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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