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.

_________________________________

I love numbers

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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.

$\displaystyle \{35,70,85,105,115,119,140,161,170,175,210,230,238 ,245,255,280,315,322,340,345,350,357,385,391,420,4 25,455,460,476,483,490,510,525,560,575,595,595,595 ,630,\\644,665,680,690,700,714,735,765,770,782,805 ,805,805,833,840,850,875,910,920,935,945,952,966,9 80,1015,1020,1035,1050,1071,1085,1105,1120,1127,11 50,1155,1173\\,1190,1190,1190,1225,1260,1265,1275, 1288,1295,1309,1330,1360,1365,1380,1400,1428,1435, 1445,1449,1470,1495,1505,1530,1540,1547,1564,1575, 1610,1610,1610,1615\\,1645,1666,1680,1700,1715,172 5,1750,1771,1785,1785,1785,1820,1840,1855,1870,189 0,1904,1925,1932,1955,1955,1955,1960,1995,2023,203 0,2040,2065,2070,2093,2100\\,2125,2135,2142,2170,2 185,2205,2210,2240,2254,2261,2275,2295,2300,2310,2 345,2346,2380,2380,2380,2415,2415,2415,2450,2465,2 485,2499\}$