How many even numbers. Help

Oct 2012
4
0
Sweden
Hey guys.

I need a some help with the following problem. Not sure how to start.

You have 50 integers.
27 of these can be divided by 3
17 of them can be divided by 5
16 of them can be divided by 6
11 of them can be divided by 10
7 of them can be divided by 15
4 of them can be divided by 30.
3 of the numbers can't be divided by either 2,3 or 5.

How many of the original 50 integers are even numbers?


Thanks in advance

Yahikko
 
Jan 2008
484
109
UK
I would draw a Venn diagram. Draw circles for numbers divisible by 2, by 3 and by 5.

The various intersections contain numbers divisible

by 2 and by 3 [these are divisible by 6]

by 2 and by 5 [these are divisible by 10]

by 3 and by 5 [these are divisible by 15]

and the intersection of all three has numbers divisible by 2, by 3 and by 5 [these are divisible by 30].
 

Plato

MHF Helper
Aug 2006
22,507
8,664
You have 50 integers.
27 of these can be divided by 3
17 of them can be divided by 5
16 of them can be divided by 6
11 of them can be divided by 10
7 of them can be divided by 15
4 of them can be divided by 30.
3 of the numbers can't be divided by either 2,3 or 5.
How many of the original 50 integers are even numbers?
Do a Venn diagram. Let A be divisible by 3, B be divisible by 2, and C be divisible by 5.
I will get you started.
 

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Oct 2012
259
19
israel
use inclusion and exlusion formula.see the attached solution-verify the sises of the intersections there.
 

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Plato

MHF Helper
Aug 2006
22,507
8,664
use inclusion and exlusion formula.see the attached solution-verify the sises of the intersections there.
@hedi, If you want to continue to post useful answers, why don't you learn some basic LaTeX coding. Your images are messy in the extreme. Often they are posted in the wrong orientation making this hard to read. Moreover, they are handwritten which means that I for one tend to ignore them. I think you have good things to contribute but learn to post using LaTeX please.
 
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Reactions: 1 person
Oct 2012
259
19
israel
I would love to use LaTeX ,but it sounds like chineese to me.How can i learn it easily?
 
Dec 2011
2,314
916
St. Augustine, FL.
Do a search here and online for tutorials and tips on its usage, quote the posts of others who are using it (without submitting the quoted post of course) to see the code they use. Once you dive in and begin using it, you will find it's not that difficult, and your posts will be easy to read and look great!

I, and many others I'm sure, will for the most part ignore posts with hand-written attachments, and even all but the simplest expression typed without LaTeX. I'm not trying to come down on you, I'm just being honest. If I have to struggle to read something, most times I move along.
 
Oct 2012
4
0
Sweden
Do a Venn diagram. Let A be divisible by 3, B be divisible by 2, and C be divisible by 5.
I will get you started.

Thanks a lot for your help! I'm sorry but I really can't figure out how to insert the numbers in the Venn diagram. I'm really tired and just don't get it...
 

Plato

MHF Helper
Aug 2006
22,507
8,664
Thanks a lot for your help! I'm sorry but I really can't figure out how to insert the numbers in the Venn diagram. I'm really tired and just don't get it...
With respect to reply #3, do you understand how I found the numbers in \(\displaystyle A\), the multiples of three?
 
Oct 2012
259
19
israel
with respect to reply 3:
A^B are rhe numbers divisible by 2 and3 ,that is,by 6.the data says there are 16 such numbers.
A6B6C are the numbers divisible by 2,3 and 5,that is,divisible by 30.there are 4 such numbers ,as given in the data.
In like manner compute the other intersections.That is what i was trying to explain in answer 4 (which you didn't like)