Answer to Question #8762 in Combinatorics | Number Theory for Clad

Question

At a factory where they made toy cars, they have 4 quality inspectors inspecting the cars as they come off the assembly line.
A batch of toy cars is numbered in ORDER from 1 to 2500 and is sent for inspection with each inspector inspecting 1 part.
- every 5th car gets its screen inspected
- every 7th car gets its handle checked
- every 17th car get its wheels tested
- every 23rd car gets its control panel wiring examined

a. explain why NO car is checked by all 4 inspectors.
b. make a list of the numbers of all the cars which are checked by 3 inspectors
d. find a pair of consecutively-numbered cars which are checked by 2 inspectors