# Quick questionWatch

#1
From the numbers 1 to 6000, how many numbers aren't divisible by 2,3 or 5?
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13 years ago
#2
Have you heard of the inclusion-exclusion principle?
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#3
No It is 125 numbers?
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13 years ago
#4
You got the right answer but you could do it more systematically

Written in full:-

From 1-6000:
2|3000 numbers (this notation isn't recommended)
3|2000 ''
5|1200 ''

But
2,3|1000 ''
2,5|600 ''
3,5|400 ''

and
2,3,5|200 ''

So the number which ARE divisible by 2,3 or 5 is:
6000-4400=1600
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13 years ago
#5
crap method when you have more, but:

6000 - (6000/2+ 6000/3 + 6000/5) + (6000/6 + 6000/10 + 6000/15) - (6000/30) = 1600

the way i was told to do this kind of question, which i shun as being pretty much the same, is to right out the numbers 1-abc... where abc... is the product of all the numbers you want, and let it have a number of columns equal to one of the numbers. now cross out all the numbers that are factors, then times the number you're going up to by the fraction of the numbers that weren't crossed out.
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#6
No It is 125 numbers?
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13 years ago
#7
1/2 x 2/3 x 4/5 x 6000 = 1600

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13 years ago
#8
(Original post by Vazzyb)
No It is 125 numbers?
no it's not. that's just silly. there are more primes than that (probably)...
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#9
No It is 125 numbers?

--------------

But then was asked a question if i was "using the right method" so i deleted it...

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(Original post by e-unit)
1/2 x 2/3 x 4/5 x 6000 = 1600

Ahh brilliant..
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13 years ago
#10
Wrangler's method only works nicely if all the numbers are coprime and also if the large number is divisible by each the small numbers (as in this case).
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