ps question 34

[magical cook]

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
-4
-2
-1
2
5

Hi, I know -1 and 2 will work cause that will make consective integers but dont know why -4 and 5 work....can anyone help?

[kajcha]

IMO, best way to solve such problems is to assume an integer such that x and (x-1) both are not divisible by 3 directly.

I took 11. So, (x-1) is 10. Now we have to evaluate (x-k)

11-(-4) = 15. Works
11-(-2) = 13. Does not work
11-(-1) = 12 Works
11-2 = 9 Works
11-5 = 6 Works

Ans (2)