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# Boolean Algebra/How many numbers between 1 and 1000

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Manager
Joined: 12 Feb 2012
Posts: 136
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Kudos [?]: 46 [0], given: 28

Boolean Algebra/How many numbers between 1 and 1000 [#permalink]

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29 Jul 2013, 14:52
Hey Guys,

I have been having difficulty with converting problems into a logical boolean sentence in order to solve them. In the problem below I am not so much concerned with finding the answer but writing out the sentence in order to find the solution. Maybe if there is a guide/book/etc. that can help me out with this subject.

For example: How many numbers between 1 and 1000 are divisible by 2 and 3?

Let A=total amount of numbers divisible by 2 between 1 and 1000
B=total amount of numbers divisible by 3 between 1 and 1000
T=total amount of numbers between 1 and 1000

So AnB=A+B-AuB

1) How many numbers between 1 and 1000 are not divisible by 2 and 3?
~(AnB)=~Au~B (Demorgan's Law)=~A+~B-(~An~B)
could we also write ~(AnB)=T-(AnB)
OR is this question asking ~An~B which does not equal ~(AnB)
~An~B

2) How many numbers between 1 and 1000 are divisible by 2 but not divisible by 3?
An~B=A+B-(Au~B)

3) How many numbers between 1 and 1000 are divisible by either 2 or 3?
AuB=A+B-AnB

4) How many numbers between 1 and 1000 are divisible by neither 2 or 3?
~(AuB)=T-(AuB)
where AuB=A+B-AnB
Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 46 [0], given: 28

Re: Boolean Algebra/How many numbers between 1 and 1000 [#permalink]

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05 Aug 2013, 20:50

Posted from my mobile device
Manager
Joined: 12 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 46 [0], given: 28

Re: Boolean Algebra/How many numbers between 1 and 1000 [#permalink]

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20 Aug 2013, 19:28
I would really appreciate someones help please. This is extremely relevant to the gmat.
Intern
Joined: 07 Mar 2013
Posts: 14
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Re: Boolean Algebra/How many numbers between 1 and 1000 [#permalink]

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22 Aug 2013, 13:50
Hi, I am not sure what you mean. I guess there is a right tool for the right job kind of thing. Solving it logically is easier in this case. You will use "set" theory to include / remove overlap values or invalid values.

If I need numbers divisible by 2 & 3 = That means, Numbers divisible by 6

To find total number of integers divisible by 2 and 3 in 1000 = |1000 / 6| = 166

So not divisble by 2& 3 = 1000 - 166 = 834

Total Number of integers divisible by 2 or 3 => needs more explanation. Is it 2 or 3 but should not be divisible by 4,6, 8, 9 , 10? Or is it allowed? because it just depends on the question actually. Sorry.
Re: Boolean Algebra/How many numbers between 1 and 1000   [#permalink] 22 Aug 2013, 13:50
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