Sally picks four consecutive positive integers. She divides each integer by four, and then adds the remainders together. The sum of the remainders is
(A) 6
(B) 1
(C) 2
(D) 3
(E) 4
Let us try the integers $5,6,7,8$.

When 5 is divided by 4 , the quotient is 1 and the remainder is 1 .

When 6 is divided by 4 , the quotient is 1 and the remainder is 2 .

When 7 is divided by 4 , the quotient is 1 and the remainder is 3 .

When 8 is divided by 4 , the quotient is 2 and the remainder is 0 .

The sum of these remainders is $1+2+3+0=6$.

(When any four consecutive integers are chosen, one will have a remainder 1, one a remainder of 2 , one a remainder of 3 and one a remainder of 0 when divided by 4.)