math practice question]

What is the length of the sides of a given cube?

1) The surface area of the cube is 150
2) The volume of the cube is 125

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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.

Since a cube is uniquely determined by its side length, we have only one variable. So, we should consider each of the conditions on their own first.

Condition 1)
Let x be the side-length of the cube. Then condition 1) tells us that 6x^2 = 150. Solving this equation yields x = 5.
Condition 1) is sufficient.

Condition 2)
Let x be the side-length of the cube. Then condition 2) tells us that x^3 = 125. Solving this equation yields x = 5.
Condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

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.