swerve wrote: ↑Tue Oct 13, 2020 8:17 am
Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?
A. 2
B. 3
C. 4
D. 8
E. 12
The OA is
C
Solution:
Since the problem asks for the maximum number of cars that could contain exactly 1 person, let’s analyze the answer choices in reverse order.
E. 12
If 12 cars contain 1 person each, then we have 68 - 12 = 56 people for the remaining 20 - 12 = 8 cars. This makes an average of 56/8 = 7 people per car, which is impossible since each car can contain at most 4 people.
D. 8
If 8 cars contain 1 person each, then we have 68 - 8 = 60 people for the remaining 20 - 8 = 12 cars. This makes an average of 60/12 = 5 people per car, which is also impossible.
C. 4
If 4 cars contain 1 person each, then we have remaining 68 - 4 = 64 people for remaining 20 - 4 = 16 cars. This makes an average of 64/16 = 4 people per car, which is possible.
So the maximum number of cars that could contain exactly 1 person each is 4.
Alternate Solution:
To maximize the number of cars with only one person, let’s suppose all the remaining cars contain 4 people. Let n denote the number of cars with only one person. Then, the remaining 20 - n cars contain 4(20 - n) people. We are given that the 4(20 - n) people together with the n people each of whom ride alone must add up to 68; therefore we have:
4(20 - n) + n = 68
80 - 4n + n = 68
12 = 3n
n = 4
So the maximum number of cars that could contain exactly 1 person each is 4.
Answer: C
