Bunuel wrote:

If a is positive integer less than or equal to 100, what is the probability that a(a – 1) is a multiple of 5?

A. 1/5

B. 39/100

C. 2/5

D. 1/2

E. 29/50

Positive integers are > 0: {1,2,3,57,99...}

From 1 to 100 there are: \(Number.Terms=Last.term-First.term+1=100-1+1=100\) total outcomes.

If x is a multiple of 5 then x(x+1) = multiple of 5.

If x+1 is a multiple of 5 then x(x+1) = multiple of 5.

From 1 to 100 there are: \(Number.Multiples=\frac{Largest.multiple-Smallest.multiple}{Multiple}+1=\frac{100-5}{5}+1=20\) multiples of 5 that fit x, and \(20\) multiples of 5 that fit \(x-1\).

Probability: \(\frac{Favorable.Outcomes}{Total.Outcomes}=\frac{(20+20)}{100}=2/5\).

(C) is the answer.