Carcass wrote:
n is Even
Since n is divisible by 2 then either one of n or n+2 will be divisible by 4. Hence the product ?(?+1)(?+2)will be divisible by 8. Total choices 36.
n is Odd
Then n and n+2 will both be odd and the only way this expression is divisible by 8 is when n+1 is divisible by 8. There are 72/8 such choices : (7,15,23,..,71).
So, combining 1 and 2 we have 36 + 9 = 45 choices for n. Which results in a probability of 45/72=5/8
This is not a GRE. You are doing the wrong practice
(7,15,23,..,
71) This case has already been counted as n being even(70). So the total cases are 44
It's a GRE question. I have the same username on GMAT club, so won't post a GMAT question here.