SAT Question of the Day #22

On a certain radio station, every 3rd song played is “classic rock,” and a prize is given away during the 4th song played.  If a song is selected at random from 120 consecutive songs that the radio station will play one night, what is the probability that the song will be “classic rock” and that a prize will be given away during that song?

A.  1/12
B.  1/10
C.  1/5
D.  1/4
E.  1/3

The answer is:    A.  1/12

How to get to this answer:   Every third song is “classic rock,” which means song numbers 3, 6, 9, 12, 15, 18… The prize is given away during every fourth song which means song numbers 4, 8, 12, 16, 20… Every twelfth song is a “classic rock” song during which a prize will be given away.  There are 120/12 = 10 “classic rock” prize songs in 120 songs, so the probability that a randomly selected song will be a “classic rock” prize song is: 10/120 = 1/12.