VJesus12 wrote: ↑

Sun Dec 27, 2020 7:40 am

In a locality, for every person, who owns only a car, there are 3 people who own only a bike. The number of people who own both a car and a bike is half the number of people who either own only a car or only a bike. If the number of people who neither own a car nor a bike is equal to the number of people who own a bike, which of the following can be the total number of people in the locality?

A. 27
B. 40
C. 66
D. 105
E. None of the above

Answer: C

Solution:

If we let x = the number of people who own only a car, then 3x = the number of people who own only a bike. Furthermore, if we let y = the number of people who own both, then y = ½(x + 3x). Simplifying this, we have 2y = x + 3x → y = 2x. Finally, the number of people who own neither is 3x + y = 3x + 2x = 5x.

Now, we can use the formula:

Total = Car Only + Bike Only + Both + Neither

Total = x + 3x + 2x + 5x

Total = 11x

We see that the total number of people is a multiple of 11; thus 66 is the correct answer.

Answer: C