If an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?  Choose the correct option
A) 1 / 4 B) 3 / 8 C) 1 / 2 D) 29 / 46 E) 3 / 4

Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 46 + 12 ) / 92 = 58 / 96 = 29 / 46 ans is d"
Answer: D