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Out of a certain group of 100 people, 65 have a Volkswagen [#permalink]

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13 Jun 2003, 00:42

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Out of a certain group of 100 people, 65 have a Volkswagen Corrado, 40 have a Bentley Azure, and 30 have a Lincoln Navigator. What is the greatest possible number of people in this group who do not have a Corrado, do not have an Azure, and do not have a Navigator?

I think the greatest possible value is 35.
My reasoning is that if 65 people have a volkswagen, there are 35 people that don┬┤t. Then I supose that the other cars are hold by the same owners as those of the Volkswagen, leaving 35 people without a car

yes it has been just under 3 weeks or so since I joined...I know, I've been around..

yes, one answer is fine...I'm looking for the greatest possible number

Skoper, it is time for me to go to a dump - I can't hold anything in my head except.... (you can fill in)..........ough. I now understand how it feels when you are 40 and they say "And now we will make your life easier and will force you to use computers"

P.S. We had some irregularities with the board lately - due to some experiments so I was wondering... I am still surprised.

V = 65 B = 40, L = 30
V = V + VB + VL + VBL
L = L + VL + BL + VBL
B = B + VB + BL + VBL

Total = V + B + L + None - (Sum of both) - 2All
None = Total - (V+B+L) + (Sum of Both ) + 2All
To maximize None we can set Sum of Both = 0 and Maximize All
Also we know that All cannot be greater than 30 because then B would be greater than 30 if we made All >30

My answer is 35 by Venn diagram in which this will form three circles, larger circle encircling the smaller totally. The circle with value 65 is the largest , so 100 -65 = 35 should be the max that will have none of the vehicles.

100 - 65 = 35. Same approach as Paul using a venn diagram, we can see that 40 people who own a VW also owns at least another car, and out of the 40, 30 people can own all three cars.

Out of a certain group of 100 people, 65 have a Volkswagen Corrado, 40 have a Bentley Azure, and 30 have a Lincoln Navigator. What is the greatest possible number of people in this group who do not have a Corrado, do not have an Azure, and do not have a Navigator?

This is a silly question. A much better question is what is the smallest possible number of people given the above information that do not own a car?
_________________

Best,

AkamaiBrah Former Senior Instructor, Manhattan GMAT and VeritasPrep Vice President, Midtown NYC Investment Bank, Structured Finance IT MFE, Haas School of Business, UC Berkeley, Class of 2005 MBA, Anderson School of Management, UCLA, Class of 1993