Three consecutive integers are selected from the integers \(1\) to \(50,\) inclusive. What is the sum of the remainders

[Gmat_mission]

Three consecutive integers are selected from the integers \(1\) to \(50,\) inclusive. What is the sum of the remainders that result when each of the three integers is divided by \(x?\)

(1) When the greatest of the consecutive integers is divided by \(x,\) the remainder is \(0.\)

(2) When the least of the consecutive integers is divided by \(x,\) the remainder is \(1.\)

Answer: C

Source: Manhattan GMAT