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# Set W= how many integers are there such that they are

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SVP
Joined: 03 Feb 2003
Posts: 1608
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Set W= how many integers are there such that they are [#permalink]  17 Aug 2003, 09:39
Set W=[100, 101, 102, .... ,1000]
how many integers are there such that they are divisible by 3, but not by 5?
Manager
Joined: 14 Aug 2003
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Location: barcelona
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there are 999/3=333 numbers div by 3 between 1 and 1000... there are 99/3=33 numbers div by 3 between 1 and 100... thus there are 300 numbers div by 3 between 100 and 1000... now we have to substract the numbers div by both 3 and 5, ie, div by 15... there are 990/15-90/15=60 such numbers... so answer is 300-60=240?
Manager
Joined: 28 Feb 2003
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Location: Kiev
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We have a set of 900 integers (1000-100). Therefore, we meet an integer that is divisible by 3, 900/3=300 times.

Then, if we look at an array of the integers divisible by 3 {102, [b]105[/b], 108, 111, 114, 117, [b]120[/b], 123, 126, 129, 132, [b]135[/b]} we can see that each fifth integer is divisible by 5.

Hence, the number of integers divisible by 5 is 300/5=60

Therefore, the number of integers divisible by 3, but not by 5 is 300-60=[b]240[/b]

stolyar, what do you think?
Manager
Joined: 10 Jun 2003
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Location: Maryland
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bono wrote:
We have a set of 900 integers (1000-100). Therefore, we meet an integer that is divisible by 3, 900/3=300 times.

Then, if we look at an array of the integers divisible by 3 {102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135} we can see that each fifth integer is divisible by 5.

Hence, the number of integers divisible by 5 is 300/5=60

Therefore, the number of integers divisible by 3, but not by 5 is 300-60=240

stolyar, what do you think?

I like the answer and explanation - I would like to change mine to match yours!
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