GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Oct 2019, 15:54 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

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.  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  Joined: 27 Mar 2010
Posts: 77
If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

7 00:00

Difficulty:   65% (hard)

Question Stats: 30% (01:28) correct 70% (01:24) wrong based on 130 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
Manager  Joined: 13 Dec 2009
Posts: 106
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

2
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).
_________________
Senior Manager  B
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 274
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

Answer should be I,II and III because what we are asked in "COULD" not "MUST" here
Manager  Joined: 27 Jul 2010
Posts: 138
Location: Prague
Schools: University of Economics Prague
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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!
SVP  Joined: 06 Sep 2013
Posts: 1573
Concentration: Finance
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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 Math Expert V
Joined: 02 Sep 2009
Posts: 58335
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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
_________________
Manager  Joined: 04 Jun 2013
Posts: 61
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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.
Manager  Joined: 04 Oct 2013
Posts: 150
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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.
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1751
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

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 Intern  S
Status: One more try
Joined: 01 Feb 2015
Posts: 39
Location: India
Concentration: General Management, Economics
WE: Corporate Finance (Commercial Banking)
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4753
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
Re: If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

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 )
Senior Manager  P
Joined: 02 Apr 2014
Posts: 468
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
If k=m(m+4)(m+5) k and m are positive integers. Which of the  [#permalink]

Show Tags

One quick thing jumped into my mind while seeing this question. May be helpful

m (m+1) (m+2) (m+3) (m+4) (m+5)

if we observe, difference between (m+3) and m is 3
so properties with respect to divisiblity by 3 for (m)(m+4)(m+5) will be same for (m+3)(m+4)(m+5)

so we ll take a leap from m(m+4)(m+5) to (m+3)(m+4)(m+5) => we have 3 consecutive integers

Let us attack the options
(1). 3 => ofcourse, product of 3 consecutive integers is always divisible by 3
(2). 4
if m is odd, (m+3) = (m+5) = even, we have two 2s, definitely divisible by 4
(3) 6
as we have seen from above the product is always divisible by 3 and could be divisible by 4, the prod could be divisible by 12 => could be divisible by 6

so all three options could divide evenly => (E) If k=m(m+4)(m+5) k and m are positive integers. Which of the   [#permalink] 10 Jan 2018, 12:07
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 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  