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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.

Respuesta :

Answer:

Step-by-step explanation:

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

i.e. [tex]n=21m+k[/tex] where m is an integer and k a positive integer <21

When n is divided by 28, the remainder is 3

[tex]n=28c+3[/tex], where c is a positive integer

This can be written as

[tex]n=4(7c)+3\\n=7(4c)+3[/tex]

Since n is giving odd remainder when divided by 21,

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