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?

Question: 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?

Solution:
total number = 100
n(n+1) will be divisible by 5 if n or n + 1 is divisible by 5

when n is divisible by 5, there are 20 such number (5, 10, 15, 20, 25,.....,100)
when n + 1 is divisible by 5, there are 20 such number (4, 9, 14,.....,99)

∴ proability = (20 + 20)/100
= 40/100
= 2/5