Year 9 problem solving quiz - urgent help needed

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

QUESTIONS!

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

answers and hints both appreciated!!!

Re: Year 9 problem solving quiz - urgent help needed

hi guys, ive got all answers now but number d. can anyone get it?

Re: Year 9 problem solving quiz - urgent help needed

Quote:

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

QUESTIONS!

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

answers and hints both appreciated!!!

Hahah very simple but I cannot get LOL.

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Re: Year 9 problem solving quiz - urgent help needed

a. No car is checked by all 4 inspectors because the smaller integer divisible by 5,7,17 and 23 is 13685 > 2500. basically for this problem, "car number checked by inspector who checks every 5th car" should be thought of as "number divisible by 5" and so on.

b. 5*7*17=595, 5*7*23=805, 5*17*23=1955 . The fourth possibility 7*17*23 = 2737 > 2500 so that doesn't count.

c. These are all the numbers divisible by at least 2 of the numbers. When you eyeball them you will notice that 2345 and 2346 are the consecutive numbers you were looking for.