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

 It is currently 15 Dec 2019, 16:44 ### 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 both m and n are positive integers, is m a multiple of n?

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59730
If both m and n are positive integers, is m a multiple of n?  [#permalink]

### Show Tags 00:00

Difficulty:   45% (medium)

Question Stats: 57% (01:12) correct 43% (01:38) wrong based on 120 sessions

### HideShow timer Statistics

GMAT CLUB TESTS' FRESH QUESTION

If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
(2) 2m + n is a multiple of n

_________________
MBA Section Director V
Affiliations: GMATClub
Joined: 22 May 2017
Posts: 2757
GPA: 4
WE: Engineering (Computer Software)
If both m and n are positive integers, is m a multiple of n?  [#permalink]

### Show Tags

1
To find whether m is a multiple of n ?

Statement 1

m + 3n is a multiple of n

=> (m + 3n) = n * C (C is some integer)

=> m = nC - 3n

=> m = n(C - 3n)

m is a multiple of n

Statement 1 is sufficient

Statement 2

2m + n is a multiple of n

=> 2m + n = n * C (C is some integer)

=> 2m = n * C - n

=> 2m = n(C - 1)

=> m = $$\frac{n(C-1)}{2}$$

We don't know the divisibility of either "n" or "C-1" with respect to "2"

Hence we can't say m is a multiple of n

Statement 2 is insufficient

Hence option A
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8326
Re: If both m and n are positive integers, is m a multiple of n?  [#permalink]

### Show Tags

If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
m+3n is a multiple of n...
3n is a multiple of n, so m has to be a multiple of n otherwise 3n+m will not be a multiple of n
Sufficient

(2) 2m + n is a multiple of n
2m+n is a multiple of n..
Now n is a multiple of n so 2m will be a multiple of n..
but we cannot say if m is a multiple of n...
Say m is 12 and y is 4.....2m or 24 and also m or 12 is multiple of n or 4
But say m is 6 and y is 4.....2m or 12 is a multiple of n or 4, but m or 6 is not a multiple of 4
Insufficient

A
_________________
Math Expert V
Joined: 02 Sep 2009
Posts: 59730
Re: If both m and n are positive integers, is m a multiple of n?  [#permalink]

### Show Tags

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
(2) 2m + n is a multiple of n

_________________
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5485
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If both m and n are positive integers, is m a multiple of n?  [#permalink]

### Show Tags

Bunuel wrote:

GMAT CLUB TESTS' FRESH QUESTION

If both m and n are positive integers, is m a multiple of n?

(1) m + 3n is a multiple of n
(2) 2m + n is a multiple of n

from 1:

m=2 n =2 , yes and m=3 n = 3 sufficient

from 2:
2m+n is a multiple of n
so m 2 , n = 2 yes, m = 1, 2 in sufficient

IMOA Re: If both m and n are positive integers, is m a multiple of n?   [#permalink] 24 Dec 2018, 02:59
Display posts from previous: Sort by

# If both m and n are positive integers, is m a multiple of n?  