# Thread: Another Venn Diagram Problem :(

1. ## Another Venn Diagram Problem :(

I'm sorry but I have another problem!

In a city there are three major newspapers (A, B, C) of which at least two are read by 35% of the population. It is known that newspaper C is read by 45% of the population. A and B are read by 15% and all the three papers are read by 10%. What percent of the population read newspaper C only?

2. There are only 7 regions. Name them and label them.

A - A alone
B - B alone
C - C alone
AB - A&B but not C
AC - A&C but not B
BC - B&C but not A
ABC - All Three

at least two are read by 35% of the population
AB+AC+BC+ABC = 35

newspaper C is read by 45% of the population.
C + AC + BC + ABC = 45

all the three papers are read by 10%
ABC = 10

A and B are read by 15%
This is where I get lost. I do not know what this means.

It might be: AB = 15

If so, a little substitution and subtraction solve the problem.

AB = 15
ABC = 10
AC+BC = 10
C = 25

3. Firstly, thanks so much!

Originally Posted by TKHunny
This is where I get lost. I do not know what this means.

It might be: AB = 15

If so, a little substitution and subtraction solve the problem.

AB = 15
ABC = 10
AC+BC = 10
C = 25
Could it be that it means AB+ABC=15? That would make AB=5 and therefore C would be 15. Hmm...

4. ...or maybe all EXCEPT C?

I think you see my point. That hint is a little ambiguous. Absent clarification, on any exam or assignment, I would challenge it.

5. ## solution

Originally Posted by merenwen
I'm sorry but I have another problem!

In a city there are three major newspapers (A, B, C) of which at least two are read by 35% of the population. It is known that newspaper C is read by 45% of the population. A and B are read by 15% and all the three papers are read by 10%. What percent of the population read newspaper C only?
let the total population be 100
step: ABC is 10 ie;10 people read all the news paper
step2: therefore AB is 5 ie; 10+5 =15 people read two news paper
step3: given atleast 35% people read two news paper ie; AB+BC+CA+ABC=35
AB=5
ABC=10
BC=X
CA= X
therefore 2X=35-15
X=10
and paper read by C= 45-10-10-10
=15

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### venn diagram percentage questions on news papers

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