It is currently 22 Nov 2017, 17:31

### 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

# Is positive integer n – 1 a multiple of 3?

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

### Hide Tags

Intern
Joined: 02 Apr 2012
Posts: 8

Kudos [?]: 2 [0], given: 2

WE: Consulting (Computer Software)
Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

04 Jun 2012, 11:51
3
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

44% (01:03) correct 56% (01:30) wrong based on 192 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 2 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [3], given: 12403

Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

04 Jun 2012, 12:15
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
ShreeCS wrote:
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.
_________________

Kudos [?]: 133073 [3], given: 12403

Intern
Joined: 12 Dec 2011
Posts: 9

Kudos [?]: 24 [1], given: 5

Location: Italy
Concentration: Finance, Entrepreneurship
GMAT Date: 04-09-2013
GPA: 4
WE: Management Consulting (Consulting)
Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

12 Sep 2012, 06:17
1
This post received
KUDOS
Bunuel wrote:
ShreeCS wrote:
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

Kudos [?]: 24 [1], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [1], given: 12403

Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

12 Sep 2012, 06:29
1
This post received
KUDOS
Expert's post
mario1987 wrote:
Bunuel wrote:
ShreeCS wrote:
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

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.
_________________

Kudos [?]: 133073 [1], given: 12403

Math Expert
Joined: 02 Sep 2009
Posts: 42305

Kudos [?]: 133073 [0], given: 12403

Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

21 Aug 2013, 03:15
Bumping for review and further discussion.
_________________

Kudos [?]: 133073 [0], given: 12403

Current Student
Joined: 21 Oct 2013
Posts: 193

Kudos [?]: 46 [2], given: 19

Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

04 Sep 2014, 03:56
2
This post received
KUDOS
(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

Kudos [?]: 46 [2], given: 19

Non-Human User
Joined: 09 Sep 2013
Posts: 15546

Kudos [?]: 283 [0], given: 0

Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

26 Jan 2016, 02:22
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.
_________________

Kudos [?]: 283 [0], given: 0

Manager
Joined: 04 Jun 2015
Posts: 86

Kudos [?]: 58 [0], given: 2

Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

26 Jan 2016, 07:56
ShreeCS wrote:
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

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
_________________

Sortem sternit fortem!

Kudos [?]: 58 [0], given: 2

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4343

Kudos [?]: 3056 [0], given: 0

GPA: 3.82
Re: Is positive integer n – 1 a multiple of 3? [#permalink]

### Show Tags

27 Jan 2016, 18:58
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.
_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Kudos [?]: 3056 [0], given: 0

Re: Is positive integer n – 1 a multiple of 3?   [#permalink] 27 Jan 2016, 18:58
Display posts from previous: Sort by

# Is positive integer n – 1 a multiple of 3?

 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®.