It is currently 16 Dec 2017, 07:07

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If k=m(m+4)(m+5) k and m are positive integers. Which of the

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

Hide Tags

Manager
Manager
avatar
Joined: 26 Mar 2010
Posts: 116

Kudos [?]: 15 [0], given: 17

If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 17 Apr 2010, 00:44
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

23% (01:02) correct 77% (00:58) wrong based on 80 sessions

HideShow timer Statistics

If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6

A. I only
B. II only
C. III only
D. I and III only
E. I, II and III
[Reveal] Spoiler: OA

Kudos [?]: 15 [0], given: 17

Manager
Manager
avatar
Joined: 13 Dec 2009
Posts: 127

Kudos [?]: 313 [0], given: 10

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 17 Apr 2010, 05:58
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3 II.4 III.6


k is product of 3 numbers.
there are two possibilities when m is even and when m is odd:
1: if m is even then k will be evenly divided by 4 due to factor m and (m+4)
also it will be divided by 3 and 6 because m(m+4) is always divided by 3 [for m>0 and m is integer]and since m is even m(m+4) will always divided by 3 and 6.

2. when m is odd, it is not necessarily divided by 4. but k will be divided by 3 &6.
there will always one 2 and one 3.
e.g if m=1,3.. k is divided by 4 but if k=5 then it will not.

Kudos [?]: 313 [0], given: 10

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42628

Kudos [?]: 135818 [2], given: 12715

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 17 Apr 2010, 06:17
2
This post received
KUDOS
Expert's post
sandeep25398 wrote:
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3 II.4 III.6


k is product of 3 numbers.
there are two possibilities when m is even and when m is odd:
1: if m is even then k will be evenly divided by 4 due to factor m and (m+4)
also it will be divided by 3 and 6 because m(m+4) is always divided by 3 [for m>0 and m is integer]and since m is even m(m+4) will always divided by 3 and 6.

2. when m is odd, it is not necessarily divided by 4. but k will be divided by 3 &6.
there will always one 2 and one 3.
e.g if m=1,3.. k is divided by 4 but if k=5 then it will not.


You would be correct if question were: "Which of the following MUST divide k evenly". Then answer is I (3) and III (6).

But question asks: "Which of the following COULD divide k evenly" and in this case answer is I, II and III (m can take all three options).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135818 [2], given: 12715

Senior Manager
Senior Manager
User avatar
B
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 320

Kudos [?]: 913 [0], given: 28

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 17 May 2010, 20:57
Answer should be I,II and III because what we are asked in "COULD" not "MUST" here

Kudos [?]: 913 [0], given: 28

Manager
Manager
avatar
Joined: 27 Jul 2010
Posts: 190

Kudos [?]: 47 [0], given: 15

Location: Prague
Schools: University of Economics Prague
GMAT ToolKit User
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 03 Feb 2011, 01:42
Simple way to solve this:
m=1, m+4=5, m+5=6

Than just write numbers:

m m+4 m+5
1 4 5
2 5 6
3 6 7
4 7 8
5 8 9
6 9 10
7 10 11
8 11 12

Numbers in each column increase by one.
Now you see that each combination is divisible by 3 and 6 but not 4.

A little rough approach, but it works.
_________________

You want somethin', go get it. Period!

Kudos [?]: 47 [0], given: 15

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 22 Jan 2014, 11:42
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6


Let me take a crack at this

m(m+4)(m+5) are really three consecutive integers

(m)(m+1)(m+2)

So I is always true
II is NOT always true. Cause if m is odd then m+4 is odd too, and the only even is m+5 which can or cannot be a multiple of 4
III the product of three consecutive integers is always a multiple of 3!

Hence the answer here should be I and III

Hope it helps
Cheers!
J :)

Kudos [?]: 759 [0], given: 355

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42628

Kudos [?]: 135818 [0], given: 12715

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 23 Jan 2014, 01:00
jlgdr wrote:
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6


Let me take a crack at this

m(m+4)(m+5) are really three consecutive integers

(m)(m+1)(m+2)

So I is always true
II is NOT always true. Cause if m is odd then m+4 is odd too, and the only even is m+5 which can or cannot be a multiple of 4
III the product of three consecutive integers is always a multiple of 3!

Hence the answer here should be I and III

Hope it helps
Cheers!
J :)


ANY number COULD divide k. The correct answer is I, II and III. Check here: if-k-m-m-4-m-5-k-and-m-are-positive-integers-which-of-the-92808.html#p714621
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135818 [0], given: 12715

Manager
Manager
avatar
Joined: 04 Jun 2013
Posts: 74

Kudos [?]: 83 [0], given: 11

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 24 Jan 2014, 01:30
craky wrote:
Simple way to solve this:
m=1, m+4=5, m+5=6

Than just write numbers:

m m+4 m+5
1 4 5
2 5 6
3 6 7
4 7 8
5 8 9
6 9 10
7 10 11
8 11 12

Numbers in each column increase by one.
Now you see that each combination is divisible by 3 and 6 but not 4.

A little rough approach, but it works.

Hi,
According to your approach, the first combination ain't divisible by 3 and 6. Then how can the combination MUST be evenly divided by 3 and 6 as stated by all here.
I think the ans can be all the 3 options only because the question asked is 'WHICH COULD'. But if the question asked 'WHICH MUST', then I think there would have been no solution.
Any expert if please could comment on this.

Kudos [?]: 83 [0], given: 11

Manager
Manager
avatar
Joined: 04 Oct 2013
Posts: 161

Kudos [?]: 126 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
GMAT ToolKit User Premium Member Reviews Badge
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 24 Jan 2014, 04:08
jlgdr wrote:
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6


Let me take a crack at this

m(m+4)(m+5) are really three consecutive integers

(m)(m+1)(m+2)

So I is always true
II is NOT always true. Cause if m is odd then m+4 is odd too, and the only even is m+5 which can or cannot be a multiple of 4
III the product of three consecutive integers is always a multiple of 3!

Hence the answer here should be I and III

Hope it helps
Cheers!
J :)


It is not clear why m, m+4 and m+5 are consecutive integers.

Kudos [?]: 126 [0], given: 55

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2793 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 25 Feb 2014, 19:03
Sukant2010 wrote:
craky wrote:
Simple way to solve this:
m=1, m+4=5, m+5=6

Than just write numbers:

m m+4 m+5
1 5 6
2 6 7
3 7 8
4 8 9
5 9 10
6 10 11
7 11 12


Numbers in each column increase by one.
Now you see that each combination is divisible by 3 and 6 but not 4.

A little rough approach, but it works.

Hi,
According to your approach, the first combination ain't divisible by 3 and 6. Then how can the combination MUST be evenly divided by 3 and 6 as stated by all here.
I think the ans can be all the 3 options only because the question asked is 'WHICH COULD'. But if the question asked 'WHICH MUST', then I think there would have been no solution.
Any expert if please could comment on this.



Corrected the series
_________________

Kindly press "+1 Kudos" to appreciate :)

Kudos [?]: 2793 [0], given: 193

Manager
Manager
avatar
B
Status: One more try
Joined: 01 Feb 2015
Posts: 52

Kudos [?]: 20 [0], given: 154

Location: India
Concentration: General Management, Economics
WE: Corporate Finance (Commercial Banking)
GMAT ToolKit User
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 22 May 2016, 02:59
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6

All three divides k evenly
_________________

Believe you can and you are halfway there-Theodore Roosevelt

Kudos [?]: 20 [0], given: 154

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14813

Kudos [?]: 288 [0], given: 0

Premium Member
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 24 Sep 2017, 05:38
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

Kudos [?]: 288 [0], given: 0

Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3115

Kudos [?]: 1150 [0], given: 327

Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the [#permalink]

Show Tags

New post 24 Sep 2017, 06:06
utin wrote:
If k=m(m+4)(m+5) k and m are positive integers. Which of the following could divide k evenly?

I.3
II.4
III.6


1. Let m = 3

k=m(m+4)(m+5)

So, k=3(3+4)(3+5)

Or, k=3*7*8 ( Divisible by 3 and 4 )

2. Let m = 2

k=m(m+4)(m+5)

So, k=2(2+4)(2+5)

Or, k= 2*6*7 ( Divisible by 6 )

Thus,answer must be all three of the options....

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Kudos [?]: 1150 [0], given: 327

Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the   [#permalink] 24 Sep 2017, 06:06
Display posts from previous: Sort by

If k=m(m+4)(m+5) k and m are positive integers. Which of the

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

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®.