If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?  Choose one:  A) 3  B) 6  C) 11  D) 22  E) 222
Maybe there is a faster way to do it but I did it like this:   How many ways can you arrange abc?   abc   acb   bac   bca   cab   cba   which are equivalent to:   100a + 10b + c   100a + 10c + b   100b + 10a + c   100b + 10c + a   100c + 10a + b   100c + 10b + a   if you add them all together you get 222a + 222b + 222c   ANSW222R:222
<result>E</result>
If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?