Question

$3x - y + 3xyz - 8 + 6 - + 9mn - 3 - 6 + - 9y + y$
​solve this

Answer 1

Answer:

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