In a car repair shop there are 50 cars to be repaired . It is estimated that 23 of that cars need new brakes , and 34 of that cars need to repair the exhaust system .

Question

a. How many cars are in need of repair at least two?
b . What most cars that are not in need of repair both?

Answer 1

By the pigeon hole principle (where each hole houses one car), it is impossible to have 23+34=57 repairs in 50 lifts (cars). So the surplus must go to cars that need both repairs.

This is the least number of cars that need both repairs. Assuming that all cars need at least one repair, then the rest of the cars need exactly one repair.