Problem Solving

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

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

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).

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!

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]