Out of a certain group of 100 people, 65 have a Volkswagen : PS Archive
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# Out of a certain group of 100 people, 65 have a Volkswagen

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

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12 Jun 2003, 23:42
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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?

Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14436
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
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Kudos [?]: 22988 [0], given: 4514

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12 Jun 2003, 23:51
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
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13 Jun 2003, 00:26
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
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13 Jun 2003, 10:54
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
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 14436
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
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Kudos [?]: 22988 [0], given: 4514

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16 Jun 2003, 21:48
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.

-=-=
SVP
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26 Jan 2004, 19:51
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
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26 Jan 2004, 20:51
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
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26 Jan 2004, 21:47
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.
GMAT Club Legend
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30 Oct 2004, 19:38
35
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Best Regards,

Paul

Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Technology, Entrepreneurship
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GMAT 6: 680 Q47 V36
GMAT 7: Q42 V44
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03 Nov 2004, 20:37
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
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04 Nov 2004, 09:32
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
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04 Nov 2004, 11:56
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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So a double digit score is a bad thing?

GMAT Instructor
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Re: PS: Cars & Numbers!!! [#permalink]

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04 Nov 2004, 22:00
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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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

Re: PS: Cars & Numbers!!!   [#permalink] 04 Nov 2004, 22:00
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