Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 19:27

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If m and k are non-zero integers, is m a multiple of k?

Author Message
TAGS:

### Hide Tags

Manager
Status: Trying.... & desperate for success.
Joined: 17 May 2012
Posts: 78
Location: India
Schools: NUS '15
GPA: 2.92
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 89 [3] , given: 61

If m and k are non-zero integers, is m a multiple of k? [#permalink]

### Show Tags

16 Sep 2012, 04:28
3
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

62% (02:20) correct 38% (01:24) wrong based on 201 sessions

### HideShow timer Statistics

If m and k are non-zero integers, is m a multiple of k?

(1) (m^2+m)/k is an integer.
(2) m=2k^2−3k
[Reveal] Spoiler: OA
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 947 [6] , given: 43

Re: If m and k are non-zero integers, is m a multiple of k [#permalink]

### Show Tags

16 Sep 2012, 05:44
6
KUDOS
2
This post was
BOOKMARKED
navigator123 wrote:
If m and k are non-zero integers, is m a multiple of k?
(1) (m2+m)/k is an integer.
(2) m=2k2−3k

(1) $$\frac{m^2+m}{k}=\frac{m(m+1)}{k}$$.
$$m$$ and $$m+1$$ are consecutive integers, so they don't have any common factor except 1 (they are co-prime).
So, $$k$$ must be a factor of either $$m$$ or $$m+1.$$
Not sufficient.

(2) Dividing through by $$k$$ gives $$\frac{m}{k}=2k-3$$ which is an integer, therefore $$k$$ must be a divisor of $$m.$$
Sufficient.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Manager
Joined: 05 Jul 2012
Posts: 78
Location: India
Concentration: Finance, Strategy
GMAT Date: 09-30-2012
GPA: 3.08
WE: Engineering (Energy and Utilities)
Followers: 4

Kudos [?]: 42 [2] , given: 8

Re: If m and k are non-zero integers, is m a multiple of k [#permalink]

### Show Tags

16 Sep 2012, 10:37
2
KUDOS
navigator123 wrote:
If m and k are non-zero integers, is m a multiple of k?
(1) (m2+m)/k is an integer.
(2) m=2k2−3k

The catch is what eva said,
Two consecutive integers are co prime !!

if that doesnt strike you, put in some value.

Remember, the difference between an identity and an equation.
An equation is tru for certain values of variable, whereas an identity is true for all values of variables.
Here what we are given is an Identity on the set of integers so put in a value which proves this wrong

And also remember oone more thing, if a value you put into it satisfies doesn't mean that it is true, but if it doesn't satisfiy it does mean that it is not true

Here put m = 3 and take k = 4
m(m+1) = 3*4 = 12, K divides 12 but k doesnt divide 3, hence not sufficient.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15450
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If m and k are non-zero integers, is m a multiple of k? [#permalink]

### Show Tags

16 Dec 2013, 23:48
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.
_________________
Manager
Joined: 25 Oct 2013
Posts: 169
Followers: 1

Kudos [?]: 59 [0], given: 56

Re: If m and k are non-zero integers, is m a multiple of k? [#permalink]

### Show Tags

03 Feb 2014, 06:58
1
This post was
BOOKMARKED
Pretty straight forward B.

Little bit different explanation than above posts.

(1) $$\frac{(m^2+m)}{k}$$ is integer.

$$\frac{m^2}{k}+\frac{m}{k}$$ is integer. It is possible that $$\frac{m^2}{k}$$ and $$\frac{m}{k}$$ each is integer and their sum is integer. But it is also possible that both of these are non-integers that add up to an integer. Hence not sufficient.

(2) $$m = 2K^2-3k$$

$$m = k(2k-3)$$

$$\frac{m}{k} = 2k-3$$. Clearly an integer. sufficient.
_________________

Click on Kudos if you liked the post!

Practice makes Perfect.

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15450
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If m and k are non-zero integers, is m a multiple of k? [#permalink]

### Show Tags

09 Apr 2015, 18:10
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 Club Legend
Joined: 09 Sep 2013
Posts: 15450
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If m and k are non-zero integers, is m a multiple of k? [#permalink]

### Show Tags

14 Apr 2016, 23:12
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.
_________________
Re: If m and k are non-zero integers, is m a multiple of k?   [#permalink] 14 Apr 2016, 23:12
Similar topics Replies Last post
Similar
Topics:
3 If m is a positive integer with k nonzero digits and no other digits. 5 25 May 2017, 19:23
2 If m is a positive integer with k nonzero digits and no other digits. 2 24 Aug 2016, 03:10
2 Is k a multiple of 14? (1) k > 13! (2) k = m!, where m is an integer g 4 21 Aug 2016, 03:00
6 If m and k are positive integers, is m!+8k a multiple of k? 3 12 Jun 2016, 04:32
9 If m and k are non-zero integers and if y^(m+k) = y^m, what is the 11 11 Feb 2017, 08:20
Display posts from previous: Sort by