GMAT Changed on April 16th - Read about the latest changes here

 It is currently 23 May 2018, 15:24

### 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

# The positive integers m and n leave remainders of 2 and 3

Author Message
TAGS:

### Hide Tags

Director
Joined: 10 Mar 2013
Posts: 563
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

06 Feb 2016, 14:07
1
KUDOS
11
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:05) correct 32% (01:00) wrong based on 268 sessions

### HideShow timer Statistics

The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Current Student
Joined: 20 Mar 2014
Posts: 2644
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

06 Feb 2016, 14:15
1
KUDOS
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

m = 6p+2
n = 6q+3

Thus, m-n = 6p+2-6q-3 = 6p-6q-1 = 6p-6q+5-6 = (6p-6q-6)+5 = 6(p-q-1) + 5. Thus you will get a remainder of 5 when m-n is divided by 6.

E is thus the correct answer.

Hope this helps.
SVP
Joined: 12 Sep 2015
Posts: 2466
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

06 Feb 2016, 15:52
2
KUDOS
Expert's post
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Let's test out some values of m and n that satisfy the given information.

m leaves are remainder of 2 when divided by 6
So, m COULD equal 8

n leaves are remainder of 3 when divided by 6
So, n COULD equal 3

What is the remainder when m – n is divided by 6?
So, m - n = 8 - 3 = 5, and when we divide 5 by 6, we get 0 with remainder 5

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 03 Feb 2016
Posts: 10
The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

Updated on: 07 Feb 2016, 07:15
m=6q+2 (even)
n=6p+3 (odd)

m-n=odd => the remainder can only be an odd number (even*even+ an Odd remainder can only give us an odd number). So options D) and B) are eliminated.

Also put together $$\frac{m-n}{6}$$ will give us $$\frac{6(q-p)+5}{6}$$, thus having a +5, so answer choice E).

Originally posted by FelixM on 06 Feb 2016, 17:28.
Last edited by FelixM on 07 Feb 2016, 07:15, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 45305
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

07 Feb 2016, 04:07
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

m is 2 more than a multiple of 6;
n is 3 more than a multiple of 6.

m - n will be 1 less than a multiple of 6 (5, 11, 17, ...), therefore m - n will yield a remainder of 5 when divided by 6.

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 5779
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

07 Feb 2016, 04:15
Expert's post
1
This post was
BOOKMARKED
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

Hi,
since m>n..
i can say that m is 2 more than multiple of 6..
and n is 3 less than a multiple of 6..
so m-n means 2-(-3) =5 more than a multiple of 6.....
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2602
GRE 1: 323 Q169 V154
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

21 Mar 2016, 09:31
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8073
Location: Pune, India
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

21 Mar 2016, 09:58
Expert's post
1
This post was
BOOKMARKED
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

Use the basic concepts of divisibility.
m when divided by 6, will have groups of 6 and 2 leftover.
n when divided by 6 will have groups of 6 and 3 leftover.
When you subtract n from m, some groups of 6 will get subtracted out, 2 will get subtracted out and 1 more from a group of 6 will get subtracted out. From that groups of 6, only 5 will be leftover. So m - n will have groups of 6 and 5 leftover.
Remainder will be 5.

For more, check: http://www.veritasprep.com/blog/2011/04 ... unraveled/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Manager
Joined: 04 May 2014
Posts: 162
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

16 Jun 2016, 20:44
m=6q+2 possible values of m=8,14,20,26,32,38....
n=6q+3 possible values of n=9,15,21,27,33,39...

Now m is greater than n
subtract any value of n from m eg 38(m)-9(n)=29
Divide by 6 reminder is 5.
Intern
Joined: 19 Oct 2016
Posts: 1
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

27 Oct 2016, 06:17
We know, 6*1=6
6*2=12
Lets M= 12 & N= 6
According to question there will be remainder 2 & 3 dividing by 6, So adding remainder with 12 & 6
We get M= 14 & N = 9 which is M>N
So, M- N= 14-9= 5 (Ans)

Posted from my mobile device
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3452
Location: India
GPA: 3.5
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

27 Oct 2016, 09:50
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

The least value of m = 14 & the least value of n = 9 ; m > n

So, m - n = 5

Or, m – n is divided by 6 is 5

Hence correct answer must be (E) 5
_________________

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
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

04 Dec 2016, 07:12
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

In order to find the remainder of the difference we need only to take the difference of the remainders:

$$\frac{m - n}{6} = \frac{2 - 3}{6} = \frac{-1}{6} = \frac{5}{6}$$

Remainder is 5.

Director
Joined: 07 Dec 2014
Posts: 998
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

04 Dec 2016, 10:25
BrainLab wrote:
The positive integers m and n leave remainders of 2 and 3, respectively, when divided by 6. m > n.
What is the remainder when m – n is divided by 6?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Source: Gmat Math Bible

least possible value for n=3
least possible value for m>3=8
8-3=5
5/6 gives remainder of 5
E
Non-Human User
Joined: 09 Sep 2013
Posts: 6821
Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]

### Show Tags

10 Feb 2018, 11:25
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: The positive integers m and n leave remainders of 2 and 3   [#permalink] 10 Feb 2018, 11:25
Display posts from previous: Sort by