If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT  Choose the correct option
A) -4
B) -2
C) 2
D) -1
E) 5
We have the product of 3 integers: (x-1)x(x-k).   Note that the product of 3 integers is divisible by 5 if at least one multiple is divisible by 5. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 5 these numbers must have different remainders upon division by 5, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 5.   Next, if k=2 then we'll have (x-1)x(x-k)=(x-1)x(x-2) --&gt; which means that (x-1) and (x-2) will have the same remainder upon division by 5. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 5.   Answer: 2.
<result>C</result>
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by five when k is any of the following values EXCEPT