Question

When ‘m' is divided by 6 it leaves a remainder 2 and when ‘n' is divided by 6 it leaves a remainder 3. what will be remainder if ‘m-n' is divided by 6 ? (m>n)?

Answer 1

According to question

m/6 = x + 2
20 /6 = 3 + 2

Thus m = 20
Also

n/6 = y + 3
21/6 = 3 + 3
Thus
n = 21
therefore
m-n = 21 - 20
            = 1

Answer 2

The remainder of m – n divided by 6 is 5

Solution:

The question says that when m is divided by 6, it leaves remainder 2, which means  

m = 6p + 2, P being the quotient of the division

Similarly, for when n is divided by 6, it leaves remainder 3, which means

n = 6q + 3, P being the quotient of the division

Now dividing m – n by 6 we get remainder as X, now to find the value of X, we use  

m – n = ((6p + 2) – (6q + 3)) + X

m – n = 6p -6q – 1 +  X

Now we can say that 6p -6q – 1 + X, can be written as 6(p – q) – 1 + X,  

therefore dividing it by 6 we get  

$=\frac{(6(p-q) ) }{6}-\frac{(1+x) }{6}$

Now if (1 + X) was completely divided by 6 then the value of the division be 1.

Hence the value of X is  

$\frac{(1+\mathrm{X})}{6}=1$

X=5.  

Therefore, the remainder of m – n divided by 6 is 5.