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

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VP
Joined: 22 Nov 2007
Posts: 1105
Followers: 7

Kudos [?]: 193 [0], given: 0

In a village of 100 households, 75 have at least one DVD [#permalink]  24 Dec 2007, 09:03
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, x - y=

A.30
B.35
C.45
D.50
E.55
Manager
Joined: 21 May 2007
Posts: 120
Followers: 1

Kudos [?]: 11 [0], given: 0

Re: sets [#permalink]  24 Dec 2007, 09:34
marcodonzelli 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, x - y=

A.30
B.35
C.45
D.50
E.55

E
Whats the OA? will give the explanation if E is indeed the answer (my procedure requires a diagram and is time consuming to draw in computer. if it is incorrect, it will be a wasted effort)
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 407

Kudos [?]: 2149 [1] , given: 359

1
KUDOS
Expert's post
C

(75 ∩ 55) ∩ 80 = {30..55} ∩ 80 = {10..55}
x-y=55-10=45
Manager
Joined: 21 May 2007
Posts: 120
Followers: 1

Kudos [?]: 11 [0], given: 0

walker wrote:
C

(75 ∩ 55) ∩ 80 = {30..55} ∩ 80 = {10..55}
x-y=55-10=45

I got y as 0 and realized that is not possible.
Manager
Joined: 01 Sep 2007
Posts: 103
Location: Astana
Followers: 1

Kudos [?]: 20 [0], given: 0

I'm getting D over and over
y = 5 in my calculations.
Manager
Joined: 21 May 2007
Posts: 120
Followers: 1

Kudos [?]: 11 [0], given: 0

CaspAreaGuy wrote:
I'm getting D over and over
y = 5 in my calculations.

i wish that, like a cat, i too have 9 lives in GMAT!!

i now get y=5

whats the OA ?
Manager
Joined: 01 Sep 2007
Posts: 103
Location: Astana
Followers: 1

Kudos [?]: 20 [0], given: 0

Sorry man. I guess it is C.
y should be equal to 10.
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