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    Have I got this right?

    1) Of the numbers 1, 2, 3,..., 6000, how many are not multiples of 2,3 or 5?

    There are 3000 multiples of 2 between 1 and 6000, discounting 3000 integers.
    There are 2000 multiples of three between 1 and 6000, but half of these are multiples of 2 and so have already been accounted for, so a further 1000 integers are discounted.
    There are 1200 multiples of five between 1 and 6000, but half of these are also multiples of two and so have already been accounted for, leaving 600 integers, of which 200 are also multiples of 3, so in total a further 400 are discounted.

    So the number of integers between 1 and 6000 which are not multiples of 2, 3 or 5 is 6000-3000-1000-400=1600
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    Yeah, that works. You can also do it by throwing away the multiples of 2, 3 and 5, then adding back the multiples of 6,10 and 15 (they were thrown away twice), then throwing away the multiples of 30 (they were thrown away 3 times, then added back 3 times so you still need to get rid of them).
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    Cheers, I was pretty confident it was right but its good to have someone to check.
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    Yes, well done! xx
 
 
 
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