Problem Solving

I'm happy to help with this.

This is a very tricky one, about at the outer limit of difficulty of what you might see on the real GMAT.

4xy =(x^2)y+4

I notice there's a "y" in every term, so I am going to get everything on one side to factor out the y.

0 = (x^2)y+4 - 4xy + 4
0 = y*[x^2 - 4x + 4]

This can happen only if
(i) y = 0
OR
(ii) x^2 - 4x + 4 = 0 --> x = 2

The "OR" is not a piece of garnish. It's a vitally important piece of mathematical equipment. If x = 2, then y can be whatever it wants, and the equation is still satisfied. If y = 0, then x can equal whatever it wants, and the equation is still satisfied.

Statement #1: y - x = 2

If x = 2, then y = 4, and xy = 8
If y = 0, then x = 2, and xy = 0

The value of xy can be different for different choices, so this statement, by itself, is to answer to question.

Statement #2: x^3 < 0

That means that x is negative, x < 0. That means, x cannot equal 2, so the only way the prompt equation can be satisfied is if y = 0. Therefore

x*y = (negative)*(zero) = 0

This statement is sufficient to answer the question.

Answer = B

Here's another very different practice DS question that concerns thinking about different cases of factors.

https://gmat.magoosh.com/questions/153

After you submit an answer to that question, it should be followed by a page a video explanation of the solution.

I hope this helps. Please let me know if you have any questions.

Mike