An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 4 ?  Select: A) 1 / 9 B) 1 / 3 C) 1 / 2 D) 2 / 3 E) 5 / 6

Rationale: "n ( n + 1 ) to be divisible by 4 either n or n + 1 must be a multiples of 4 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 3 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 3 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c ."
Answer: C