Out of a certain group of 100 people, 65 have a Volkswagen

Question

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?

bb · Answer

2 questions:

why does your profile say you joined on May 25? You joined earlier didn't you? Am I out of my mind?

Do you need 1 answer or 3?

skoper · Answer

bogdan, you're getting old!!! :lol:

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

MBA04 · Answer

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

bb · Answer

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 :wink:

so I was wondering... I am still surprised. -=-=

anandnk · Answer

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


None = 100 - 135 + 60 = 25

Seattle_76 · Answer

I think it is 100 - 65 = 35.

In terms of a Venn diagram, we can represent this as 3 concentric circles of size (30, 40 and 65). 

THat makes the number of people who don't have any 35.

Bhai · Answer

I need some time calculating... But I would like to be in the Bentley Azure Group......For that I need 700. So guys I am off to calculation.

Paul · Answer

35

Anonymous · Answer

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.

nzgmat · Answer

I also got 35, 

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.

Atroson · Answer

Unless this question is more complicated than it appears, I thought 35 was a very easy answer to arrive at... and I suck at quants!

AkamaiBrah · Answer

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?

Out of a certain group of 100 people, 65 have a Volkswagen

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