Hi Vincen,Vincen wrote: if 6xy = x^2y + 9y, what is the value of xy?
(1) y - x = 3
(2) x^3 < 0
The OA is B.
I would appreciate an explanation here. Please.
It's a little tricky one.
We are given that 6xy = x^2y + 9y
=> y(x^2 - 6x + 9) = 0
=> y(x -3)^2 = 0
=> Either y = 0 or x = 3 or both
Statement 1: y - x = 3
Case 1: Say x = 3, then from y - x = 3, we get y = 6
This gives xy = 3*6 = 18.
Case 2: Say y = 0, then from y - x = 3, we get x = -3
This gives xy = 0*(-3) = 0. No unique value of xy. Insufficient.
Statement 2: x^3 < 0
=> x is negative.
If x is negative (≠3), y must be 0. Thus, xy = [A negative number]*0 = 0. Sufficient.
The correct answer: B
Hope this helps!
-Jay
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