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.

Step-by-step explanation:

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

i.e. where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

, where c is a positive integer

This can be written as

Since n is giving odd remainder when divided by 21,

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

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2