bubbliiiiiiii wrote:If x and y are integers and 4xy = x²y + 4y, what is the value of xy?
(1) y − x = 2
(2) x³ < 0
Rule:
If an equation includes an unknown that could be equal to 0, DO NOT DIVIDE BY THE UNKNOWN.
Here, it is possible that y=0, so we cannot divide 4xy = x²y + 4y by y.
Instead, we should COLLECT LIKE TERMS, as follows:
0 = x²y - 4xy + 4y
0 = y(x² - 4y + 4)
0 = y(x-2)².
The right side will be equal to 0 if y=0 or if x=2.
Question stem, rephrased:
If it is required that x=2 or that y=0, what is the value of xy?
Statement 1: y − x = 2
If x=2, then y=4.
In this case, xy = 2*4 = 8.
If y=0, then x=-2.
In this case, xy = (-2)(0) = 0.
Since xy can be different values, INSUFFICIENT.
Statement 2: x³ < 0
Since x=2 is not possible, the condition in red requires that y=0.
Thus, xy = (x)(0) = 0.
SUFFICIENT.
The correct answer is
B.
Last edited by
GMATGuruNY on Wed Aug 26, 2015 9:35 am, edited 1 time in total.
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