Last visit was: 18 Nov 2025, 17:19 It is currently 18 Nov 2025, 17:19
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
605-655 Level|   Remainders|      
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
 [15]
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
 [15]
If x is an even positive integer, what is the remainder when 9x^3+27x^ Updated on: 09 Apr 2020, 08:11
Originally posted by GMATWhizTeam on 09 Apr 2020, 07:52.
Last edited by GMATWhizTeam on 09 Apr 2020, 08:11, edited 2 times in total.
Kudos
Add Kudos
15
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

70% (02:14) correct 30% (02:31) wrong based on 242 sessions

History

Date
Time
Result
Not Attempted Yet
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5

GMATWhiz Quant Prepathon Lesson 5 Question 1

Share your answers with explanations to participate in the Prepathon and win exciting prizes worth upto $250! Access the 5th lesson of the Prepathon using this link.

If you want to access the other posts of the Prepathon and participate in it, bookmark the Megathread of the Prepathon. Stay tuned and Enjoy learning!
ShowHide Answer
Official Answer
B
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
If x is an even positive integer, what is the remainder when 9x^3+27x^ Updated on: 10 Apr 2020, 06:51
Originally posted by GMATWhizTeam on 09 Apr 2020, 07:59.
Last edited by GMATWhizTeam on 10 Apr 2020, 06:51, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here's the official solution of the question. Make sure that you check out the method being used to internalize the 5th skill taught during the prepathon



preetamsaha minustark shameekv1989 sauravleo123 prateek25 Sourav199201 debjit1990 razorhell - Here's the first question of Day 5. Do share your explanations after solving to get points and be eligible for the exciting prizes!
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,696
 [2]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,696
 [2]
If x is an even positive integer, what is the remainder when 9x^3+27x^ 09 Apr 2020, 08:03
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
GMATWhizTeam
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5

Show more

Simplify \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\)=\(\frac{9x^2(x+3)-1( x+3)}{3x^2+9x-x-3}\)=\(\frac{(9x^2-1)(x+3)}{3x(x+3)-1(x+3)}\)=\(\frac{9x^2-1}{3x-1}=\frac{(3x-1)(3x+1)}{3x-1}=3x+1\)

So the remainder when \(3x+1\) is divided by 6, where x ix even..
So 3x will be divisible by 6 and we are left with only 1

B
User avatar
shameekv1989
User avatar
Joined: 14 Dec 2019
Last visit: 17 Jun 2021
Posts: 820
Own Kudos:
986
Given Kudos: 354
Location: Poland
Concentration: Entrepreneurship, Strategy
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 1: 640 Q49 V27
GMAT 2: 660 Q49 V31
GMAT 3: 720 Q50 V38
GPA: 4
WE:Engineering (Consumer Electronics)
Products:
My Reviews
Schools: Cambridge '22 (D) WBS (A$) IIMA PGPX'22 (D) WHU MBA (WD) ISB'22 (D)
GMAT 3: 720 Q50 V38
Posts: 820
Kudos: 986
If x is an even positive integer, what is the remainder when 9x^3+27x^ 09 Apr 2020, 08:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5

\(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) = \(\frac{(9x^2-1)(x+3)}{(3x-1)(x+3)}\)=\(\frac{(3x+1)(3x-1)(x+3)}{(3x-1)(x+3)}\) = \(3x+1\)

Since x is even 3x will be divisible by 6 => Remainder will be 1

Answer - B
User avatar
preetamsaha
User avatar
Joined: 14 Oct 2019
Last visit: 18 Jan 2025
Posts: 337
Own Kudos:
541
Given Kudos: 127
Status:Today a Reader; Tomorrow a Leader.
Location: India
GPA: 4
WE:Engineering (Energy)
Posts: 337
Kudos: 541
If x is an even positive integer, what is the remainder when 9x^3+27x^ 09 Apr 2020, 08:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(9x3+27x2−x−3)/(3x2+8x−3 )
= (9x2−1)(x+3)/(3x−1)(x+3)
=(3x+1)(3x−1)(x+3)/(3x−1)(x+3)
= 3x+1
Since x is even 3x will be divisible by 6 => Remainder will be 1
correct answer is B
User avatar
debjit1990
User avatar
Joined: 26 Dec 2017
Last visit: 14 Nov 2025
Posts: 257
Own Kudos:
281
Given Kudos: 22
Location: India
GMAT 1: 580 Q42 V27
Products:
My Reviews GMAT Club Tests
GMAT 1: 580 Q42 V27
Posts: 257
Kudos: 281
If x is an even positive integer, what is the remainder when 9x^3+27x^ 09 Apr 2020, 09:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ans: B

(9x3+27x2−x−3)/(3x2+8x−3 )
= (9x2−1)(x+3)/(3x−1)(x+3)
=(3x+1)(3x−1)(x+3)/(3x−1)(x+3)
= 3x+1

No as x is even, so 3x must be divisible by 6. So, remainder is 1.
User avatar
robu1
User avatar
Joined: 08 Jul 2017
Last visit: 19 Apr 2021
Posts: 91
Own Kudos:
66
Given Kudos: 214
GMAT 1: 620 Q48 V29
GMAT 1: 620 Q48 V29
Posts: 91
Kudos: 66
If x is an even positive integer, what is the remainder when 9x^3+27x^ 09 Apr 2020, 11:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
GMATWhizTeam
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5


Simplify \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\)=\(\frac{9x^2(x+3)-1( x+3)}{3x^2+9x-x-3}\)=\(\frac{(9x^2-1)(x+3)}{3x(x+3)-1(x+3)}\)=\(\frac{9x^2-1}{3x-1}=\frac{(3x-1)(3x+1)}{3x-1}=3x+1\)

So the remainder when \(3x+1\) is divided by 6, where x ix even..
So 3x will be divisible by 6 and we are left with only 1

B
Show more
we can take x = 2 and get the value.
User avatar
GMATWhizTeam
User avatar
GMATWhiz Representative
Joined: 07 May 2019
Last visit: 14 Oct 2025
Posts: 3,380
Own Kudos:
2,141
Given Kudos: 69
Location: India
GMAT 1: 740 Q50 V41
GMAT 2: 760 Q51 V40
Expert
Expert reply
GMAT 2: 760 Q51 V40
Posts: 3,380
Kudos: 2,141
If x is an even positive integer, what is the remainder when 9x^3+27x^ 10 Apr 2020, 06:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The official solution is shared. You can refer to it to check your approach. :)
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 12 Aug 2025
Posts: 1,108
Own Kudos:
1,113
Given Kudos: 3,851
Posts: 1,108
Kudos: 1,113
If x is an even positive integer, what is the remainder when 9x^3+27x^ 19 Feb 2021, 06:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
chetan2u
GMATWhizTeam
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5


Simplify \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\)=\(\frac{9x^2(x+3)-1( x+3)}{3x^2+9x-x-3}\)=\(\frac{(9x^2-1)(x+3)}{3x(x+3)-1(x+3)}\)=\([fraction]9x^2-1/3x-1[/fraction]=\frac{(3x-1)(3x+1)}{3x-1}=3x+1\)

So the remainder when \(3x+1\) is divided by 6, where x ix even..
So 3x will be divisible by 6 and we are left with only 1

B
Show more

chetan2u what if you reduced numerator and denominator by 3 in the highlighted part ? how would you arrive at the correct answer in this case?
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,696
 [2]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,696
 [2]
If x is an even positive integer, what is the remainder when 9x^3+27x^ 19 Feb 2021, 07:09
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13
chetan2u
GMATWhizTeam
If x is an even positive integer, what is the remainder when \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\) is divided by 6?
    (A) 0
    (B) 1
    (C) 2
    (D) 4
    (E) 5


Simplify \(\frac{9x^3+27x^2- x-3}{3x^2+8x-3}\)=\(\frac{9x^2(x+3)-1( x+3)}{3x^2+9x-x-3}\)=\(\frac{(9x^2-1)(x+3)}{3x(x+3)-1(x+3)}\)=\([fraction]9x^2-1/3x-1[/fraction]=\frac{(3x-1)(3x+1)}{3x-1}=3x+1\)

So the remainder when \(3x+1\) is divided by 6, where x ix even..
So 3x will be divisible by 6 and we are left with only 1

B

chetan2u what if you reduced numerator and denominator by 3 in the highlighted part ? how would you arrive at the correct answer in this case?
Show more


You can reduce a fraction only when the entire numerator and entire denominator is a multiple of 3. But her only the coefficients of x^2 are multiple of 3.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
If x is an even positive integer, what is the remainder when 9x^3+27x^ 07 Nov 2023, 08:03
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:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts