Is n(n+1)(n+2) divisible by 24?

(1) n is even
(2) (n+1) is divisible by 3 but not by 6

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When n is even n(n+1)(n+2) is always divisible by 8 and 3. Hence it will be divisible by 8*3 = 24
For the explanation look at:
solving-complex-problems-using-number-line-197045.html#p1521230

Statement 1: n is even
Sufficient

Statement 2: n+1 is divisible by 3 but not by 6
-> n+1 is odd
-> n is even
Sufficient

Answer: Option (D)

be careful

n(n+1)(n+2)
is 3 consecutive numbers, one of them must be divided by 3.
n is even , then n=2k, n+2=2(K+1)
n(n+2)=2k*2(k+1)=4k(k+1),
k and k+1 is 2 consecutive interger, one of them must be divided by 2
so 4k(k+1) must be divided by 8
so, the total expresstion is divided by 24

we can pick specific numbers and find the answer,

condition 2
n+1 is divided by 3 but not 6. this mean n+1 is odd . this mean n and n+2 is two consecutive even number, product of which are multiple of 8 as I prove above.
sufficient.

the takeaway is that
the product of 2 consecutive even numbers is divided by 8. remember how to prove this
if there are 3 consecutive numbers, one of them must be divided by 3

those concept is tested many times on gmat because it is basic