Bunuel wrote:

At a car dealership, 62% of vehicles on the lot are electric and 48% are autonomous. If at least 15% of the 400 vehicles on the lot are neither electric nor autonomous, the number of electric, autonomous vehicles can be anything from:

A. 62 to 110

B. 100 to 192

C. 110 to 192

D. 100 to 248

E. 110 to 248

We are given that, of 400 cars at a dealership, 62% of the vehicles on the lot are electric, and 48% are autonomous. Thus:

Number of electric cars = 400 x 0.62 = 248. Thus, the number of cars that ARE NOT electric is 400 - 248 = 152.

Number of autonomous cars = 400 x 0.48 = 192. Thus, the number of cars that ARE NOT autonomous is 208.

We are also given that at least 15% or 0.15 x 400 = 60 of the vehicles on the lot are neither electric nor autonomous. Thus, the minimum number of cars that are neither electric nor autonomous is 60.

Since there are

152 cars that are not electric and

208 cars that are not autonomous, the maximum number of cars that could be neither electric nor autonomous is

152.

Finally we can determine the range of “both” using the following formula:

Total cars = total electric + total autonomous - both + neither

When neither is 60, we have:

400 = 248 + 192 - both + 60

400 = -both + 500

both = 100

When neither is 192, we have:

400 = 248 + 192 - both + 152

400 = -both + 592

both = 192

Thus, the range is from 100 to 192.

Answer: B

, Why the maximum number of cars that could be neither electric nor autonomous is 152 instead of 208?