Author 
Message 
TAGS:

Hide Tags

Director
Joined: 10 Mar 2013
Posts: 563
Location: Germany
Concentration: Finance, Entrepreneurship
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
This post received KUDOS
11
This post was BOOKMARKED
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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
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
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
This post received 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, mn = 6p+26q3 = 6p6q1 = 6p6q+56 = (6p6q6)+5 = 6(pq1) + 5. Thus you will get a remainder of 5 when mn is divided by 6. E is thus the correct answer. Hope this helps.



SVP
Joined: 12 Sep 2015
Posts: 2466
Location: Canada

Re: The positive integers m and n leave remainders of 2 and 3 [#permalink]
Show Tags
06 Feb 2016, 15:52
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 6So, m COULD equal 8 n leaves are remainder of 3 when divided by 6So, 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 Answer: E 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)
mn=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 \(\frac{mn}{6}\) will give us \(\frac{6(qp)+5}{6}\), 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
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



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
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 mn means 2(3) =5 more than a multiple of 6.....
_________________
Absolute modulus :http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.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
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= 149= 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
WE: Business Development (Commercial Banking)

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. Answer E.



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 83=5 5/6 gives remainder of 5 E



NonHuman 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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The positive integers m and n leave remainders of 2 and 3
[#permalink]
10 Feb 2018, 11:25






