If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 23 Jan 2017, 03:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Current Student
Status: Up again.
Joined: 31 Oct 2010
Posts: 541
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40
GMAT 2: 740 Q49 V42
Followers: 21

Kudos [?]: 413 [0], given: 75

If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) [#permalink]

### Show Tags

22 Mar 2011, 10:05
1
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

36% (01:30) correct 64% (00:56) wrong based on 91 sessions

### HideShow timer Statistics

If abc ≠ 0, what is the value of $$\frac{a^3 + b^3 + c^3}{abc}$$ ?

(1) $$|a|=1, |b|=2, |c|=3$$
(2) $$a + b + c = 0$$
[Reveal] Spoiler: OA

_________________

My GMAT debrief: http://gmatclub.com/forum/from-620-to-710-my-gmat-journey-114437.html

Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 834
Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Followers: 55

Kudos [?]: 212 [2] , given: 78

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 10:28
2
This post received
KUDOS
1
This post was
BOOKMARKED
Statement 1:

|a|=1, |b|=2, |c|=3

So a, b, c can be positive or negative. Thus, the value of the expression cannot be uniquely determined.

NS

Statement 2:

a + b + c = 0

(a + b + c)^3 = a^3 + b^3 + c^3 + (3ab + 3bc + 3ca) (a + b + c) – 3abc

Substitute for a + b + c = 0 in the above equation:

0 = a^3 + b^3 + c^3 - 3abc

=> 3abc = a^3 + b^3 + c^3

=> (a^3 + b^3 + c^3)/abc = 3

Sufficient
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Manager
Joined: 07 Oct 2010
Posts: 180
Followers: 6

Kudos [?]: 159 [1] , given: 10

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 10:29
1
This post received
KUDOS
since abc ≠ 0 , we know that either all numbers can be +ve or any two can be -ve

Option A does not help to solve the problem since we can not make out that which numbers can be -ve and value changes with every trial and error method. Therefore, A can not be the answer.

Option B tells us that A+B+C=0, therefore we can use the formula that

$$a^3 + b^3 + C^3 - 3abc = (a+b+c) (a^2 + b^2 + c^2 - ab - bc - ac)$$

and since we know that a+b+c = 0 then $$a^3 + b^3 + c^3 = 3abc$$

And thus putting "3abc" at the place of $$a^3 + b^3 + c^3$$, will give us the answer.
Therefore answer is "B"

Only thing that since I know the formula thats why I could solve this problem within seconds ..... how to solve if we do not know the formula .... please someone explain.
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 834
Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Followers: 55

Kudos [?]: 212 [0], given: 78

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 10:30
NOTE: a^3 + b^3 + c^3 = 3abc if a + b + c = 0
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1708 [0], given: 376

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 10:31
1
This post was
BOOKMARKED
gmatpapa wrote:
If abc ≠ 0, what is the value of $$\frac{a^3 + b^3 + c^3}{abc}$$ ?

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

$$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)+3abc$$

Using statement 2 & the above formula:
$$\frac{a^3 + b^3 + c^3}{abc} = \frac{(a+b+c)(a^2+b^2+c^2-ab-bc-ac)}{abc}+\frac{3abc}{abc} = 0+3=3$$
Sufficient.

Ans: "B"
_________________
Director
Status: -=Given to Fly=-
Joined: 04 Jan 2011
Posts: 834
Location: India
Concentration: Leadership, Strategy
Schools: Haas '18, Kelley '18
GMAT 1: 650 Q44 V37
GMAT 2: 710 Q48 V40
GMAT 3: 750 Q51 V40
GPA: 3.5
WE: Education (Education)
Followers: 55

Kudos [?]: 212 [0], given: 78

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 10:32
1
This post was
BOOKMARKED
By the way, are we expected to know these equations for GMAT?
_________________

"Wherever you go, go with all your heart" - Confucius

Useful Threads

1. How to Review and Analyze your Mistakes (Post by BB at GMAT Club)

2. 4 Steps to Get the Most out out of your CATs (Manhattan GMAT Blog)

My Experience With GMAT

1. From 650 to 710 to 750 - My Tryst With GMAT

2. Quest to do my Best - My GMAT Journey Log

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 115 [0], given: 42

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 17:57
1. Not sufficient as there more than one possible combination for a, b and c that satisfies the given equation.

2. Sufficient
by solving the given equation we can see that
(a+b+c)^3 = a3+b3+c3-3abc

=> a3+b3+c3 = 3abc , enough to answer the question.

Answer is B.
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

Re: Inequalities and modules DS [#permalink]

### Show Tags

22 Mar 2011, 18:31
To add some more, this has been posted earlier, please take a look at the solution step suggesting c = -(a+b).

ds-1543.html
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 14

Kudos [?]: 341 [0], given: 123

Re: Inequalities and modules DS [#permalink]

### Show Tags

23 Mar 2011, 06:23
I seriously don't know how to use this in real life. I am not good in algebra. Not my style
Director
Joined: 26 Mar 2013
Posts: 677
Followers: 3

Kudos [?]: 133 [1] , given: 96

Re: If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1) [#permalink]

### Show Tags

27 Jun 2016, 20:50
1
This post received
KUDOS
gmatpapa wrote:
If abc ≠ 0, what is the value of $$\frac{a^3 + b^3 + c^3}{abc}$$ ?

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

Alternative approach

statement 1: Clearly there are many different values that will lead to various results . Insuff

statement 2: we plug numbers that stefiey the fact a+b+c=0

a=1, b= 1, c=-2........apply in question stem (1+1-8)/-2= -6/-2=3

a=1, b=2, c=-3.........apply in question stem (1+8-27)/-6=-18/-6=3

a=1, b=3, c=-4.........apply in question stem (1+27-64)/-12= -36/-12=3

clearly the answer is B
Re: If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1)   [#permalink] 27 Jun 2016, 20:50
Similar topics Replies Last post
Similar
Topics:
What is the value of a/3-b/3 1 14 Jan 2017, 06:14
1 What is the value a^3 - b^3? 3 25 Oct 2016, 22:03
11 If a^6-b^6=0 what is the value of a^3+b^3? 7 29 Dec 2013, 06:29
1 If b does not equal 0, what is the value of 4a/3b? 1) a = b 2 16 Dec 2010, 08:13
1 What is the value of (a^-2)(b^-3)? (1) (a^-3)(b^-2) = 36^-1 4 08 May 2010, 08:53
Display posts from previous: Sort by

# If abc 0, what is the value of a^3 + b^3 + c^3/abc ? (1)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.