Math Is Fun Forum

Abbey78336

Member

Registered: 2022-08-15

Posts: 37

How many integers

How many positive integers less than 2002 are a multiple of 3 or 4 but not 5

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: How many integers

hi Abbey,

I would start by drawing three overlapping circles to show T = {set of numbers in the 3x table under 2002}, F = {set of numbers in the 4x table under 2002} and V = {set of numbers in the 5x table under 2002}

It should be fairly straight forward to work out how many in T. 2001/3 = 667

You can do a similar calculation for F.

But some numbers have been counted twice; 12, 24, 36 etc (numbers in the 12x table) have been counted once in T and again in F. So you need to subtract one copy of these double counted numbers.

Then you need to take off the multiples of five.

Numbers like 15, 30, 45 are in T and V so you need to work out how many of these there are and *subtract that figure*.  Similarly the numbers  20, 40 etc are in the overlap of F and V and #need to be subtracted#.

But hang on a minute.  There are numbers in all three sets 60 120, 180 etc.  You will have taken off these at * * and again at # # so once again some numbers have been accounted for twice.

The overlapping sets diagram is called a Venn diagram.
Have a look at this page https://www.mathsisfun.com/sets/venn-diagrams.html 
About half way down the page it shows an example of three overlapping sets.

For your problem, try to work out how many numbers there will be in each of the regions {only in the 3x table} {in both T and F but not V} etc etc.  Then you can calculate the answer to the problem without any double counting.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob