Data Sufficiency

[GMAT math practice question]

$$If\ x+\ y>0,\ is\ xy^2+x^2y>0?$$

$$1)\ x>y$$
$$2)\ xy>1$$

Max@Math Revolution wrote:[GMAT math practice question]

$$If\ x+\ y>0,\ is\ xy^2+x^2y>0?$$

$$1)\ x>y$$
$$2)\ xy>1$$

Since x+y>0, the inequality in the question stem can safely be divided by x+y, as follows:
xy² + x²y > 0
xy(y + x) > 0
[xy(y+x)]/(x+y) > 0/(x+y)
xy > 0.

Question stem, rephrased:
Is xy > 0?

Statement 1: x>y
Case 1: x=2 and y=1, satisfying the constraints that x+y > 0 and x>y
In this case, xy > 0, so the answer to the rephrased question stem is YES.
Case 2: x=2 and y=-1, satisfying the constraints that x+y > 0 and x>y
In this case, xy < 0, so the answer to the rephrased question stem is NO.
Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

Statement 2: xy>1
Here, xy>0, so the answer to the rephrased question stem is YES.
SUFFICIENT.

The correct answer is 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.

Question:
xy^2 + x^2y > 0
=> xy(x+y) > 0
=> xy > 0, since x + y > 0
So, the question asks if xy > 0.

Since xy > 1 > 0 can be derived from condition 2), it is sufficient.
Condition 1) gives us no information about the sign of xy.

Therefore, B is the answer.

Answer: B