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In a village of 100 households, 75 have at least one DVD

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In a village of 100 households, 75 have at least one DVD [#permalink]

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New post 14 Jul 2006, 13:00
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In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, then x^2-y^2 is a number from

(A) 1000 to 2500 (B) 2501 to 2800 (C) 2801 to 3000 (D) 3001 to 3100 (E) 3001-3150
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New post 14 Jul 2006, 13:18
C.

55^2 - 10^2 = 2925.

[100-55=45 households don't have a mp3-player. At least 80-45=35 have both a cell phone and a mp3-player. At least 75-(100-35)=10 have all these devices.]
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New post 14 Jul 2006, 13:38
A

Maximum could be 55.

Minimum is tricky: If we take zero then the total number of people will exceeed 100. So To make all three minimum possible we must take
DVD Only = 0
DVD + Cell = 75
Cell Only = 0
Cell+MP3 = 5
MP3 only = 20
DVD+MP3 = 0
All three = 30

So answer is 55^2 - 30^2 = 2925-900 = 2025
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Re: PS: High-tech village [#permalink]

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New post 14 Jul 2006, 13:54
kevincan wrote:
In a village of 100 households, 75 have at least one DVD player, 80 have at least one cell phone, and 55 have at least one MP3 player. If x and y are respectively the greatest and lowest possible number of households that have all three of these devices, then x^2-y^2 is a number from

(A) 1000 to 2500
(B) 2501 to 2800
(C) 2801 to 3000
(D) 3001 to 3100
(E) 3001-3150


d = 75
p = 80
m = 55
dpm = x, when dpm is max
dpm = y, when dpm is min

100 = 75 + 80+ 55 - (dp + pm + md) - 2(x)
to maximize dpm (x), minimize (dp + pm + md) to 0.
x = 55

to minimize dpm (y), maximize (dp + pm + md) to the possible extent so that we can get y = 0

x^2-y^2 = 3025 - 0 = 3025.
its D.
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New post 14 Jul 2006, 14:00
You know it's a good question when you get three different answers: One is the the OA and OE. Which is it? :)
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New post 14 Jul 2006, 14:16
kevincan wrote:
You know it's a good question when you get three different answers: One is the the OA and OE. Which is it? :)


your all questions are tough buddy. :wink:

its another tough question.
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New post 14 Jul 2006, 23:09
ps_dahiya wrote:
A

Maximum could be 55.

Minimum is tricky: If we take zero then the total number of people will exceeed 100. So To make all three minimum possible we must take
DVD Only = 0
DVD + Cell = 75
Cell Only = 0
Cell+MP3 = 5
MP3 only = 20
DVD+MP3 = 0
All three = 30

So answer is 55^2 - 30^2 = 2925-900 = 2025

My answer is still A except a small calculation mistake.

55^2 - 30^2 = 3025-900 = 2125
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New post 21 Jul 2006, 16:20
Good god, this is a tough one. What's the source ?
  [#permalink] 21 Jul 2006, 16:20
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