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A survey agency reported their results in the local newspaper.

The report ststes that exactly one hundred local lawyers were interviewed.

Of the 100, seventy five own BMWs,

Ninety five own volvos and

fifty own both.

Within a short time after the report, sevral lawyers argue that the results are incorrect.

How can they tell?

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Posted · Report post

Let B =BMW and V=Volvo

Num(B)=75 and Num(V)=50 .... and Num(B U V)=100

Num(B)+Num(V)=Num(B U V)+Num(B & V) ... & used for intersection.

Num(B&V)=70.

But the newspaper reports 50. So, it must be incorrect.

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Posted · Report post

75/100 = BMW

95/100 = VOLVO

50/100 = BMW and VOLVO

the five that don't own a Volvo must own a BMW only. So there is 75-5=70 people that own a BMW that might also have a Volvo

the 25 that dont have a BMW must own a Volvo only. So there is 95-25=70 people that own a Volvo that might also own a BMW

So I would say that it would be 70, not 50... though maybe there is 20 of each type of car that just has that kind of car. So I don't really know if the 70 matters... it would for sure be wrong if the number was less than 50, but since it's 70, maybe 20 on both sides just own one car. But maybe I'm wrong.

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Posted (edited) · Report post

thats right brhan but i thought of it like this

25 own only BMWs 45 own only Volvos and 50 own both

45+25+50=120 responses

100 does not equal 120

Edited by TwoaDay
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Posted · Report post

if you draw a venn diagram(the two overlapping circles) it might make this problem a little easyer

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Posted · Report post

post-4396-1203249959_thumbjpg
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Posted · Report post

yep thats what i meant

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Posted · Report post

seventy five own BMWs,

Ninety five own volvos and

fifty own both.

25 don't own BMWs.

5 don't own Volvos.

So at most 30 don't own both.

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