Here we consider all the cases when n is divided by 3, we have three options, either n is divisible by 3 or we end up with a remainder of 1 or 2. This is because any integer divided by 3, can only lead to three cases: a remainder of 0, 1, or 2. That is why n can have only three possible forms: n = 3q, n = 3q+1, or n+3q+2. If n is a multiple of 3, then all the answer choices are divisible by 3, because they are all multiples of n. Next, I go on to examine the two other cases where n takes the form of 3q+1 or 3q+2, and as I show in the video only the expression in Choice A is a multiple of 3 in both cases.

Abu Zafor says

Hello sir!

I don’t understand the Alternative formula. So, please explain that short technique with an example.

your obedient student

GMAT Quantum says

Hi Abu,

Here we consider all the cases when n is divided by 3, we have three options, either n is divisible by 3 or we end up with a remainder of 1 or 2. This is because any integer divided by 3, can only lead to three cases: a remainder of 0, 1, or 2. That is why n can have only three possible forms: n = 3q, n = 3q+1, or n+3q+2. If n is a multiple of 3, then all the answer choices are divisible by 3, because they are all multiples of n. Next, I go on to examine the two other cases where n takes the form of 3q+1 or 3q+2, and as I show in the video only the expression in Choice A is a multiple of 3 in both cases.

I hope this makes sense.

Dabral