1. Simplify the question: The GMAT will rarely give you a question in the most useful 'format', especially when you're doing a hard problem. Since the statements are both in 'multiplied out' form, simplify the question by getting it into the same form.

Remember to retain the question mark.

Is (2a - b)(b - 3c) > 0?

Is 2ab - 6ac - b^2 + 3bc > 0?

2. Pick a statement to start with. They both look about the same, so I'll start with statement 1. Does statement 1 give me enough information to answer the question? I'm not sure, so I'll simplify it to see what it tells me:

2ab - 6ac > b^2 - 3bc

2ab - 6ac - b^2 + 3bc > 0

The statement tells me the above, so I can answer the question with a "yes". Yes, if we have the info from statement 1, then the quantity in the question is positive. This is a trick you'll see occasionally with tough rephrasing problems: both the question and the statement simplify to essentially the same thing. Since the statement

tells you information, while the question

asks you about the exact same information, the statement is sufficient.

3. Move to the next statement. On a first glance, this one is giving me an equation, rather than an inequality. It's interesting, because it contains

some of the same pieces as the question, but not all of them. That makes me think that I should simplify it by putting everything that looks similar to the question on one side, and everything that doesn't on the other.

2ab + 9c^2 = 3bc + 6ac

2ab - 6ac + 9c^2 = 3bc

2ab - 6ac = 3bc - 9c^2

Now, I have something that appears in the question on the left side of the equation. Since the two sides are equal, I can replace one with the other, and still be asking essentially the same question.

Question: Is (2ab - 6ac) - b^2 + 3bc > 0?

Is (3bc - 9c^2) - b^2 + 3bc > 0?

Is 6bc - 9c^2 - b^2 > 0?

This kind of looks like a special quadratic. With a little manipulation, I managed to factor it.

Is (3c - b)(b - 3c) > 0?

At this point, I noticed that one of the factors was the 'opposite' of the other. To make everything look even simpler, I replaced "3c-b" with "-(b-3c)", which is mathematically the same.

Is -(b - 3c)(b - 3c) > 0?

Is -(b - 3c)^2 > 0?

Using the rule for negatives and inequalities, I flip the sign and remove the negative:

Is (b - 3c)^2 < 0?

This is still a rephrase of the original question - don't forget. If it has only one answer, then 2 is sufficient. If it has more than one answer, then 2 is insufficient. In this case, it has only one possible answer. A perfect square is never negative. The answer is always "no". 2 is sufficient, and the answer is D.

That makes this a bad/invalid GMAT question, since on the test, the two statements will never contradict each other. That is, if one gives you a definite answer of "yes", then the other will never give you a definite answer of "no". It'll either give you a definite answer of "yes", or it won't give you enough information to come up with a specific answer. That isn't a very useful thing on the test in most situations, although I can think of a few

OG problems where you can use that fact to save a couple of seconds.

_________________