Manhnip wrote:
The equation in question can be rephrased as follows:
x^2 y – 6xy + 9y = 0
y(x^2 –6x+9)=0
y(x–3)^2=0
Therefore, one or both of the following must be true: y = 0 or
x=3
It follows that the product xy must equal either 0 or 3y. This question can therefore be rephrased “What is y?”
(1) INSUFFICIENT: This equation cannot be manipulated or combined with the original equation to solve directly for x or y. Instead, plug the two possible scenarios from the original equation into the equation from this statement:
If x = 3, then y = 3 + x = 3 + 3 = 6, so xy = (3)(6) = 18. If y = 0, then x = y – 3 = 0 – 3 = -3, so xy = (-3)(0) = 0.
Since there are two possible answers, this statement is not sufficient.
(2) SUFFICIENT: If x3 < 0, then x < 0. Therefore, x cannot equal 3, and it follows that y = 0. Therefore, xy = 0.
Ans B
Please someone confirm on the solution, if the approach is correct
Yes, that's correct.
If 6xy = x^2y + 9y, what is the value of xy? \(6xy=x^2y + 9y\) --> \(y(x^2-6x+9)=0\) --> \(y(x-3)^2=0\) --> either \(x=3\) or \(y=0\) (or both).
(1) y – x = 3. If \(y=0\) and \(x=-3\), then \(xy=0\) but if \(x=3\) and \(y=6\), then \(xy=18\). Not sufficient.
(2) x^3 < 0 --> \(x<0\) --> \(x\neq{3}\), then \(y=0\) and \(xy=0\). Sufficient.
Answer: B.
Similar question to practice:
if-6xy-x-2y-9y-what-is-the-value-of-xy-106556.htmlHope it helps.
Aaah this formatting.. I read the stem as x^(2y) and was totally stuck. Can this ambiguity in notation come in actual test ? I would have expected a bracket or at the least correct ordering like 6xy = yx^2