I came across this post in gmatclub.com.

Source:

[spoiler]https://gmatclub.com/forum/collection-of ... 74776.html[/spoiler]

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

The possible reminders can be 1,2,3,4,5 and 6. We have the pinpoint the exact remainder from this 6 numbers.

St 1: when n is divided by 21 ( 7 and 3) the remainder is an odd number.
But it cannot be 7, 3 or 9 . Hence the possibilities are : 1 and 5.
Hence there can be two remainders ,1 and 5, when divided by 7.
NOT SUFFICIENT

St 2: when n is divided by 28 the remainder is 3.
As 7 is a factor of 28, the remainder when divided by 7 will be 3
SUFFICIENT

As per the reasoning given in 2nd case,it says that since the remainder when divided by 28 is 3 and since 7 is a factor of 28, therefore the remainder will be 3 for 7 also.

My question here is that if we consider the case: 19 divided by 4
remainder is 3. So 19 when divided by 2 should also give a remainder of 3. Since 2 is a factor 4.
Can somebody explain this??