Question

If r is the remainder when the positive integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.

Answer 1

Explanation:

Given that When n is divided by 21, the remainder is an odd number.

i.e.
`n=21m+k` where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

`n=28c+3`, where c is a positive integer

This can be written as

`n=4(7c)+3\\n=7(4c)+3`

Since n is giving odd remainder when divided by 21,

we get r =3 as n is a multiple of 7 +3