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

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Manager
Joined: 25 May 2003
Posts: 54

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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?

Kudos [?]: 3 [0], given: 0

Founder
Joined: 04 Dec 2002
Posts: 15578

Kudos [?]: 28495 [0], given: 5112

Location: United States (WA)
GMAT 1: 750 Q49 V42

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13 Jun 2003, 00:51
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?

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Manager
Joined: 25 May 2003
Posts: 54

Kudos [?]: 3 [0], given: 0

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13 Jun 2003, 01:26
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

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Manager
Joined: 03 Jun 2003
Posts: 83

Kudos [?]: 1 [0], given: 0

Location: Uruguay

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13 Jun 2003, 11:54
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

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Founder
Joined: 04 Dec 2002
Posts: 15578

Kudos [?]: 28495 [0], given: 5112

Location: United States (WA)
GMAT 1: 750 Q49 V42

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16 Jun 2003, 22:48
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.

-=-=

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SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 112 [0], given: 0

Location: NewJersey USA

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26 Jan 2004, 20:51
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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Intern
Joined: 08 Jan 2004
Posts: 31

Kudos [?]: 3 [0], given: 0

Location: Seattle

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26 Jan 2004, 21:51
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.

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SVP
Joined: 16 Oct 2003
Posts: 1798

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26 Jan 2004, 22:47
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.

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GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4285

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30 Oct 2004, 20:38
35
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Best Regards,

Paul

Kudos [?]: 527 [0], given: 0

Joined: 31 Dec 1969

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Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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03 Nov 2004, 21:37
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.

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Manager
Joined: 18 Sep 2004
Posts: 150

Kudos [?]: 12 [0], given: 0

Location: Dallas, TX

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04 Nov 2004, 10:32
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.

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Intern
Joined: 29 Aug 2004
Posts: 12

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04 Nov 2004, 12:56
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?

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GMAT Instructor
Joined: 07 Jul 2003
Posts: 769

Kudos [?]: 235 [0], given: 0

Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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?
_________________

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

Kudos [?]: 235 [0], given: 0

Re: PS: Cars & Numbers!!!   [#permalink] 04 Nov 2004, 23:00
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Out of a certain group of 100 people, 65 have a Volkswagen

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