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 5 ?
Pick:
A) 1/9
B) 1/3
C) 1/2
D) 2/3
E) 2/5
n(n+1) to be divisible by 3 either n or n+1 must be a multiples of 3.   In each following group of numbers: {1, 2, 3, 4, 5}, { 6, 7, 8, 9, 10}, ..., {96, 97, 98, 99,100} there is EXACTLY 1 numbers out of 5 satisfying the above condition. For example in {1, 2, 3, 4, 5} n can be: 4 or 5. Thus, the overall probability is 2/5.   Answer: D.
<result>E</result>
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 5 ?