Integers Expression

[baily106]

Hello,

I am referring to question #1 on page 178 in Book 4 (Number Properties). The question asks, "If A is a positive integer, then which of the following must be true of (a-1)(a)(a+1). The options are a) it is always positive, b) it is always odd, c) it is always divisible by 3, d) it is always divisible by 4, and e) it is non-prime. The correct choices are C & E. My question is this: choice C indicates that it is always divisible by 3. If one replaces a with a "1" then 1-1 is zero, and the entire expression becomes 0. So is it correct because 0 is divisible 3 (and any other number) because it simply yields a 0 or is there some other reason?

Thanks.

[tommywallach]

Hey Baily,

Yes indeed. 0 is divisible by 3 because the result is an integer:

0/3 = 0

-t

P.S. As far as we know, GRE questions tend not to test this issue, so don't worry about it too much moving forward.

[baily106]

Got it; thank you!

[tommywallach]

It's what I do!

-t