Hi ColdSushi,

This DS question is loaded with Number Property rules; you'll actually see Number Properties on many DS questions, so it's a good area to spend some extra time on.

We're asked if X > 0. This is a YES/NO question.

Fact 1: (Z+1)(Z)(Z-1) < 0

This looks like a great opportunity to TEST VALUES. Before randomly TESTing a value though, I want to note the Number Property patterns in this question. Since the product is LESS than 0, we cannot have a product that equals 0.

Looking at the three parentheses, we can see that the product will equal 0 if Z is -1, 0 or 1. This means that we CANNOT TEST any of those values.

The first TEST should be something fairly obvious. We need a negative product, so let's choose a negative value.

IF...

Z = -2

(-1)(-2)(-3) = -6, which is < 0

The answer to the question is NO.

Notice how in the first Test we had the product of 3 negative numbers. We can also get a negative product with just 1 negative number, so we should look for that option next.

IF....

Z = 1/2

(3/2)(1/2)(-1/2) = -3/8, which is < 0

The answer to the question is YES.

Fact 1 is INSUFFICIENT

Fact 2: |Z| < 1

This means that -1 < Z < 1

IF...

Z = 1/2

The answer to the question is YES

IF...

Z = -1/2

The answer to the question is NO

Fact 2 is INSUFFICIENT

Combined, we know....

(Z+1)(Z)(Z-1) < 0

-1 < Z < 1

Since Z is greater than -1, there's no way for (Z+1) to be negative. By extension, we can't end up with the product of 3 negative numbers, so the only way to satisfy the first Fact is if we have JUST 1 negative number (which will be the (Z-1) piece of the product. Z itself must be positive....which will give us...

(Z+1)(Z)(Z-1)

(+)(+)(-)

The answer to the question is ALWAYS YES

Combined, SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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