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# greatest and smallest possible

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Intern
Joined: 05 Feb 2009
Posts: 7
greatest and smallest possible  [#permalink]

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19 Feb 2009, 04:45
In the village of 100 households 75 have at least 1 DVD player, 80 have at least 1 cell phone, 55 have at least 1 mp3 player.
If X and Y are respectively the greatest and smallest possible number of households that have all 3 of the devices, X-Y=

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Senior Manager
Joined: 08 Jan 2009
Posts: 310
Re: greatest and smallest possible  [#permalink]

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19 Feb 2009, 05:32
This problem has worked on before.Please see the below link

7-t75656
Intern
Joined: 02 Jun 2008
Posts: 4
Re: greatest and smallest possible  [#permalink]

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19 Feb 2009, 10:22
1
its a typical set theory question for such question start with the following find the net value greater than 75 + 80 +55 = 210 so its 110 greater than 100
now divide 110/x (here x is no of elements-1) here x = 3-1 =2
so surplus is 55, this has to be the min value, and from the question max value can be ofcourse 100 so max-min =45 i hope this help
Director
Joined: 04 Jan 2008
Posts: 818
Re: greatest and smallest possible  [#permalink]

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19 Feb 2009, 10:34
thanks. thats good shortcut
sanjaysingh82 wrote:
its a typical set theory question for such question start with the following find the net value greater than 75 + 80 +55 = 210 so its 110 greater than 100
now divide 110/x (here x is no of elements-1) here x = 3-1 =2
so surplus is 55, this has to be the min value, and from the question max value can be ofcourse 100 so max-min =45 i hope this help

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Director
Joined: 29 Aug 2005
Posts: 808
Re: greatest and smallest possible  [#permalink]

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19 Feb 2009, 16:07
I found the explanation here useful: http://www.manhattangmat.com/forums/vie ... &view=next

what is the source of the question?
Senior Manager
Joined: 08 Jan 2009
Posts: 310
Re: greatest and smallest possible  [#permalink]

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19 Feb 2009, 22:23
1
We know the
maximum value of all the 3 intersections = 55 ( Contained in all three intersections).

DVD = 75 Cellphone = 80 MP3 = 55
Minimun value :

Minimum value of dvd and cell = ( 75+80) - 100 = 55
Min val of cell and MP3 = 80 + 55 - 100 = 35
Min val of dvd and MP3 = 75 + 55 - 100 = 30

thefore 100 = 75 + 80 + 55 - ( 55 + 35 + 30 ) + ( Minmum val of all three)

solve u get = 10

So Max - MIN = 55 - 10 = 45.
VP
Joined: 05 Jul 2008
Posts: 1328
Re: greatest and smallest possible  [#permalink]

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20 Feb 2009, 14:41
sanjaysingh82 wrote:
its a typical set theory question for such question start with the following find the net value greater than 75 + 80 +55 = 210 so its 110 greater than 100
now divide 110/x (here x is no of elements-1) here x = 3-1 =2
so surplus is 55, this has to be the min value, and from the question max value can be ofcourse 100 so max-min =45 i hope this help

What is this number of elements.? Why do you subtract one?

How are you getting max value of 100? The number of people who can have all three is 55 not 100.

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Re: greatest and smallest possible &nbs [#permalink] 20 Feb 2009, 14:41
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# greatest and smallest possible

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