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

 It is currently 21 Nov 2018, 12:13

### 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

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Key Strategies to Master GMAT SC

November 24, 2018

November 24, 2018

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

# What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6535
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x?  [#permalink]

### Show Tags

Updated on: 25 Oct 2018, 22:27
00:00

Difficulty:

15% (low)

Question Stats:

73% (00:55) correct 27% (00:53) wrong based on 67 sessions

### HideShow timer Statistics

[Math Revolution GMAT math practice question]

What is the number of roots of the equation $$\frac{(x^3-1)}{(x^2+x+1)}=x$$?

$$A. 1$$
$$B. 2$$
$$C. 3$$
$$D. 4$$
$$E. no solution$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 22 Oct 2018, 00:29. Last edited by MathRevolution on 25 Oct 2018, 22:27, edited 1 time in total. Director Status: Learning stage Joined: 01 Oct 2017 Posts: 931 WE: Supply Chain Management (Energy and Utilities) Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x? [#permalink] ### Show Tags 22 Oct 2018, 01:24 1 1 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the number of roots of the equation $$\frac{(x^3-1)}{(x^2+x+1)}=x$$? $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. no solution$$ You know, $$a^3-b^3=(a-b)(a^2+ab+b^2)$$ Factorizing numerator of the given expression(LHS), we have $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ Or, $$\frac{(x-1)(x^2+x+1)}{(x^2+x+1)}=x$$ Or, x-1=x Substracting x from both LHS & RHS, -1=0 Therefore, No Solution. Ans. (E) Another approach:- $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ Or, $$(x^3-1)=x(x^2+x+1)$$ Or, $$x^3-1=x^3+x^2+x$$ Or, $$x^3+x^2+x=x^3-1$$ Or, $$x^2+x+1=0$$ is a quadratic equation with a=b=c=1 $$D=b^2-4ac=1^2-4*1*1=-3<0$$; so no real roots. Hence, No Solution exists. Ans. (E) _________________ Regards, PKN Rise above the storm, you will find the sunshine Intern Joined: 06 Feb 2017 Posts: 38 Location: India Schools: HBS '22, HEC '22 GMAT 1: 570 Q39 V28 GMAT 2: 620 Q49 V26 GPA: 4 Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x? [#permalink] ### Show Tags 22 Oct 2018, 03:31 Ans is E as after solving we will get x2+x+1=0 and D is negative for this equation. Hence No real solution is possible. _________________ I hope this helped. If this was indeed helpful, then you may say Thank You by giving a Kudos! VP Joined: 09 Mar 2016 Posts: 1116 Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x? [#permalink] ### Show Tags 22 Oct 2018, 07:09 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the number of roots of the equation $$\frac{(x^3-1)}{(x^2+x+1)}=x$$? $$A. 0$$ $$B. 1$$ $$C. 2$$ $$D. 3$$ $$E. no solution$$ $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ $$x^3-1 = x(x^2+x+1)$$ $$x^3-1 = x^3+x^2+x$$ $$-1 = x^6-x^3+x$$ $$-1 = x^2+x$$ $$x^2+x+1 = 0$$ $$B^2 - 4 *C = 1^2 - 4 *1 *1 = -3$$ since the root is less than 0, there are no solutions pushpitkc, interesting if I couldn't use a factoring method, like product of C equals the sum of B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6535 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x? [#permalink] ### Show Tags 24 Oct 2018, 00:18 => The original condition $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ is equivalent to $$x – 1 = x$$ as shown below: $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ $$=> \frac{(x-1) (x^2+x+1)}{(x^2+x+1)} = x$$ by factoring $$=> x – 1 = x$$ But $$x – 1 = x$$ has no solution. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Joined: 04 Jun 2018
Posts: 61
Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x?  [#permalink]

### Show Tags

24 Oct 2018, 00:24
MathRevolution wrote:
=>

The original condition $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ is equivalent to $$x – 1 = x$$ as shown below:

$$\frac{(x^3-1)}{(x^2+x+1)}=x$$
$$=> \frac{(x-1) (x^2+x+1)}{(x^2+x+1)} = x$$ by factoring
$$=> x – 1 = x$$

But $$x – 1 = x$$ has no solution.

math revoultion
I completely agree that there are no solutions for the equation. Bbt Answer option A tells us the number of solutions is 0, which is the same as No solution for any equation. Only if an equation has 0 solutions, will it have no equations.
Where am I wrong here?
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6535
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x?  [#permalink]

### Show Tags

25 Oct 2018, 22:27
nitesh50 wrote:
MathRevolution wrote:
=>

The original condition $$\frac{(x^3-1)}{(x^2+x+1)}=x$$ is equivalent to $$x – 1 = x$$ as shown below:

$$\frac{(x^3-1)}{(x^2+x+1)}=x$$
$$=> \frac{(x-1) (x^2+x+1)}{(x^2+x+1)} = x$$ by factoring
$$=> x – 1 = x$$

But $$x – 1 = x$$ has no solution.

math revoultion
I completely agree that there are no solutions for the equation. Bbt Answer option A tells us the number of solutions is 0, which is the same as No solution for any equation. Only if an equation has 0 solutions, will it have no equations.
Where am I wrong here?

You are right.
0 should be eliminated from the choices.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: What is the number of roots of the equation (x^3-1)/(x^2+x+1)=x? &nbs [#permalink] 25 Oct 2018, 22:27
Display posts from previous: Sort by