If n is a positive integer and r is the remainder when 4+7n is divided by 3, what is the value of r?
1. n+1 is divisible by 3
My answer is A.
4 + 7n can be written as (6n + 6) + (n-2), if n+1 is divisible by 3, 6n+6 is also divisible by 3.
And, if n+1 is divisible by 3, then (n-2) is also divisible by 3. Hence 4+7n is divisible by 3, and the remainder is zero.
N can take different numbers greater than 20, and will not help.
Hence the answer is A.