Hi vinay1983,

You made a mistake in your approach, so I'm going to give you hint and you can retry this question.

In Fact 1, you assumed that all 3 values were either all positive or all negative, BUT what if you have a MIX of positive and negative numbers???

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

MBAsa wrote:If abc ≠ 0, what is the value of (a^3 + b^3 + c^3)/abc?

(1) |a| = 1, |b| = 2, |c| = 3
(2) a + b + c = 0

Target question: What is the value of (a^3 + b^3 + c^3)/abc ?


Statement 1: |a| = 1, |b| = 2, |c| = 3
For each variable, there are two possible values. For example, c can equal 3 or -3.
Let's test 2 different sets of values that satisfy statement 1.
Case a: a = 1, b = 2, and c = 3, in which case (a^3 + b^3 + c^3)/abc = 6
Case b: a = 1, b = 2, and c = -3, in which case (a^3 + b^3 + c^3)/abc = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: a + b + c = 0
If this is true, let's see what a^3 + b^3 + c^3 looks like.

If a + b + c = 0, then c = -a - b
So, a^3 + b^3 + c^3 = a^3 + b^3 + (-a - b)^3 =
= a^3 + b^3 - a^3 - 3a²b - 3ab² - b^3
= -3a²b - 3ab²
= -a(3ab) - b(3ab)
= 3ab(-a - b)
= 3abc

So, if a + b + c = 0, then a^3 + b^3 + c^3 MUST equal 3abc, which means (a^3 + b^3 + c^3)/abc = 3abc/abc = 3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

IMPORTANT: The GMAT does not require students to know/memorize the following identity:
If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc
In my solution, I showed that this identity is true, BUT it required more work than a reasonable GMAT question requires. So, unless there's a nicer (i.e., faster) way to verify this identity, I'd say this question is out of scope (barely).

Cheers,
Brent