Last visit was: 20 Nov 2025, 03:22 It is currently 20 Nov 2025, 03:22
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
avatar
ShreeCS
avatar
Joined: 02 Apr 2012
Last visit: 04 Jun 2012
Posts: 7
Own Kudos:
21
 [21]
Given Kudos: 2
WE:Consulting (Computer Software)
Posts: 7
Kudos: 21
 [21]
Is positive integer n – 1 a multiple of 3? 04 Jun 2012, 11:51
1
Kudos
Add Kudos
20
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:

75% (hard)

Question Stats:

52% (01:55) correct 48% (02:09) wrong based on 440 sessions

History

Date
Time
Result
Not Attempted Yet
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,459
 [5]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,459
 [5]
Is positive integer n – 1 a multiple of 3? 04 Jun 2012, 12:15
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ShreeCS
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3
Show more

Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> \(n^3-n=n(n^2-1)=(n-1)n(n+1)=3q\). Now, \(n-1\), \(n\), and \(n+1\) are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> \(n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p\) --> so either \(n\) or \(n+1\) is a multiple of 3, as out of 3 consecutive integers \(n-1\), \(n\), and \(n+1\) only one is a multiple of 3 then knowing that it's either \(n\) or \(n+1\) tells us that \(n-1\) IS NOT multiple of 3. Sufficient.

Answer: B.
General Discussion
avatar
marioslash
avatar
Joined: 12 Dec 2011
Last visit: 27 Jun 2014
Posts: 7
Own Kudos:
53
 [1]
Given Kudos: 5
Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE:Management Consulting (Consulting)
Posts: 7
Kudos: 53
 [1]
Is positive integer n – 1 a multiple of 3? 12 Sep 2012, 06:17
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
ShreeCS
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3

Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> \(n^3-n=n(n^2-1)=(n-1)n(n+1)=3q\). Now, \(n-1\), \(n\), and \(n+1\) are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> \(n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p\) --> so either \(n\) or \(n+1\) is a multiple of 3, as out of 3 consecutive integers \(n-1\), \(n\), and \(n+1\) only one is a multiple of 3 then knowing that it's either \(n\) or \(n+1\) tells us that \(n-1\) IS NOT multiple of 3. Sufficient.

Answer: B.
Show more

Hi Bunuel,
I got a question. "Is positive integer n-1 a multiple of 3" doesn't require a specific answer?
Through the Statement 2 we figure out that n-1 is a multiple of 3 only if n+1 would be as well, and the answer is yes, conversely if n would be a multiple of 3, in this case the answer is no.
Could me please explain better this doubt
Thank you
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,459
 [1]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,459
 [1]
Is positive integer n – 1 a multiple of 3? 12 Sep 2012, 06:29
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
mario1987
Bunuel
ShreeCS
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3

Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3 --> \(n^3-n=n(n^2-1)=(n-1)n(n+1)=3q\). Now, \(n-1\), \(n\), and \(n+1\) are 3 consecutive integers and one of them must be multiple of 3, so no wonder that their product is a multiple of 3. However we don't know which one is a multiple of 3. Not sufficient.

(2) n^3 + 2n^2+ n is a multiple of 3 --> \(n^3 + 2n^2+ n=n(n^2+2n+1)=n(n+1)^2=3p\) --> so either \(n\) or \(n+1\) is a multiple of 3, as out of 3 consecutive integers \(n-1\), \(n\), and \(n+1\) only one is a multiple of 3 then knowing that it's either \(n\) or \(n+1\) tells us that \(n-1\) IS NOT multiple of 3. Sufficient.

Answer: B.

Hi Bunuel,
I got a question. "Is positive integer n-1 a multiple of 3" doesn't require a specific answer?
Through the Statement 2 we figure out that n-1 is a multiple of 3 only if n+1 would be as well, and the answer is yes, conversely if n would be a multiple of 3, in this case the answer is no.
Could me please explain better this doubt
Thank you
Show more

In a Yes/No Data Sufficiency question, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

The question asks whether n-1 is a multiple of 3, and from (2) we have a definite NO answer to this question, so this statement is sufficient.

Hope it's clear.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 20 Nov 2025
Posts: 105,408
Own Kudos:
778,459
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,459
Is positive integer n – 1 a multiple of 3? 21 Aug 2013, 03:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bumping for review and further discussion.
avatar
unceldolan
avatar
Joined: 21 Oct 2013
Last visit: 03 Jun 2015
Posts: 151
Own Kudos:
243
 [3]
Given Kudos: 19
Location: Germany
Schools: Owen '17 (A$) Sauder '17 (A$) Schulich '17 (WD) Anderson FEMBA '17 (S) McDonough '17 (A) Desautels '17 (S)
GMAT 1: 660 Q45 V36
GPA: 3.51
Schools: Owen '17 (A$) Sauder '17 (A$) Schulich '17 (WD) Anderson FEMBA '17 (S) McDonough '17 (A) Desautels '17 (S)
GMAT 1: 660 Q45 V36
Posts: 151
Kudos: 243
 [3]
Is positive integer n – 1 a multiple of 3? 04 Sep 2014, 03:56
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(1): Pick numbers. If n=5 then 5³-5 = 120 = multiple of 3, but n-1 = 4 no multiple of 3. And 4³-4 = 60 = multiple of 3 and 4-1 = 3 which is a multiple of 3. Insufficient. This will stay IS so the answer will be B or E.

(2) This is a bit trickier. First, simplify the expression:
n³+2n²+n = n(n²+2n+1) = n(n+1)² --> Multiple of 3. For this to be a multiple of 3, EITHER n OR n+1 is a multiple of 3 (both is not possible since they are consecutive integers).
Now pick numbers again: if n=5, then n+1 = 6 = multiple of 3, which satisfies the equation.
If n=3, then n is a multiple of 3, which again satisfies the equation.
Note that in both cases n - 1 is NOT a multiple of 3, which answers the question is n-1 a multiple of 3?

The Answer is B
User avatar
Sash143
User avatar
Joined: 04 Jun 2015
Last visit: 26 Jul 2022
Posts: 62
Own Kudos:
744
Given Kudos: 2
Posts: 62
Kudos: 744
Is positive integer n – 1 a multiple of 3? 26 Jan 2016, 07:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ShreeCS
Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3
Show more


WKT 0 is a multiple of any number.
(3*0=0)
Fact (1) \(n^3-n=0\)
\(n(n^2-1)=0\)
n=0,1 or -1. When n=0 ans is NO; when n=1 ans is YES. Hence INSUFF
Fact (2) \(n^3+2n^2+n=0\)
\(n(n^2+2n+1)=0\)
\(n(n+1)(n+1)=0\)
n=0,-1. When n=0 ans is NO; when n=-1 ans is NO. Hence SUFF
Ans: B
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,070
Own Kudos:
19,394
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,070
Kudos: 19,394
Is positive integer n – 1 a multiple of 3? 27 Jan 2016, 18:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is positive integer n – 1 a multiple of 3?

(1) n^3 – n is a multiple of 3

(2) n^3 + 2n^2+ n is a multiple of 3


When you modify the original condition and the question, they become n-1=3t(t is a positive integer)? --> n=3t+1?. There is 1 variable(n), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), it becomes n^3-n=(n-1)n(n+1). The multiplication of three consecutive integers is always a multiple of 6. So, n=3 -> no, n=4 -> yes, which is not sufficient.
For 2), n^3 + 2n^2+ n=3k(k is a positive integer) → n(n+1)^2=3k. In n(n+1)^2=3k, either n=3k or n=3k-1 should be valid. So, it is always no and sufficient.
Therefore, the answer is B.


--> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,597
Own Kudos:
1,079
Posts: 38,597
Kudos: 1,079
Is positive integer n – 1 a multiple of 3? 22 Aug 2025, 14:14
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
105408 posts
kingbucky
496 posts