An advertising firm found that a certain ad that ran on both radio and TV was only heard on the radio by 23 percent of the people and was only seen on TV by 32 percent of the people. Just 14 percent of the population both heard the ad on the radio and saw it on TV. What percent of the people in the area only heard the ad on radio or only saw the ad on TV?
A) 73 percent
B) 9 percent
C) 27 percent
D) 18 percent
E) 86 percent

Question

Quizplus · Accepted Answer

We can use a Venn diagram to represent the information given:

[asy]
label("Radio", (0,70));
label("TV", (110,70));
draw(Circle((35,35), 25));
draw(Circle((75,35), 25));
label(scale(0.8)*"$23$", (17,54));
label(scale(0.8)*"$14$", (55,20));
label(scale(0.8)*"$32$", (93,54));
label(scale(0.8)*"$x$", (60,45));
label(scale(0.8)*"$y$", (50,25));
[/asy]

Let x be the percent of people who only heard the ad on the radio, and y be the percent of people who only saw the ad on TV. We know that:

- 23% heard the ad on the radio (which includes the 14% who also saw it on TV), so x + 14 = 23, or x = 9.
- 32% saw the ad on TV (which includes the 14% who also heard it on the radio), so y + 14 = 32, or y = 18.

Therefore, the percent of people who only heard the ad on radio or only saw the ad on TV is x + y = 9 + 18 = 27%. Thus, the answer is (C) 27%.

An Advertising Firm Found That a Certain Ad That Ran