Question

A number when divided successively by 4 and 5 leaves remainder 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be

Answer 1

Answer:

2 & 3

Step-by-step explanation:

When dividing a positive integer nn by another positive integer DD (divider), we obtain a quotient QQ, which is a non-negative integer and a remainder R, which is an integer such that 0≤R<D0≤R<D. We can write n=DQ+R.n=DQ+R.

When dividing our number nn by 4 we obtain a remainder of 1, so, if the quotient is some integer QQ, we can write n=4Q+1.n=4Q+1.

Now, dividing QQ by 5, we obtain another quotient say qq and remainder 4, thus we can write Q=5q+4.Q=5q+4.

It follows that n=4(5q+4)+1=20q+17.n=4(5q+4)+1=20q+17.

Since n=20q+17=5(4q+3)+2n=20q+17=5(4q+3)+2,

it means that when dividing nn by 5 first,

we get a quotient

4q+34q+3 and remainder 2.

Then dividing 4q+34q+3 by 4 we obviously obtain a remainder of 3.