PROBLEM SOLVING

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dell2: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Thu Jun 02, 2011 10:28 am

by dell2 » Fri Jun 10, 2011 10:33 am

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 divisible by 6 ?

A-1
B-2
C-3
D-4
E-5

PLEASE SOLVE HOW
THANKS

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Fri Jun 10, 2011 10:42 am

dell2 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 divisible by 6 ?

A-1
B-2
C-3
D-4
E-5

PLEASE SOLVE HOW
THANKS

m=6k+2;
n=6t+3;
k,t (1,2,3 are +ve integers..)

since m>n; one way is to solve it by substituting values, put k=2 and t=1; we have m=14 and n=9;
m-n=5 hence remainder is 5; by substituting different values of k and t remainder we will find that remainder is always 5,, to understand why its coming 5 all the time we need to be familiar with the concept of -ve remainder,,,!!! if you know it.. then implement it.. if you don't send me a PM i'll explain it to you...!!!
E

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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greenshadow: Newbie | Next Rank: 10 Posts; Posts: 9; Joined: Tue May 24, 2011 10:38 am; Thanked: 3 times

by greenshadow » Fri Jun 10, 2011 11:01 am

From the given information,
m = 6k + 2
n = 6l + 3

m-n = 6(k-l) - 1
= 6(k-l-1) + 5

As m is greater than n, m will be at least 5 greater than n. Hence, "k-l-1" will be positive.

Therefore, the remainder will be 5, which is (E).

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Jun 10, 2011 11:31 am

dell2 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 divisible by 6 ?

A-1
B-2
C-3
D-4
E-5

PLEASE SOLVE HOW
THANKS

Hi!

The GMAT is in part about math, but it's also in part about speed. Without any doubt the quickest way to solve this problem, and many problems in which you're given rules about how variables behave but no actual values, is by picking numbers.

m/6 has rem 2, so let's pick m=8
n/6 has rem 3; we can't pick n=9 (because m>n), so let's pick n=3.

m-n = 8-3 = 5

5/6 has a quotient of 0 and a remainder of 5... choose E!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Fri Jun 10, 2011 9:13 pm

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 divisible by 6 ?

A-1
B-2
C-3
D-4
E-5

m=14, n=9
m-n=5
rermainder=5
IMO E[spoiler]

If my post helped you- let me know by pushing the thanks button

Contact me about long distance tutoring!
[email protected]

Cans!!

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