If an integer n is to be selected at random from 1 to 99, inclusive, what is probability n(n+1) will be divisible by 3?
Choose the correct answer: A) 1 / 4 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 3 / 4

Rationale: "for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ."
Answer: D