Thanks Rich. I've tried this one again after practicing a lot of other absolute value questions and I got it.
The most important concept for me was that |b - c| can be interpreted as the distance between b and c.

Also, I've tried using values like you've mentioned and it worked. Thanks for that too!

Just to verify, my resolution was:

1) In order for the distance between b and c to be equal to |b| - |c|, b and c are greater than 0. No info on a though. Not sufficient.

2) no info on signal of b or any clue about b. Not sufficient.

1 and 2) I know that b and c are greater than 0. With this and statement 2 it is possible to conclude that a > 0. Therefore a(b + c) > 0.

Answer: C

fambrini wrote:If a ≠ 0, b ≠ 0, c ≠ 0, is a(b + c) > 0?

1) |b - c| = |b| - |c|

2) |a + b| = |a| + |b|

OA: C

We need to determine whether a(b + c) > 0.

Statement One Alone:

|b - c| = |b| - |c|

In analyzing statement one, we can use the following rule: When we are given the absolute value equation |b - c| = |b| - |c|, we know that

1) The values of b and c have the same sign.

2) |b| > |c|

However, because we do not know the sign of the value of a, statement one is not enough information to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

|a + b| = |a| + |b|

In analyzing statement two we can use the following rule:when we are given the absolute value equation |a + b| = |a| + |b|, we know that

1) The values of a and b have the same sign.

However, because we do not know the sign of the value of c, statement two is not enough information to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we know the following:

The values of b and c have the same sign and the values of a and b have the same sign. Thus, we know that the values of a, b, and c all have the same sign. With that information we can determine that a(b + c) > 0.

Answer: C

fambrini wrote:If a ≠ 0, b ≠ 0, c ≠ 0, is a(b + c) > 0?

1) |b - c| = |b| - |c|

2) |a + b| = |a| + |b|

Question stem, rephrased:
Do a and b+c have the SAME SIGN?

Statement 1:
No information about a.
INSUFFICIENT.

Statement 2:
No information about c.
INSUFFICIENT.

Statements combined:
|b - c| = |b| - |c|
|b - c|² = (|b| - |c|)²
b² + c² - 2bc = b² + c² - 2|b||c|
-2bc = -2|b||c|
bc = |b||c|.
bc = (positive)(positive) = positive.
Implication:
b and c have the SAME SIGN.

|a + b| = |a| + |b|
|a + b|² = (|a| + |b|)²
a² + b² + 2ab = a² + b² + 2|a||b|
2ab = 2|a||b|
ab = |a||b|.
ab = (positive)(positive) = positive.
Implication:
a and b have the SAME SIGN.

Since a and b have the same sign, and b and c have the same sign, all three variables -- a, b and c -- have the same sign.
Thus, a and b+c must have the same sign.
SUFFICIENT.

The correct answer is C.