Hello Sandeep,
Is (n-1) div 3 is the same as asking if n-1 is a multiple of 3.
Statement 1:
n^2 + n = n(n+1)
n(n+1) is not a multiple of 3.
Number properties of consecutive integers says that in every three consecutive integers, one of the numbers will be a multiple of three. Since both n and n+1 are not multiples of three, then both n+2 AND n-1 will be a multiple of three.
Example: n = 4.
n+1 = 5.
So n+2 = 6 and n-1 = 3 --- both are multiples of three.
Statement 1 is Sufficient.
Statement 2:
3n + 5 >= k + 8
3n >= k + 3
n >= k/3 + 1
So k/3 is an integer: 1, 2, 3, etc.
k/3 + 1 will also be an integer: 2, 3, 4, etc.
n >= 2, 3, 4, etc.
n can be either a multiple of three or not a multiple of three.
Example: k = 6.
k/3 = 2
k/3 + 1
= 2 + 1
= 3
n >= 3, so n can be 3, 4, 5, etc. , sometimes it is a multiple, sometimes it is not.
Statement 2 is Insufficient.
The answer is thus, A, Statement 1 ALONE is sufficient.
Hope this helps!
--Rishi
