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.

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).

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.....
_________________

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/
_________________

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

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.

m>n
14>9

14-9 = 5/6

Remainder = 5

E
_________________