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29 Jul 2013, 14:52
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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
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
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05 Aug 2013, 20:50
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Can anyone please take a crack at the setence structure. I would really appreciate your advice.
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Posted from my mobile device
20 Aug 2013, 19:28
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I would really appreciate someones help please. This is extremely relevant to the gmat.
