Problem Solving

If 75 percent of all Americans own an automobile, 15 percent of all Americans own a bicycle, and 20 percent of all Americans own neither an automobile nor a bicycle, what percent of Americans own both an automobile and a bicycle?

(A) 0%
(B) 1.33%
(C) 3.75%
(D) 5%
(E) 10%

[spoiler]OA=E[/spoiler]

Source: Princeton Review

Given: 75 percent of all Americans own an automobile, 15 percent of all Americans own a bicycle, and 20 percent of all Americans own neither an automobile nor a bicycle

Seeking: We want to know what percent of Americans own both an automobile and a bicycle

Formula: 100% = % own Automobile + % own Bicycle + %own neither an automobile nor a bicycle - % own both Automobile and Bicycle

Solution: 100% = 75 + 15 + 20 - % own both Automobile and Bicycle
=> 100 = 110 - % own both Automobile and Bicycle
=> % own both Automobile and Bicycle = 10

Answer: E

Because we are dealing with percentages, we can say that there are 100 Americans. 100 is a great number to pick because it makes our math easy.

Let's break it down:
We are told that 75% of Americans have an automobile...so 75 people have an auto
That means that 25% don't have an automobile...so 25 people don't have an auto

We are also told that 15% of Americans own a bike...so 15 people own a bike
And we are told that 20% of Americans neither own a bike or an auto...so 20 people own neither

Because 25 people own a bike and 20 people own neither, that means 5 people own a bike but not an auto (25-20). And because we know that a total of 15 people own a bike, that means that 10 people must own a bike AND a car (15-5). Since we said that there were originally 100 Americans, 10/100 = 10%

Answer choice E