enigma123 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 OA is B. I am trying to use the concept of consecutive numbers but got stuck. Can someone please help?

Question says x(x – 1)(x – k) must be evenly divisible by three which means x(x-1) (x-k) should be consecutive.

This problem is best done via testing cases.

If x = 0, then all values are equal to zero and thus divisible by 3 evenly.

If x = 1, then all values are divisible by 3.

If x = 2, then we have the following situation:

A. K = -4

2*1*6 = 12, divisible by 3.

B. K = -2

2*(1)*2 = 4,

not divisible by 3.

C. K = -1

2*1*3 = 6, divisible by 3.

D. K = 2

2*(1)*0 = 0, divisible by 3.

E. K = 5

2*(1)(-3) = -6, divisible by 3.