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?
I think E.
6 ways to rearrange a,c,b; thus, we have the sum of...
x = abc + acb + bac + bca + cab + cba
x = 100*(2a+2b+2c) + 10*(2a+2b+2c) + (2a+2b+2c)
x = (2a+2b+2c) * (100+10+1)
x = 2 * 111 * (a+b+c)
x = 222 * (a+b+c)
This means that x must be divisible by 222