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Joined: 25 May 2003
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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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This topic is locked. If you want to discuss this question please repost it in the respective forum. 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?



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Joined: 04 Dec 2002
Posts: 15143
Location: United States (WA)

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?



Manager
Joined: 25 May 2003
Posts: 54

bogdan, you're getting old!!!
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



Manager
Joined: 03 Jun 2003
Posts: 84
Location: Uruguay

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



Founder
Joined: 04 Dec 2002
Posts: 15143
Location: United States (WA)

skoper wrote: bogdan, you're getting old!!! 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.
==



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Joined: 30 Oct 2003
Posts: 1790
Location: NewJersey USA

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



Intern
Joined: 08 Jan 2004
Posts: 31
Location: Seattle

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.



SVP
Joined: 16 Oct 2003
Posts: 1801

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.



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Joined: 15 Dec 2003
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35
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Joined: 31 Dec 1969
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WE: Supply Chain Management (Energy and Utilities)

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.



Manager
Joined: 18 Sep 2004
Posts: 151
Location: Dallas, TX

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.



Intern
Joined: 29 Aug 2004
Posts: 12

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!
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Re: PS: Cars & Numbers!!! [#permalink]
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04 Nov 2004, 23:00
skoper wrote: 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?
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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




Re: PS: Cars & Numbers!!!
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04 Nov 2004, 23:00






