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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
In a village of 100 households, 75 have at least one DVD player, 80 ha
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09 Apr 2022, 02:57
09 Apr 2022, 02:57
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Expert Reply
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Question Stats:
28% (02:49) correct
71% (03:03) wrong based on 14 sessions
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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, x – y is:
A. 65
B. 55
C. 45
D. 35
E. 25
A. 65
B. 55
C. 45
D. 35
E. 25
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Re: In a village of 100 households, 75 have at least one DVD player, 80 ha
[#permalink]
14 Apr 2022, 02:24
14 Apr 2022, 02:24
1
Expert Reply
First of all maximum number of households: We want to bring the circles to overlap as much as possible.
80 - Cell phone
75 - DVD
55 - MP3
Let's take a Cell phone and DVD circles since they will have maximum overlap. They must overlap in 55 households so that the total number of households is 100. Now put the MP3 households in a way to maximize all three overlaps.
So at most 55 households can have all 3.
Now, the minimum number of households: We want to take the circles as far apart from each other as possible. Now put the MP3 households in a way to minimize all three overlaps. So make the MP3 households occupy the shaded region i.e. region occupied by DVD players alone and cell phones alone. You will be able to adjust 45 MP3s outside the common area but you will need to put 10 of the MP3 households in the common area. So minimum overlap is 10.
x - y = 55 - 10 = 45
Answer: C
80 - Cell phone
75 - DVD
55 - MP3
Let's take a Cell phone and DVD circles since they will have maximum overlap. They must overlap in 55 households so that the total number of households is 100. Now put the MP3 households in a way to maximize all three overlaps.
So at most 55 households can have all 3.
Now, the minimum number of households: We want to take the circles as far apart from each other as possible. Now put the MP3 households in a way to minimize all three overlaps. So make the MP3 households occupy the shaded region i.e. region occupied by DVD players alone and cell phones alone. You will be able to adjust 45 MP3s outside the common area but you will need to put 10 of the MP3 households in the common area. So minimum overlap is 10.
x - y = 55 - 10 = 45
Answer: C
Re: In a village of 100 households, 75 have at least one DVD player, 80 ha
[#permalink]
29 Apr 2022, 02:50
29 Apr 2022, 02:50
How did you find 20 & 25 for the minimum value? I'm unable to split 55 between DVD & Cell phone
GeminiHeat wrote:
First of all maximum number of households: We want to bring the circles to overlap as much as possible.
80 - Cell phone
75 - DVD
55 - MP3
Let's take a Cell phone and DVD circles since they will have maximum overlap. They must overlap in 55 households so that the total number of households is 100. Now put the MP3 households in a way to maximize all three overlaps.
So at most 55 households can have all 3.
Now, the minimum number of households: We want to take the circles as far apart from each other as possible. Now put the MP3 households in a way to minimize all three overlaps. So make the MP3 households occupy the shaded region i.e. region occupied by DVD players alone and cell phones alone. You will be able to adjust 45 MP3s outside the common area but you will need to put 10 of the MP3 households in the common area. So minimum overlap is 10.
x - y = 55 - 10 = 45
Answer: C
80 - Cell phone
75 - DVD
55 - MP3
Let's take a Cell phone and DVD circles since they will have maximum overlap. They must overlap in 55 households so that the total number of households is 100. Now put the MP3 households in a way to maximize all three overlaps.
So at most 55 households can have all 3.
Now, the minimum number of households: We want to take the circles as far apart from each other as possible. Now put the MP3 households in a way to minimize all three overlaps. So make the MP3 households occupy the shaded region i.e. region occupied by DVD players alone and cell phones alone. You will be able to adjust 45 MP3s outside the common area but you will need to put 10 of the MP3 households in the common area. So minimum overlap is 10.
x - y = 55 - 10 = 45
Answer: C
