(Car Sales) Of the cars sold during the month of July, 89 had air conditioning, 99 had automatic transmission, and 74 had power steering. 5 cars had all three of these extras. 24 cars had none of these extras. 24 cars had only air conditioning, 65 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had air conditioning and automatic transmission but not power steering?

Question

(Car Sales) Of the cars sold during the month of July, 89 had air conditioning, 99 had automatic transmission, and 74 had power steering. 5 cars had all three of these extras. 24 cars had none of these extras. 24 cars had only air conditioning, 65 cars had only automatic transmissions, and 26 cars had only power steering. 11 cars had both automatic transmission and power steering. How many cars had air conditioning and automatic transmission but not power steering?

a) 6
b) 23
c) 28
d) 5
e) 37

Answer 1

To find the number of cars that had air conditioning and automatic transmission but not power steering, we need to calculate the value of the overlapping regions in the Venn diagram.

Let's break down the information given in the problem:

- Total number of cars sold: Not given
- Cars with air conditioning (A): 89
- Cars with automatic transmission (T): 99
- Cars with power steering (P): 74
- Cars with all three extras (A, T, P): 5
- Cars with none of these extras: 24
- Cars with only air conditioning (A only): 24
- Cars with only automatic transmission (T only): 65
- Cars with only power steering (P only): 26
- Cars with both automatic transmission and power steering (T and P): 11

To find the number of cars that had air conditioning and automatic transmission but not power steering, we can subtract the overlapping regions from the total count of cars with air conditioning and automatic transmission.

First, let's determine the total count of cars with air conditioning and automatic transmission:

A ∩ T = (A only) + (A, T, P) + (T only) + (T and P)
= 24 + 5 + 65 + 11
= 105

To find the number of cars with air conditioning and automatic transmission but not power steering, we subtract the count of cars with all three extras (A, T, P):

Difference = (A ∩ T) - (A, T, P)
= 105 - 5
= 100

Therefore, the number of cars that had air conditioning and automatic transmission but not power steering is 100.

However, none of the answer choices provided matches this value. Please double-check the given options or verify the information provided in the problem statement.