GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Jun 2018, 03:00

### 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

# What is the average (arithmetic mean) of all solutions to the equation

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46161
What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

14 Feb 2017, 02:03
1
00:00

Difficulty:

(N/A)

Question Stats:

77% (00:38) correct 23% (00:45) wrong based on 86 sessions

### HideShow timer Statistics

What is the average (arithmetic mean) of all solutions to the equation $$x^3 − 2x^2 − 8x = 0$$?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3

_________________
Senior Manager
Joined: 06 Jan 2015
Posts: 386
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

14 Feb 2017, 03:06
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation $$x^3 − 2x^2 − 8x = 0$$?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3

Hi

$$x^3 − 2x^2 − 8x = 0$$==>x$$(x^2-2x-8)$$==>x(x-4)(x+2)=0

Sum of all solution =0-2+4=2

Average=2/3

Hence C
_________________

आत्मनॊ मोक्षार्थम् जगद्धिताय च

Resource: GMATPrep RCs With Solution

Intern
Joined: 11 Jan 2016
Posts: 19
GMAT 1: 700 Q50 V33
GPA: 2.34
Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

14 Feb 2017, 04:38
sum of all roots is 2..so 2/3

Sent from my Mi 4i using GMAT Club Forum mobile app
Manager
Joined: 24 Oct 2013
Posts: 150
Location: India
Concentration: General Management, Strategy
WE: Information Technology (Computer Software)
Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

14 Feb 2017, 06:01
0, 4, -2 are the roots of the given equation.

Average = (0 + 4 -2)/3 = 2/3

Option C
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3505
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

14 Feb 2017, 08:19
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation $$x^3 − 2x^2 − 8x = 0$$?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3

$$x^3 − 2x^2 − 8x = 0$$

Or, $$x(x^2 − 2x − 8) = 0$$

Or, Either $$x = 0$$ or $$x^2 − 2x − 8 = 0$$

If, $$x^2 − 2x − 8 = 0$$

Or, $$x^2 − 4x + 2x − 8 = 0$$

Or, $$x ( x − 4 ) +2 ( x − 4 ) = 0$$

Or, $$x = -2$$ or , $$x = 4$$

Here we have three values of x as :

(1) x = 0
(2) x = -2
(3) x = 4

Average will be $$\frac{( 0 + 4 - 2 )}{3} = \frac{2}{3}$$

Hence, answer will be (C) $$\frac{2}{3}$$
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570
Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

### Show Tags

15 Feb 2017, 16:16
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation $$x^3 − 2x^2 − 8x = 0$$?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3

We can simplify the given equation, first by factoring out the common x from each term:

x^3 - 2x^2 - 8x = 0

x(x^2 - 2x - 8) = 0

Now factor the expression in the parentheses:

x(x - 4)(x + 2) = 0

x = 0 or x = 4 or x = -2

The average of these terms is (0 + 4 + (-2))/3 = ⅔.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: What is the average (arithmetic mean) of all solutions to the equation   [#permalink] 15 Feb 2017, 16:16
Display posts from previous: Sort by

# What is the average (arithmetic mean) of all solutions to the equation

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.