If n is an integer greater than 7, which of the following must be divisible by 3?
Choose one.
A) n(n-5)(n-2)  B) n(n+5)(n+3)  C) n(n+2)(n-1)  D) n(n-4)(n-2)  E) n(n-7)(n+3)
Let us start with C -&gt; n(n+2)(n-1) = n(n+2)(n-3+2). Thus we can see that n+2 and (n-3+2) will leave the same remainder. But we need 3 terms with 3 different remainders.   Now let's look at D -&gt; n(n-4)(n-2) = n(n-3 -1)(n-2). This represents 3 terms with 3 different remainders, and one of them will be divisible by 3.   ANSWER:n(n-4)(n-2)
<result>D</result>
If n is an integer greater than 7, which of the following must be divisible by 3?