If x is an integer, then x(x – 1)(x – k) must be evenly divisible by seven when k is any of the following values EXCEPT  Choose the correct option
A) -4 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 3 if at least one multiple is divisible by 7. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 7 these numbers must have different remainders upon division by 7, 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 7.   Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --&gt; which means that (x-1) and (x-2) will have the same remainder upon division by 7. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 7.   Answer: 5.
<result>E</result>
If x is an integer, then x(x – 1)(x – k) must be evenly divisible by seven when k is any of the following values EXCEPT