BTGmoderatorLU wrote:Source: Manhattan GMAT

If n is a positive integer, is n - 1 divisible by 3?

(1) n^2 + n is not divisible by 6.
(2) 3n = k + 3, where k is a positive multiple of 3.

The OA is A.

Given: n is a positive integer.
Question: Is (n - 1) divisible by 3?

Let's take each statement one by one.

(1) (n^2 + n) is not divisible by 6.

=> n(n + 1) is not divisible by 6 (= 2*3).

We see that n and (n + 1) are two consecutive integers. Note that every second integer is even, thus, it is divisible by 2. Thus, Statement 2 can be rephrased as: n^2 + n is not divisible by 3. Also, note that one among the three consecutive integers is divisible by 3.

Thus, one among (n - 1)n(n + 1) is divisible by 3. Since we deduced that neither n nor (n + 1) is divisible by 3, this means that (n - 1) must be divisible by 3. Sufficient.

(2) 3n = k + 3, where k is a positive multiple of 3.

=> 3n - 3 = k
k = 3(n - 1)

(n - 1) may or may not be a multiple of 3. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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