Problem Solving

bryan88 wrote:If x is an integer, then x(x - 1)(x - k) must be evenly divisible by three when k is any of the following values EXCEPT

A)-4

B)-2


C)-1

D)2

E)5

The product of 3 integers is divisible by 3 if at least one multiple is divisible by 3. Now, to find if at least one integer out of x, (x - 1), and (x - k) is divisible by 3 these numbers must have different remainders on division by 3, which means that one of them should have remainder of 1, another one should have remainder of 2 and the last one should have remainder of 0.

If k = -2 then (x - 1)x(x + 2) = (x - 1)x(x - 1 + 3), which means that (x - 1) and (x + 2) will have the same remainder on division by 3. So, for k = -2 we are not sure if (x - 1)x(x - k) is divisible by 3.

The correct answer is B.