ACT Question of the Week #1: Math

Solve the problem and choose the correct answer.

In one year, a certain radio station plays 800 hours of commercials. If each commercial is 30 seconds long, how many commercials does the radio station play in one year? (1 hour = 3,600 seconds)

A) 26
B) 135
C) 24,000
D) 28,800
E) 96,000

Explanation

Since 1 hour equals 3,600 seconds, 800 hours equal (800)(3,600) seconds. Therefore, the number of 30-second commercials that the radio station plays is $\tfrac{800(3{,}600)}{30}=800(120)=96{,}000$.

The correct answer is Choice (E).

We can use reasoning to eliminate answer Choices (A) and (B) as too small. Since a single hour is much longer than 30 seconds, the number of 30-second commercials played in 800 hours must be significantly larger than 800.