# Venn Diagram Problem

• Aug 3rd 2011, 07:16 AM
FailInMaths
Venn Diagram Problem
Hi guys, please give me some clues into solving this question from a workbook.

Question: There are 50 units in an apartment block. 40 units subscribe to the Straits Times, 20 units subscribe to the Business Times, m units subscribe to both Straits Times and Business Times, and n units subscribe to neither Straits Times nor Business Times.
By drawing Venn diagrams, find
a) the smallest possible value of n,
b) the largest possible value of n,
c) the largest possible value of m,
d) the smallest possible value of m.

Thanks a lot! (Happy)
• Aug 3rd 2011, 07:35 AM
e^(i*pi)
Re: Venn Diagram Problem
A picture really does speak a thousand words when it comes to Venn diagrams. What have you tried?

Surely the smallest possible value of n is 0? In other words everyone subscribes to one or the other.
• Aug 3rd 2011, 07:39 AM
FailInMaths
Re: Venn Diagram Problem
Quote:

Originally Posted by e^(i*pi)
A picture really does speak a thousand words when it comes to Venn diagrams. What have you tried?

Surely the smallest possible value of n is 0? In other words everyone subscribes to one or the other.

Well, I would had been able to solve if there were only one unknown, but now there are two unknowns and i am totally clueless =(
• Aug 3rd 2011, 07:49 AM
Plato
Re: Venn Diagram Problem
Quote:

Originally Posted by FailInMaths
Well, I would had been able to solve if there were only one unknown, but now there are two unknowns and i am totally clueless =(

Surely you can see that $60-m+n=50$.
If both $m\text{ and }n$ are non-negative integers, what can be said about their possible values?
• Aug 3rd 2011, 07:53 AM
FailInMaths
Re: Venn Diagram Problem
Quote:

Originally Posted by Plato
Surely you can see that $60-m+n=50$.
If both $m\text{ and }n$ are non-negative integers, what can be said about their possible values?

I don't get it.....
• Aug 3rd 2011, 08:17 AM
e^(i*pi)
Re: Venn Diagram Problem
Quote:

Originally Posted by FailInMaths
I don't get it.....

You know that $-m+n = -10$. As you only have one equation and two unknowns you won't be able to get just one pair of values - but the question isn't asking you that. It's asking you questions about certain values.

For example, is it possible for all 50 units to subscribe to one, the other or both?