Find all School-related info fast with the new School-Specific MBA Forum

It is currently 18 Apr 2014, 10:55

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Given that n is an integer, is n 1 divisible by 3?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 10

Kudos [?]: 220 [1] , given: 20

GMAT Tests User
Given that n is an integer, is n 1 divisible by 3? [#permalink] New post 18 May 2010, 04:36
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

62% (02:10) correct 37% (01:34) wrong based on 107 sessions
Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3
[Reveal] Spoiler: OA
Senior Manager
Senior Manager
Joined: 25 Jun 2009
Posts: 315
Followers: 2

Kudos [?]: 64 [0], given: 6

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 04:59
dimitri92 wrote:
Given that n is an integer, is n — 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3


A,

St1 n^2 + n = n* (n +1) is not divisible by 3

which means neither n nor n+1 is divisble by 3 hence n-1 will be divisble by 3

St2 - 3n +5 >= k +8 = > 3n >= K

Now n can be a divisble by 3 or not

for .e g take n = 3 and k = 2 then n is divisble by 3 but if n =4 and k = 2 then n is not.

OA please?
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 161

Kudos [?]: 829 [0], given: 235

GMAT Tests User Reviews Badge
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 06:48
dimitri92 wrote:
Given that n is an integer, is n — 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3


IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.


3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks



Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

1 KUDOS received
Senior Manager
Senior Manager
Joined: 25 Jun 2009
Posts: 315
Followers: 2

Kudos [?]: 64 [1] , given: 6

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 06:55
1
This post received
KUDOS
gurpreetsingh wrote:
dimitri92 wrote:
Given that n is an integer, is n — 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3


IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.


3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C


n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.


I guess you overlooked some facts,

Let me try to explain them with examples,

Say, n=0 then n(n+1) = 0 -> which is divisble by 3 and hence the st 1 is not valid for this example
Now let n=1 then n(n+1) - > 2 which is not diviable by 3 but then n-1 = 0 which is divisble by 3
Now let n=-1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well.

Cheers,
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 10

Kudos [?]: 220 [0], given: 20

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 07:07
nitishmahajan wrote:
gurpreetsingh wrote:
dimitri92 wrote:
Given that n is an integer, is n — 1 divisible by 3?
(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3


IMO C.

n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.


3n +5 >= k+8
=> 3n >= k+3 , take k = 3m as k is positive multiple of 3

=> 3n>=3m+3
=> n >= m+1 => n>1 Not sufficient.

But if we combine the both then n-1 is divisible by 3 when n>1
Thus C


n^2+n = n(n+1) is not divisible by 3 => n-1 is divisible by 3 IF N is no equal to 0,1,-1 else this wont hold true, thus not sufficient.


I guess you overlooked some facts,

Let me try to explain them with examples,

Say, n=0 then n(n+1) = 0 -> which is divisble by 3 and hence the st 1 is not valid for this example
Now let n=1 then n(n+1) - > 2 which is not diviable by 3 but then n-1 = 0 which is divisble by 3
Now let n=-1 then n(n+1) = 0 which is again divisble y 3 and hence St 1 does not hold true for this example as well.

Cheers,


ok great catch ..but are you suggesting A or C then ?
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2793
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 161

Kudos [?]: 829 [0], given: 235

GMAT Tests User Reviews Badge
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 07:08
yes right, got it Thanks

should be A
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks



Gmat test review :
670-to-710-a-long-journey-without-destination-still-happy-141642.html

2 KUDOS received
Manager
Manager
Joined: 04 Feb 2010
Posts: 64
Schools: IESE '13
WE 1: Engineer
Followers: 3

Kudos [?]: 9 [2] , given: 0

Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 18:47
2
This post received
KUDOS
1 - neither n or n+1 are divisible by 3. Thus, n-1 must be divisible by 3, since every 3rd integer is divisible by 3. SUFF

2 - 3n + 5 >= k + 8

3n - 3 >= k

3(n-1) >= k

Because we know k is divisible by 3, but not 9 (3x3), n-1 could or could not be divisible by 3. INS

Answer A
Manager
Manager
Joined: 08 May 2010
Posts: 144
Followers: 0

Kudos [?]: 51 [0], given: 39

GMAT ToolKit User
Re: is n — 1 divisible by 3? [#permalink] New post 18 May 2010, 21:39
I completely understand how statement 1 is sufficient, but am going to have to review statement 2 further to understand why it is not sufficient. I understand the simple math just not the explanation that follows.

Good question though. Had me thinking. Thank you very much.
Current Student
Joined: 26 May 2005
Posts: 571
Followers: 18

Kudos [?]: 97 [0], given: 13

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 19 Jul 2011, 02:30
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n +
1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does
not tell us this, it is not sufficient.

I dont buy this ...
Current Student
User avatar
Joined: 08 Jan 2009
Posts: 335
GMAT 1: 770 Q50 V46
Followers: 21

Kudos [?]: 75 [0], given: 7

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 19 Jul 2011, 02:45
sudhir18n wrote:
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n +
1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does
not tell us this, it is not sufficient.

I dont buy this ...


Neither.

Here is my logic:

We know this from the question stem:
n = Set of all integers = {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ... }

1) n^2 + n is not divisible by 3

We now know:
n = {... -11, -8, -5, -2, 1, 4, 7, 10, ...} <--- very clear pattern here

We are interested in n-1 (but only from the above set, which meet our condition imposed on 1)
n - 1 = {..., -12, -9, -6, -3, 0, 3, 6, 9, ... }

Let's check these against what ware testing for, are these divisible by three? Very clearly, yes.

1 is sufficient.
_________________

My Debrief

Manager
Manager
User avatar
Joined: 14 Apr 2011
Posts: 203
Followers: 2

Kudos [?]: 18 [0], given: 19

GMAT Tests User Reviews Badge
Re: is n — 1 divisible by 3? [#permalink] New post 19 Jul 2011, 03:47
Answer seems to be A.

if n(n+1) is not divisible by 3 that itself means that n or n+1 cannot be 0.
_________________

Looking for Kudos :)

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2058
Followers: 123

Kudos [?]: 827 [0], given: 376

GMAT Tests User
Re: is n — 1 divisible by 3? [#permalink] New post 19 Jul 2011, 04:48
sudhir18n wrote:
its MGMAT

The OE for statement 1.

Since we are told in Statement (1) that the product n^2+n is not divisible by 3, we know that neither n nor n +
1 is divisible by 3. Therefore it seems that n — 1 must be divisible by 3.
However, this only holds if the integers in the consecutive set are nonzero integers. Since Statement (1) does
not tell us this, it is not sufficient.
I dont buy this ...


Thanks Sudhir. Please notify MGMAT. Product of three consecutive integers must be divisible by 3 irrespective of 0, -ves or +ves.

(n-1)n(n+1) must be divisible by 3.
n(n+1): Not Divisible
(n-1): must be divisible
_________________

~fluke

Manager
Manager
Joined: 07 Mar 2011
Posts: 53
Followers: 0

Kudos [?]: 7 [0], given: 3

Re: is n — 1 divisible by 3? [#permalink] New post 19 Jul 2011, 04:58
A is the answer, if we consider "0" is divisible by "3" otherwise C.
I would lean towards A
Senior Manager
Senior Manager
User avatar
Joined: 23 Oct 2010
Posts: 380
Location: Azerbaijan
Concentration: Finance
GMAT 1: 690 Q47 V38
Followers: 11

Kudos [?]: 111 [0], given: 72

GMAT ToolKit User
Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink] New post 31 Mar 2013, 06:16
Can experts say the final word regarding option (1)? I wonder whether A is sufficient
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17317
Followers: 2873

Kudos [?]: 18374 [2] , given: 2348

GMAT Tests User CAT Tests
Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink] New post 31 Mar 2013, 06:55
2
This post received
KUDOS
Expert's post
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient


Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Answer: A.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Intern
Intern
Joined: 28 Jan 2013
Posts: 9
Location: India
Concentration: Marketing, International Business
Schools: HBS '16, HEC '17
GPA: 3
WE: Marketing (Manufacturing)
Followers: 0

Kudos [?]: 5 [0], given: 27

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink] New post 02 Jun 2013, 12:25
Bunuel wrote:
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient


Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Answer: A.

Hope it's clear.


Can you kindly explain why B is not sufficient...
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 17317
Followers: 2873

Kudos [?]: 18374 [1] , given: 2348

GMAT Tests User CAT Tests
Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink] New post 02 Jun 2013, 12:56
1
This post received
KUDOS
Expert's post
karjan07 wrote:
Bunuel wrote:
LalaB wrote:
Can experts say the final word regarding option (1)? I wonder whether A is sufficient


Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3 --> n(n+1) is not divisible by 3 --> neither n nor n+1 is divisible by 3. Now, n-1, n and n+1 are three consecutive integers, thus one of them must be divisible by 3, so if n and n+1 are NOT, then n-1 must be. Sufficient.

(2) 3n +5 >= k+8 , where k is a positive multiple of 3. Not sufficient.

Answer: A.

Hope it's clear.


Can you kindly explain why B is not sufficient...


Sure.

(2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 --> k=3x, for some positive integer x --> 3n +5\geq{3x+8} --> 3n-3\geq{3x} --> n-1\geq{x}. So, basically we just have that n-1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Manager
Manager
Joined: 06 Feb 2013
Posts: 60
Followers: 1

Kudos [?]: 1 [0], given: 33

Re: Given that n is an integer, is n 1 divisible by 3? (1) n^2 + [#permalink] New post 03 Sep 2013, 05:12
Quote:
(2) says that 3n +5 >= k+8 , where k is a positive multiple of 3 --> k=3x, for some positive integer x --> 3n +5\geq{3x+8} --> 3n-3\geq{3x} --> n-1\geq{x}. So, basically we just have that n-1 is greater or equal to some positive integer x, thus it may or may not be a multiple of 3.


Just to go a bit further on this, in what case would n-1 be divisible by 3? Say if you ended up with n-1\geq{3x} it would still be insufficient, is not it so? The fact that we have \geq seems to necessarily mean that n-1 may not necessarily be divisible because we have so many options, or I am missing the point here?
_________________

There are times when I do not mind kudos...I do enjoy giving some for help

VP
VP
User avatar
Status: I'm back and not stopping until I hit 760+
Joined: 06 Sep 2013
Posts: 1339
Location: United States
Concentration: Finance, General Management
Schools: Wharton '17
GPA: 3.5
WE: Corporate Finance (Investment Banking)
Followers: 7

Kudos [?]: 86 [0], given: 175

GMAT ToolKit User CAT Tests
Re: Given that n is an integer, is n 1 divisible by 3? [#permalink] New post 30 Dec 2013, 09:10
dimitri92 wrote:
Given that n is an integer, is n — 1 divisible by 3?

(1) n^2 + n is not divisible by 3
(2) 3n +5 >= k+8 , where k is a positive multiple of 3


The product of three consecutive integers (n-1)(n)(n+1) must be divisible by 2

Statement 1

If n^2+n= n(n+1) is not divisible by three then (n-1) must be divisible by 3

Suff

Statement 2

If k is a multiple of three
Then we get that 3n >= k + 3
This only tell us that n >=1 but nothing else. Could be any number

Hence, answer is A

Hope it helps
Cheers!
J :)

That means that n
Re: Given that n is an integer, is n 1 divisible by 3?   [#permalink] 30 Dec 2013, 09:10
    Similar topics Author Replies Last post
Similar
Topics:
Popular new posts Given that n is an integer, is n 1 divisible by 3? (1) n^2 + ivymba 12 20 Oct 2006, 05:19
New posts Given that n is an integer, is n 1 divisible by 3? (1) n^2 + AK 7 28 Dec 2006, 20:06
New posts Given that n is an integer, is n 1 divisible by 3? (1) n^2 + vineetgupta 4 02 Aug 2007, 21:08
New posts Given that n is an integer, is n 1 divisible by 3? (1) n^2+n 12345678 1 19 Sep 2007, 12:28
New posts Given that n is an integer, is n-1 divisible by 3? (1) n^2+n kirankp 4 03 Dec 2009, 07:17
Display posts from previous: Sort by

Given that n is an integer, is n 1 divisible by 3?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

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®.