Venn diagram

Question

150 men live in a certain town.
85 are married
70 have a telephone
75 own a car
55 are married and have a telephone
35 have a telephone and a car
40 are married and have a car
30 are married, have a car, and have a telephone

Use a Venn Diagram to illustrate this information.
1) How many men only have a car?
2) How many men have a car and a telephone, but are not married?
3) How many men have are married or have a car, but do not have a telephone?

Answer 1

1) 30 men have only a car

2) 45 men are single yet own a car and a telephone 

3) 60 married men have only a car

 

Though not asked, 20 men are single without a car or a phone. Poor guys!

 

Draw three overlapping circles, like the Olympic rings, for your Venn diagram.

Label each circle "Married", "Car", "Phone"

 

My best piece of advice is to begin filling in the numbers with the data where ALL THREE

categories overlap. In this case, are married with phone and car. It is the last statement in

the problem, which is 30 of the men surveyed are married with phone and car. So 30 goes

into the region of the Venn diagram where all 3 circles overlap.

 

Now go backwards through the problem.

 

40 are married and have a car, so 10 goes into the region where the

circles for married and car overlap, since 30 of them already meet this criteria.  

 

35 have a phone and a car, so 5 goes into the region where the circles

for phone and car overlap, since 30 of them already meet this criteria.

 

55 are married with a phone, so 25 goes into the region where the circles

for phone and married overlap, since 30 of them already meet this criteria.

 

 

75 men own a car, and we have accounted for 45 of them already. They

are the numbers highlighted in bold above, that's 30+10+5.  So 30 men have a car only,

no phone and no spouse. Put 30 in the region for car that does not 

overlap either of the other two circles.

 

70 men have a phone, and we have accounted for 60 of them already.

They are the the numbers underlined above, that's 30 + 5+25. So 10 men have only a phone.

Put 10 in the region for phone that does not overlap either of the other two circles.

 

85 men are married, and we have accounted for 65 of them already.

They are the numbers in italic font above, that's 30+10+25. So 20 men are married

with no phone nor car. Put 20 in the region for married that does not overlap

either of the other two circles. 

 

Adding up these figures in the Venn diagram gives a total of 130, which means

20 unlucky men are single with neither a phone nor a car.

 

I have the diagram saved  as a jpeg if you want it.