If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?

Alternating digit sum from the right: 0 - 9 + 7 - y + 5 - x + 4 = 7 - (x + y), which must be divisible by 11, so x + y = 7 or 18. Either way the remainder on division by 11 is 7.