Help needed with Absolutes

[MBAsa]

If abc ≠ 0, what is the value of (a3 + b3 + c3) / abc?
(1) |a|=1, |b|=2, |c|=3
(2) a + b + c = 0

[vinay1983]

I would proceed like this:

Statement 1

a can be 1 or -1
b can be 2 or -2
c can be 3 or -3

let us assume a, b and c to be negative then

(a3 + b3 + c3) / abc = (-1)^3 + (-2)^3 + (-3)^3 divided by (-1)(-2)(-3)

(-1-8-27)-6 is equal to -36/-6 = 6

If we assume all 3 numbers a b and c to be positive

i.e (1+8+27)6 = 6

We got the same value 6

This should be sufficient.

Statement 2

Does not provide any values for a b and c

A= 1 or -1 b can be -2 or 2 and c can be 3 or -3 in order that a+b+c=0

or a b and c can have any values, summation of which will lead to 0. Hence A

What is the source and the OA?

Am i correct in this approach?

[MBAsa]

My apologies, I made an error in the question. The actual question is:

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

[[email protected]]

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

[vinay1983]

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

Actually Rich, I had that feeling of missing something, but I was in a hurry to go somewhere. Just saw this.Yes you are right A cannot be sufficient, since we are unaware about the signs of the numbers. My bad.

Answer is E?

But what about Statement 2, Am I Correct in that part?

[Mission2012]

If abc ≠ 0, what is the value of (a3 + b3 + c3) / abc?
(1) |a|=1, |b|=2, |c|=3
(2) a + b + c = 0

Answer B

when a + b + c = 0

a^3 + b^3 + c^3 = 3abc (polynomial identity .. learned in class 9 )

therefore from 2 where know a^3 + b^3 + c^3/abc = 3abc/abc = 3

[Brent@GMATPrepNow]

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

[GMATGuruNY]

If abc ≠ 0, what is the value of (a³ + b³ + c³) / abc?
(1) |a|=1, |b|=2, |c|=3
(2) a + b + c = 0

Statement 1: |a|=1, |b|=2, |c|=3
Try one case that also satisfies statement 2.
Case 1: a=1, b=2, and c=-3.
In this case, (a³ + b³ + c³) / abc = (1³ + 2³ + (-3)³)/(1 * 2 * -3) = -18/-6 = 3.

Try one case that DOESN'T also satisfy statement 2.
Case 2: a=1, b=2, and c=3.
In this case, (a³ + b³ + c³) / abc = (1³ + 2³ + 3³)/(1 * 2 * 3) = 36/6 = 6.

Since the two cases yield different resulting values, INSUFFICIENT.

Statement 2; a + b + c = 0
Case 1 satisfies statement 2 and yields a resulting value of 3.
Try another random case.
Case 3: a=-4, b=1, c=3.
In this case, (a³ + b³ + c³) / abc = ((-4)³ + 1³ + 3³)/(-4 * 1 * 3) = -36/-12 = 3.
Since Case 3 yields the same resulting value as Case 1, statement 2 implies that the resulting value will always be 3.
SUFFICIENT.

The correct answer is B.