Last visit was: 15 Jul 2025, 14:54 It is currently 15 Jul 2025, 14:54
Close
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
18,746
 [5]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,746
 [5]
Kudos
Add Kudos
5
Bookmarks
Bookmark this Post
User avatar
PKN
Joined: 01 Oct 2017
Last visit: 22 Jan 2025
Posts: 816
Own Kudos:
1,543
 [2]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 816
Kudos: 1,543
 [2]
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
avatar
rajamech
Joined: 06 Feb 2017
Last visit: 07 Jun 2020
Posts: 30
Own Kudos:
Given Kudos: 5
Location: India
Schools: HBS '22 HEC '22
GMAT 1: 570 Q39 V28
GMAT 2: 620 Q49 V26
GPA: 4
Schools: HBS '22 HEC '22
GMAT 2: 620 Q49 V26
Posts: 30
Kudos: 28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
dave13
Joined: 09 Mar 2016
Last visit: 23 Nov 2024
Posts: 1,114
Own Kudos:
Given Kudos: 3,851
Posts: 1,114
Kudos: 1,087
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
[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 :?
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,746
Kudos
Add Kudos
Bookmarks
Bookmark this Post
=>

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
User avatar
nitesh50
User avatar
Current Student
Joined: 04 Jun 2018
Last visit: 09 Aug 2021
Posts: 140
Own Kudos:
Given Kudos: 139
GMAT 1: 690 Q50 V32
GMAT 2: 710 Q50 V36
GMAT 3: 610 Q48 V25
GMAT 3: 610 Q48 V25
Posts: 140
Kudos: 69
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MathRevolution
=>

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


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?
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,078
Own Kudos:
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,078
Kudos: 18,746
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nitesh50
MathRevolution
=>

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


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.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,412
Own Kudos:
Posts: 37,412
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102582 posts
PS Forum Moderator
695 posts