Dhaka Higher Secondary 2010/4

Problem for Higher Secondary Group from Divisional Mathematical Olympiad will be solved here.
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BdMO
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Dhaka Higher Secondary 2010/4

Unread post by BdMO » Tue Jan 18, 2011 2:04 pm

From $1$ to $1000$, how many integers are multiples of $3$ or $6$ but not of $5$?

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leonardo shawon
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Location: Dhaka

Re: Dhaka Higher Secondary 2010/4

Unread post by leonardo shawon » Tue Jan 18, 2011 6:54 pm

if u say 3 or 6 then the answer is 133.
as 6 is divided by 3, so the common multiple between 6 and 5 will be cancelled. They r 33 numbers who are divided by both 5 and 6. And there are 166 numbers who are divided by both 3 and 6. So the answer is 166-33=133
Ibtehaz Shawon
BRAC University.

long way to go .....

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leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

Re: Dhaka Higher Secondary 2010/4

Unread post by leonardo shawon » Tue Jan 18, 2011 6:57 pm

but if u say either 3 or 6 then the answer is 267.

There are 333 numbers who are multiple of either 6 or 3. And 66 numbers are common between them. So the rest is answer
Ibtehaz Shawon
BRAC University.

long way to go .....

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