GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 22 Jun 2018, 00:19

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a certain city, 80 percent of the households have cable

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

13 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 293
In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post Updated on: 30 Sep 2013, 08:19
13
33
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:07) correct 34% (01:11) wrong based on 879 sessions

HideShow timer Statistics

In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive

Originally posted by imhimanshu on 30 Sep 2013, 08:11.
Last edited by Bunuel on 30 Sep 2013, 08:19, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
19 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46271
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 30 Sep 2013, 08:38
19
13
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


120 have TV and 90 have radio. Obviously the number of households that have both cannot be greater than 90. Eliminate B, D, and E.

Next:
{Total} = {TV} + {Radio} - {Both} + {Neither}

150 = 120 + 90 - {Both} + {Neither}

{Both} = 60 + {Neither}

Thus {Both}>=60.

Answer: C.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 07 Jan 2014
Posts: 4
Location: India
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 10 Mar 2015, 04:54
Bunuel wrote:
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


120 have TV and 90 have radio. Obviously the number of households that have both cannot be greater than 90. Eliminate B, D, and E.

Next:
{Total} = {TV} + {Radio} - {Both} + {Neither}

150 = 120 + 90 - {Both} + {Neither}

{Both} = 60 + {Neither}

Thus {Both}>=60.

Answer: C.


Hi Bunuel,

There are 2 options greater than 60- C & D.
Can u pls explain how you narrowed down on C..?
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46271
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 10 Mar 2015, 04:57
1
TuringMachine wrote:
Bunuel wrote:
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


120 have TV and 90 have radio. Obviously the number of households that have both cannot be greater than 90. Eliminate B, D, and E.

Next:
{Total} = {TV} + {Radio} - {Both} + {Neither}

150 = 120 + 90 - {Both} + {Neither}

{Both} = 60 + {Neither}

Thus {Both}>=60.

Answer: C.


Hi Bunuel,

There are 2 options greater than 60- C & D.
Can u pls explain how you narrowed down on C..?


Have you read the red part in my solution?
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
9 KUDOS received
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1545
In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post Updated on: 07 Dec 2016, 04:06
9
2
Here's how you can solve this question using the Double Matrix Structure:

Image

We need to find the minimum and maximum possible values of X.

From the matrix, it is clear that X cannot be greater than 90,000 (because x + y = 90,000. So, if x > 90,000 then y will have to take a negative value, and that is not allowed since y denotes the number of things. So it cannot be negative)

Let's now try to find the lowest possible value of x.

You can use either Equation 1: Using x + y = 90,000

=> x = 90,000 - y

So, x will be minimum when y is maximum

The maximum possible value of y = 30,000

So, minimum possible value of x from this equation = 90,000 - 30,000 = 60,000

Or you can use Equation 2: Using x + z = 120,000

The maximum possible value of z = 60,000

So, minimum possible value of x from this equation is also 60,000


anewbeginning, TuringMachine: Hope this helped! Please let me know if something is not clear :)

Japinder

Image
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com


Originally posted by EgmatQuantExpert on 12 May 2015, 01:13.
Last edited by EgmatQuantExpert on 07 Dec 2016, 04:06, edited 1 time in total.
1 KUDOS received
VP
VP
avatar
S
Joined: 09 Jun 2010
Posts: 1188
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 12 May 2015, 02:14
1
I missed this question though it tests the same basic. practice is important.
_________________

visit my facebook to help me.
on facebook, my name is: thang thang thang

8 KUDOS received
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3511
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 22 May 2016, 02:55
8
1
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


The highlighted part is the most important part of the question....

Posting the Venn Diagram approach hope it clears the concept further

Attachment:
Venn Diagram.png
Venn Diagram.png [ 18.55 KiB | Viewed 13679 times ]


So, the possible range of values is between 40% to 60%

40% of 150,000 = 60,000 ( Minimum Value )
60% of 150,000 = 90,000 ( Maximum Value )

Hence answer will be C. 60,000 to 90,000 inclusive

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Current Student
User avatar
S
Joined: 28 Nov 2014
Posts: 895
Concentration: Strategy
Schools: Fisher '19 (M)
GPA: 3.71
Reviews Badge
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 24 Sep 2016, 07:47
Bunuel - Thank you for the solution. Do you have any link to similar questions? I'm bad with these questions and I'd like to practise them. Please if you can help.
Thank You!
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46271
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 25 Sep 2016, 03:17
1
2
Keats wrote:
Bunuel - Thank you for the solution. Do you have any link to similar questions? I'm bad with these questions and I'd like to practise them. Please if you can help.
Thank You!


Data Sufficiency Questions on Overlapping Sets
Problem Solving Questions on Overlapping Sets
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
avatar
Joined: 20 Sep 2016
Posts: 6
In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 25 Sep 2016, 06:49
1
General Formula:
Sum = Gr A + Gr B - (A and B) + (neither A nor B)
With that we have: (Z = 150,000)
Z = 0.8Z + 0.6Z - (A and B) + (none)
(A and B) = 0.4Z + none
To get min(A and B), (none) will be 0, hence min(A and B) = 0.4Z = 60,000
To get max(A and B), we know that (A and B: the number of pp who own both items) will be maximum only when all of those who own recorders also have cable TV, therefore the largest value of (A and B) is the number of people who own recorders, which is equal to 0.6Z=90,000
Manager
Manager
avatar
B
Joined: 18 Jun 2016
Posts: 97
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 700 Q49 V36
WE: Business Development (Computer Software)
GMAT ToolKit User Reviews Badge
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 25 Sep 2016, 16:35
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive



80 has tv
60 has videocassettes
There are 100 people in total.
Manima would be (80+60) - 100 = 40(consider some videocassete holders do not own tv, maximizing those people we get minima)
Mixima would be 60(consider all the videocassete holder has tv, minimizing non-tv holders we get maxima)

Hence range would be from 40% of 150,000 to 60% of 150,000.
So option C is correct.
_________________

If my post was helpful, feel free to give kudos!

Manager
Manager
avatar
S
Joined: 13 Dec 2013
Posts: 162
Location: United States (NY)
Concentration: Nonprofit, International Business
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 30 Mar 2017, 21:06
Bunuel wrote:
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


120 have TV and 90 have radio. Obviously the number of households that have both cannot be greater than 90. Eliminate B, D, and E.

Next:
{Total} = {TV} + {Radio} - {Both} + {Neither}

150 = 120 + 90 - {Both} + {Neither}

{Both} = 60 + {Neither}

Thus {Both}>=60.

Answer: C.


Hi Bunuel, the formula you use, {Total} = {TV} + {Radio} - {Both} + {Neither}, is a modified version of the following formula for three overlaps, correct?

Total = (members of one group) - (members of two groups) + (members of all three groups) + neither
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 46271
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 30 Mar 2017, 22:10
Cez005 wrote:
Bunuel wrote:
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


120 have TV and 90 have radio. Obviously the number of households that have both cannot be greater than 90. Eliminate B, D, and E.

Next:
{Total} = {TV} + {Radio} - {Both} + {Neither}

150 = 120 + 90 - {Both} + {Neither}

{Both} = 60 + {Neither}

Thus {Both}>=60.

Answer: C.


Hi Bunuel, the formula you use, {Total} = {TV} + {Radio} - {Both} + {Neither}, is a modified version of the following formula for three overlaps, correct?

Total = (members of one group) - (members of two groups) + (members of all three groups) + neither


This is a formula for 2 overlapping sets. Don't know what formula you are referring though.


Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2771
Location: United States (CA)
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 04 Apr 2017, 16:16
2
imhimanshu wrote:
In a certain city, 80 percent of the households have cable television, and 60 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:

A. 30,000 to 90,000 inclusive
B. 30,000 to 120,000 inclusive
C. 60,000 to 90,000 inclusive
D. 60,000 to 120,000 inclusive
E. 90,000 to 120,000 inclusive


We are given that there are 150,000 households in the city, that 60%, or 0.6 x 150,000 = 90,000, have videocassette recorders, and that 80%, or 0.8 x 150,0000 = 120,000, have cable television.

We can create the following equation:

150,000 = 90,000 + 120,000 - number who have both (b) + number who have neither (n)

150,000 = 210,000 - b + n

b = 60,000 + n

To minimize b, we can let n = 0, and thus b = 60,000.

To maximize b, we need to use the fact that b is the number of households that have both cable television and videocassette recorders; thus, it can’t be more than the smaller of the number of households that have cable television and the number of households with videocassette recorders. Since 90,000 households have videocassette recorders, which is less than the 150,000 households that have cable television, the maximum value of b is 90,000.

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 7021
Premium Member
Re: In a certain city, 80 percent of the households have cable [#permalink]

Show Tags

New post 09 May 2018, 13:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: In a certain city, 80 percent of the households have cable   [#permalink] 09 May 2018, 13:19
Display posts from previous: Sort by

In a certain city, 80 percent of the households have cable

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.