Data Sufficiency

[GMAT math practice question]

$$Is\ \frac{x}{y^3}>0?$$

$$\left(1\right)\ x-y\ >\ 0$$
$$\left(2\right)\ xy\ >\ 0$$

I would solve it like this:

the sign of y is the same of y^3. Hence, the question is the same as $$\text{Is}\ \ \frac{x}{y}>0\ ?$$ (1) x-y>0.

This implies that x>y. But it doesn't say anything about the sign of x and y. INSUFFICIENT.

(2) xy>0.

This implies that x and y has the same sign, therefore $$\frac{x}{y}>0 $$ SUFFICIENT.

The correct answer should be B.

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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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

The question can be modified as follows:
x/y^3>0 => xy>0.
This can be seen by multiplying both sides by y^4.
It is same as condition 2).

Condition 1)
If x = 2 and y = 1, xy = 2 > 0, and the answer is 'yes'.
If x = 2 and y = -1, xy = -2 < 0, and the answer is 'no'.
Since we don't have a unique answer, condition 1) is not sufficient.

Therefore, the answer is B.

Answer: B

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.