The 5 -digit number $5228 \square$ is a multiple of 6 . Which digit is represented by $\square$ ?
(A) 0
(B) 3
(C) 4
(D) 6
(E) 8
Since $5228 \square$ is a multiple of 6 , then it must be a multiple of 2 and a multiple of 3 .

Since it is a multiple of 2 , the digit represented by $\square$ must be even.

Since it is a multiple of 3 , the sum of its digits is divisible by 3 .

The sum of its digits is $5+2+2+8+\square=17+\square$.

Since $\square$ is even, the possible sums of digits are 17, 19, 21, 23, 25 (for the possible values 0,2 , $4,6,8$ for $\square)$.

Of these possibilities, only 21 is divisible by 3 , so $\square$ must equal 4 .

We can check that 52284 is divisible by 6 .

(An alternate approach would have been to use a calculator and test each of the five possible values for $\square$ by dividing the resulting values of $5228 \square$ by 6 .)

ANSWER: (C)