In a village of 100 households, 75 have at least one DVD : PS Archive
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 04:57

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1264
Followers: 29

Kudos [?]: 298 [0], given: 0

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

### Show Tags

14 Jul 2006, 13:00
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
Manager
Joined: 04 Jul 2006
Posts: 57
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

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.]
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 24

Kudos [?]: 273 [0], given: 0

### Show Tags

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
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 25 Nov 2004
Posts: 1493
Followers: 7

Kudos [?]: 98 [0], given: 0

### Show Tags

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.
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1264
Followers: 29

Kudos [?]: 298 [0], given: 0

### Show Tags

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?
VP
Joined: 25 Nov 2004
Posts: 1493
Followers: 7

Kudos [?]: 98 [0], given: 0

### Show Tags

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.

its another tough question.
CEO
Joined: 20 Nov 2005
Posts: 2911
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 24

Kudos [?]: 273 [0], given: 0

### Show Tags

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
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Manager
Joined: 05 Jun 2006
Posts: 113
Location: London
Followers: 1

Kudos [?]: 2 [0], given: 0

### Show Tags

21 Jul 2006, 16:20
Good god, this is a tough one. What's the source ?
21 Jul 2006, 16:20
Display posts from previous: Sort by