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Please help me with this question that I have been stuck on. It is an APMOPS question.

2 Answers 2

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They are all multiples of $40$ from $10000$ to $100000$(remove $100000$).

$2500-250=2250$.

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    not sure you need to subtract 1 – 2017-02-26
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    You should not substract 1 as it will also 10000 – 2017-02-26
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First 5 digit number divisible by 5 is 10000. And last 5 digit number divisible by 5 is 99995. So you can find the total 5 digit numbers divisible by 5 which are 18000.

Similarly for 8 first is 10000 and last is 99992. So total are 11250.

Now numbers divisible by both 5 and 8 i.e by 40 are counted twice so 5. Digit numbers by 40 are (doing in similar way) are 2250.

So total 5 digit numbers divisible by 5 and 8 are

$18000+11250-2250=27000$

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    The answer i of numbers divisible by either 5 or 8 or by both. You haven't mentioned it in your question . – 2017-02-26