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earth@work
- Master | Next Rank: 500 Posts
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What you have to remember is that the product of any three consecutive integers is divisible by three. This is the starting point:
n(n + 1)(n + 2) - divisible by 3
Now, another thing you should notice is that, if you have a similar series as the above, you can subtract various numbers from one or more of the terms, IF those numbers are divisible by 3, and the product will still be divisible by 3. Let me give you an example:
n(n + 1 - 3)(n + 2 - 6) = n(n - 2)(n - 4) will be divisible by 3.
n(n + 1 + 9)(n +2) = n(n + 10)(n + 2) will also be divisible by 3.
Now apply all this on your products and you get that:
a. n(n + 1)(n - 4) = n(n + 1)(n + 2 - 6) is divisible by 3.
You stop here, since this as a PS problem.
So the answer is indeed A
