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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