Problem Solving

We can approach this problem using a double matrix (diagrams linked below):

The question gives us the following: https://cl.ly/0o243n000d1B
Then, we can gradually fill in information:
https://cl.ly/3m0A210E2X22
https://cl.ly/3t3c2G2v0U2h
https://cl.ly/033e2R0P0v0U

Now we know that the electric, autonomous cars can make up from 25-48% of the total. There are 400 cars in total, which means there can be anywhere from 100-192 electric, autonomous cars, which is answer choice B.

Note: while we could have converted all of our percents into number of cars out of 400 from the beginning, keeping everything in percents meant that we only needed to do one conversion at the very end, saving us some time.

AAPL 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 152, we have:

400 = 248 + 192 - both + 152

400 = -both + 592

both = 192

Thus, the range is from 100 to 192.

Answer: B