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