Question: v-w

Given: [x] denotes the least integer greater than or equal to x.
So, for example, [1.3] = 2, since 2 is the smallest INTEGER that's greater than 1.3
Likewise, [8.8] = 9, since 9 is the smallest INTEGER that's greater than 8.8
[-3.5] = -3, since -3 is the smallest INTEGER that's greater than -3.5
[-0.9] = 0, since 0 is the smallest INTEGER that's greater than -0.9

Target question: Is [x] = 0?
In order for [x] to equal 0, x must be greater than -1 and less than or equal to zero.

So... REPHRASED target question: Is -1 < x ≤ 0?

Statement 1: –1 < x < 1
This is not enough information to answer the REPHRASED target question.
case a: x = -0.5, in which case -1 < x ≤ 0
case b: x = 0.5, in which case 0 < x
Since we cannot answer the REPHRASED target question, statement 1 is NOT SUFFICIENT

Statement 2: x < 0
This is not enough information to answer the REPHRASED target question.
case a: x = -0.5, in which case -1 < x ≤ 0
case b: x = -2, in which case x < -1
Since we cannot answer the REPHRASED target question, statement 2 is NOT SUFFICIENT

Statements 1 and 2 COMBINED
Statement 1 tells us that -1 < x
Statement 2 tells us that x < 0
When we combine these inequalities, we get: -1 < x < 0
PERFECT.
This is EXACTLY what the REPHRASE target question is asking.

Since we can answer the REPHRASED target question, the COMBINED statements are SUFFICIENT

Answer: C

Here's a related question to practice: http://www.beatthegmat.com/number-property-question-t271768.html

Plugging in values yields conclusive results IF doing so yields conflicting answers to the target question, in which case the statement is NOT sufficient.

However, in cases where a statement is sufficient, plugging in values will help us feel more confident about the sufficiency of the statement, but it doesn't yield conclusive results.

More on this here: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values

Your solution is perfect! Nice work.

Cheers,
Brent

Question link: https://www.beatthegmat.com/is-b-0-t298460.html

That's a great idea. However, you made one small error.
It's true to write: b³ - b² < 0
But, when you factored it, you got: b²(b-1) > 0 (notice that you accidentally reversed the direction of the inequality symbol)

ASIDE: If we had been able to conclude that b>1, then that would be SUFFICIENT to answer the target question (i.e., if b>1, then b is definitely not less than 0)

Cheers,
Brent

The strategies we use for these kinds of questions must be determined on a question-by-question manner.

When we scan the two statements, we see that each statement provides two separate inequalities.
Since we can only add two inequalities (we can't subtract them), it's useful to rephrase the target question in such a way that we can take advantage of our ability to add two inequalities.

That said, we also have the option of keeping the target question as it is and then manipulating the two statements. Here's what I mean:

TARGET QUESTION: Is v - w > x - y?

STATEMENT 1: v > x and w < y
Take the second inequality and multiply both sides by -1 to get: -w > -y
Aside: Since I multiplied both sides by a negative value, I reversed the direction of the inequality symbol.
We now have:
v > x
-w > -y
When we ADD the two inequalities we get: v + (-w) > x + (-y)
Simplify to get: v - w > x - y
Perfect. The answer to the target question is YES.
Statement 1 is sufficient.

STATEMENT 2: w < v and x < y
If w < v, then we know that v - w = some POSITIVE number
If x < y, then we know that x - y = some NEGATIVE number
This means we can be certain that v - w > x - y
Once again, the answer to the target question is YES.
Statement 2 is sufficient.

Does that help?

Cheers,
Brent

Let's find out...

Target question: Is vw > xy?
(1) v > x and w < y
(2) w < v and x < y

Since no relationship with ZERO is provided, it seems that there can be many different cases in which some values are negative, zero values are negative, and all values are negative.

Given all of this, go straight to the two statements COMBINED and test some values.
There are several sets of values that satisfy all of the given conditions. Here are two:

CASE I: v = -2, w = -10, x = -4 and y = 3
In this case, vw = (-2)(-10) = 20 and xy = (-4)(3) = -12
So the answer to the target question is "YES, vw is greater than xy"

CASE II: v = 2, w = 0, x = 1 and y = 3
In this case, vw = (2)(0) = 0 and xy = (1)(3) = 3
So the answer to the target question is "NO, vw is not greater than xy"

Since we get conflicting answers to the target question, the correct answer is E

That's correct. If you hover your cursor over each button, you'll see the difficulty level of the question.