M7MBA wrote: ↑

Sun Jan 24, 2021 12:21 am

All the cars in the lot of a particular dealership have either a manual transmission or an automatic transmission, and all have either two doors or four doors. In this lot, 60% of the cars have a manual transmission and 70% of the cars have four doors. If 90% of the cars in the lot have either a manual transmission or four doors or both, then what percentage of the automatic transmission cars have four doors?

a) 25%
b) 37.5%
c) 50%
d) 62.5%
e) 75%

Answer: E

Solution:

We can let the total number of cars be 100. So 60 cars have a manual transmission, 40 have an automatic transmission, 70 have four doors, and 30 have two doors. Since 90 cars have either a manual transmission or four doors, 60 + 70 - 90 = 40 cars have both a manual transmission and four doors. Therefore, of the 70 cars that have four doors, 70 - 40 = 30 of them must have an automatic transmission. Since 40 cars have an automatic transmission and 30 of them have four doors, the percentage of the automatic transmission cars that have four doors is 30/40 = 3/4 = 75%.

Answer: E