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

It is currently 27 May 2015, 22:45

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

If n and k are positive integers, is n divisible by 6?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
SVP
SVP
avatar
Joined: 21 Jul 2006
Posts: 1551
Followers: 8

Kudos [?]: 315 [1] , given: 1

If n and k are positive integers, is n divisible by 6? [#permalink] New post 27 Aug 2009, 16:15
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

62% (01:37) correct 38% (00:41) wrong based on 201 sessions
If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)

(2) k – 1 is a multiple of 3
[Reveal] Spoiler: OA
1 KUDOS received
Manager
Manager
avatar
Joined: 25 Aug 2009
Posts: 176
Followers: 1

Kudos [?]: 68 [1] , given: 12

Re: Is n divisible by 6? [#permalink] New post 27 Aug 2009, 16:22
1
This post received
KUDOS
1.) Sufficient

Always remember, when 3 consecutive integers are multiplied, then one should be a multiple of 3 and atleast one (or max 2) number is even. Also, if the multiple of 3 is also the even number like 6, 12, 18 then it is divisible by 6 always..

For ex:- 1*2*3 ; -4*-5*-6 ; 4*5*6 ; 11*12*13..


In any case; the product would be divisible by 6.

2.) insufficient.. does not say anything about n..

Ans. A
1 KUDOS received
Manager
Manager
avatar
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Followers: 6

Kudos [?]: 61 [1] , given: 12

Re: Is n divisible by 6? [#permalink] New post 27 Aug 2009, 20:47
1
This post received
KUDOS
tarek99 wrote:
If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3

Please explain your answer.
Thanks


My answer would be A.
Since n = product of 3 consecutive numbers, it will be divisible by 3. We should also remember that 0 is also a multiple of 6. For eg : if k = 1,
n = 1*2*0 => n = 0 which IS divisible by 6.

I hope I am right. "0 is divisible by any number" right?
_________________

GMAT offended me. Now, its my turn!
Will do anything for Kudos! Please feel free to give one. :)

Manager
Manager
avatar
Joined: 09 Aug 2009
Posts: 53
Followers: 1

Kudos [?]: 6 [0], given: 1

Re: Is n divisible by 6? [#permalink] New post 27 Aug 2009, 22:50
(1) n = k(k + 1)(k - 1) --- Sufficient
(2) k – 1 is a multiple of 3 --- insufficient
Manager
Manager
User avatar
Joined: 18 Jul 2009
Posts: 170
Location: India
Schools: South Asian B-schools
Followers: 2

Kudos [?]: 65 [0], given: 37

Re: Is n divisible by 6? [#permalink] New post 28 Aug 2009, 02:30
bhanushalinikhil wrote:
tarek99 wrote:
If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3

Please explain your answer.
Thanks


My answer would be A.
Since n = product of 3 consecutive numbers, it will be divisible by 3. We should also remember that 0 is also a multiple of 6. For eg : if k = 1,
n = 1*2*0 => n = 0 which IS divisible by 6.

I hope I am right. "0 is divisible by any number" right?


I slightly differ on your explination......specially if k = 1...

If k = 1 then n = 0*1*2 then n = 0 ... zero is not a positive integer hence all values of k will start from 2 onwards
hence values of n will start from 6 onwards.....but yes your ans is right A it is
_________________

Bhushan S.
If you like my post....Consider it for Kudos :-D

Manager
Manager
avatar
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Followers: 6

Kudos [?]: 61 [0], given: 12

Re: Is n divisible by 6? [#permalink] New post 28 Aug 2009, 03:35
bhushan252 wrote:
bhanushalinikhil wrote:
tarek99 wrote:
If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)
(2) k – 1 is a multiple of 3

Please explain your answer.
Thanks


My answer would be A.
Since n = product of 3 consecutive numbers, it will be divisible by 3. We should also remember that 0 is also a multiple of 6. For eg : if k = 1,
n = 1*2*0 => n = 0 which IS divisible by 6.

I hope I am right. "0 is divisible by any number" right?


I slightly differ on your explination......specially if k = 1...

If k = 1 then n = 0*1*2 then n = 0 ... zero is not a positive integer hence all values of k will start from 2 onwards
hence values of n will start from 6 onwards.....but yes your ans is right A it is


Right. Now see the mistake.
Thanks!
_________________

GMAT offended me. Now, its my turn!
Will do anything for Kudos! Please feel free to give one. :)

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4946
Followers: 300

Kudos [?]: 55 [0], given: 0

Premium Member
Re: Is n divisible by 6? [#permalink] New post 15 Apr 2014, 06:54
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4946
Followers: 300

Kudos [?]: 55 [0], given: 0

Premium Member
Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 24 Apr 2015, 15:17
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Manager
Manager
avatar
Joined: 27 Jan 2015
Posts: 125
GMAT Date: 05-30-2015
Followers: 0

Kudos [?]: 15 [0], given: 51

Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 16 May 2015, 03:15
Unsure how A is sufficient (I know that's the answer but I'm hoping someone could help show me why)

For me A is insufficient because:

if n= k(k+1)(k-1)

we can get several cases, such as

k= 0
0*1*(-1) = -1 <-- not divisible by 6

k=1
1*2*0 = 0 <-- not divisible by 6

k=2
2*3*1 = 6 <--- divisible by 6

And so on. Statement 2 could supplement to my dilemma here, but since the answer is A, does anyone have a dumbed down explanation?
Manager
Manager
avatar
Joined: 27 Jan 2015
Posts: 125
GMAT Date: 05-30-2015
Followers: 0

Kudos [?]: 15 [0], given: 51

Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 16 May 2015, 03:22
sabineodf wrote:
Unsure how A is sufficient (I know that's the answer but I'm hoping someone could help show me why)

For me A is insufficient because:

if n= k(k+1)(k-1)

we can get several cases, such as

k= 0
0*1*(-1) = -1 <-- not divisible by 6

k=1
1*2*0 = 0 <-- not divisible by 6

k=2
2*3*1 = 6 <--- divisible by 6

And so on. Statement 2 could supplement to my dilemma here, but since the answer is A, does anyone have a dumbed down explanation?



JUST realised that the two first instances that I listed up are NOT positive integers hence they cannot be N. Ooops. Forget my question :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27512
Followers: 4319

Kudos [?]: 42465 [0], given: 6029

Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 16 May 2015, 03:54
Expert's post
sabineodf wrote:
Unsure how A is sufficient (I know that's the answer but I'm hoping someone could help show me why)

For me A is insufficient because:

if n= k(k+1)(k-1)

we can get several cases, such as

k= 0
0*1*(-1) = -1 <-- not divisible by 6 = 0

k=1
1*2*0 = 0 <-- not divisible by 6

k=2
2*3*1 = 6 <--- divisible by 6

And so on. Statement 2 could supplement to my dilemma here, but since the answer is A, does anyone have a dumbed down explanation?


0 is divisible by every integer (except 0 itself).
_________________

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

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 27 Jan 2015
Posts: 125
GMAT Date: 05-30-2015
Followers: 0

Kudos [?]: 15 [0], given: 51

Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 16 May 2015, 05:18
Bunuel wrote:
sabineodf wrote:
Unsure how A is sufficient (I know that's the answer but I'm hoping someone could help show me why)

For me A is insufficient because:

if n= k(k+1)(k-1)

we can get several cases, such as

k= 0
0*1*(-1) = -1 <-- not divisible by 6 = 0

k=1
1*2*0 = 0 <-- not divisible by 6

k=2
2*3*1 = 6 <--- divisible by 6

And so on. Statement 2 could supplement to my dilemma here, but since the answer is A, does anyone have a dumbed down explanation?


0 is divisible by every integer (except 0 itself).



Oh! Thanks, that´s good to know :D
Manager
Manager
User avatar
Joined: 29 Apr 2015
Posts: 157
Followers: 1

Kudos [?]: 50 [0], given: 93

GMAT ToolKit User
Re: If n and k are positive integers, is n divisible by 6? [#permalink] New post 23 May 2015, 01:54
tarek99 wrote:
If n and k are positive integers, is n divisible by 6?

(1) n = k(k + 1)(k - 1)

(2) k – 1 is a multiple of 3


Here's my way to solve this:

Statement (1):
Rewrite n = k(k + 1)(k - 1) to: \(k^3-k\) and plug in various positive integers to see that the result will alsways be divisible by 3. Therefore AC 1 = Sufficient

Statement (2)
Gives you just an idea about the term k-1, but nothing about k or k+1 itself. Therefore clearly insufficient.
_________________

KUDOS? You can make my happy with just one click! :-) Thanks

Re: If n and k are positive integers, is n divisible by 6?   [#permalink] 23 May 2015, 01:54
    Similar topics Author Replies Last post
Similar
Topics:
8 Experts publish their posts in the topic Is the positive integer n divisible by 6? Bunuel 4 12 Nov 2014, 09:05
24 Experts publish their posts in the topic If k is a positive integer and n = k(k + 7k), is n divisible Jem2905 15 02 Nov 2013, 13:01
If n and k are positive integers, is n divisible by 6? (1) n kapilnegi 15 29 May 2008, 12:31
If n and k are positive integers, is n divisible by 6? (1) n Balvinder 5 01 Oct 2007, 05:47
If n and k are positive integers, is n divisible by 6? (1) n TOUGH GUY 7 12 May 2006, 10:54
Display posts from previous: Sort by

If n and k are positive integers, is n divisible by 6?

  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®.