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A polling company found that, of 300 households surveyed [#permalink]

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06 Oct 2010, 17:35

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A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

(A) 24 (B) 30 (C) 36 (D) 90 (E) 96

120 spend $100 on gas & electricity 60 spend $100 on gas but not on electricity For every one that spent <$100 on both there are 4 that spent $100 on electricity not gas

Let the ones that spent on neither be x The ones that spent on just electricity will be 4x

Total households = Those who spend >$100 on both + Those who spend >$100 on just one + Those who spend <$100 on both = 120 + 60 + 4x + x

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

(A) 24 (B) 30 (C) 36 (D) 90 (E) 96

Can anyone provide a better explanation to this one , I am confused about the portion " for every household that did not spend at least $100 per month on gasoline or electricity, " How to calculate this portion

is A or B = AUB ? ? how to calculate A or B in this scenario ?
_________________

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

Hi,

Please refer to the attached Venn diagram: Here, x = Number of households neither using electricity nor gasoline. Now, \(60+120+4x+x=300\) or x = 24

Answer (A)

Regards,

Attachments

Venn.jpg [ 22.47 KiB | Viewed 4152 times ]

Last edited by cyberjadugar on 09 Jul 2012, 00:08, edited 1 time in total.

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

Re: A polling company found that, of 300 households surveyed [#permalink]

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21 Jun 2012, 03:20

Bunuel wrote:

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

\(300 = 60 + 4x + 120 + x\) --> \(x=24\).

Answer: A.

Hope it's clear.

I know this is very basic , but a reconfirmation will help

" My confusion was the term " OR "

A OR B means AUB ( Total ) right so in this case E OR G means EUG( Total )

so EUG = only E + Only G + Both + Neither ( This one we are using ) also EUG = Group E + group G - both + Neither ( This one we are not using here )

Please let me now if anything that I have written in Blue is wrong !!

I want to understand if A or B = AUB = Total ??
_________________

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

\(300 = 60 + 4x + 120 + x\) --> \(x=24\).

Answer: A.

Hope it's clear.

I know this is very basic , but a reconfirmation will help

" My confusion was the term " OR "

A OR B means AUB ( Total ) right so in this case E OR G means EUG( Total )

so EUG = only E + Only G + Both + Neither ( This one we are using ) also EUG = Group E + group G - both + Neither ( This one we are not using here )

Please let me now if anything that I have written in Blue is wrong !!

I want to understand if A or B = AUB = Total ??

Two formulas are: {Total} = {Group #1} + {Group #2} - {Both} + {Neither} {Total} = {Only Group #1} + {Only Group #2} + {Both} + {Neither}

Now, if we are told that there are 10 people in {Group #1} and 15 people in {Group #2}, then the number of people in {Group #1} OR in {Group #2} can be expressed as {Group #1} + {Group #2} - {Both}. But to get the total number of people you should add to that the number of people who are in neither of groups.

Re: A polling company found that, of 300 households surveyed [#permalink]

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17 Sep 2012, 05:25

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Different approach: I think if there are two overlapping sets then quick way to solve the problem is to form a chart rather than to draw a Venn diagram..here's the solution for above problem in chart way.. --------------Electricity----Non-Electricity--Total Gasoline------120-----------60--------------180 Non-Gasln-----4x-------------x--------------120 Total -------------------------------------------300 now 4x + x =120, so 5x=120 and hence x=24.
_________________

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Re: A polling company found that, of 300 households surveyed [#permalink]

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17 Sep 2012, 06:27

Bunuel wrote:

stne wrote:

Bunuel wrote:

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

\(300 = 60 + 4x + 120 + x\) --> \(x=24\).

Answer: A.

Hope it's clear.

I know this is very basic , but a reconfirmation will help

" My confusion was the term " OR "

A OR B means AUB ( Total ) right so in this case E OR G means EUG( Total )

so EUG = only E + Only G + Both + Neither ( This one we are using ) also EUG = Group E + group G - both + Neither ( This one we are not using here )

Please let me now if anything that I have written in Blue is wrong !!

I want to understand if A or B = AUB = Total ??

Two formulas are: {Total} = {Group #1} + {Group #2} - {Both} + {Neither} {Total} = {Only Group #1} + {Only Group #2} + {Both} + {Neither}

Now, if we are told that there are 10 people in {Group #1} and 15 people in {Group #2}, then the number of people in {Group #1} OR in {Group #2} can be expressed as {Group #1} + {Group #2} - {Both}. But to get the total number of people you should add to that the number of people who are in neither of groups.

Hope it's clear.

Hi Bunuel,

Can you please explain , when to you use these formulae?

Two formulas are: {Total} = {Group #1} + {Group #2} - {Both} + {Neither} {Total} = {Only Group #1} + {Only Group #2} + {Both} + {Neither}.

Re: A polling company found that, of 300 households surveyed [#permalink]

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18 Nov 2013, 14:48

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Re: A polling company found that, of 300 households surveyed [#permalink]

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07 Aug 2014, 11:06

Bunuel wrote:

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

\(300 = 60 + 4x + 120 + x\) --> \(x=24\).

Answer: A.

Hope it's clear.

HI Bunuel,

I know its a silly question but i didn't understand how you took 4x from question stem.

A polling company found that, of 300 households surveyed [#permalink]

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07 Aug 2014, 23:19

PathFinder007 wrote:

Bunuel wrote:

A polling company found that, of 300 households surveyed, 120 spent at least $100 per month on both gasoline and electricity, 60 spent at least $100 per month on gasoline but not on electricity, and for every household that did not spend at least $100 per month on gasoline or electricity, 4 spent at least $100 per month on electricity but not on gasoline. How many of the 300 households did not spend at least $100 per month on either gasoline or electricity?

A. 24 B. 30 C. 36 D. 90 E. 96

{Total} = {Only Gasoline} + {Only Electricity} + {Both} + {Neither}. Notice that this formula is different from {Total} = {Group #1} + {Group #2}} - {Both} + {Neither};

\(300 = 60 + 4x + 120 + x\) --> \(x=24\).

Answer: A.

Hope it's clear.

HI Bunuel,

I know its a silly question but i didn't understand how you took 4x from question stem.

Please clarify.

Thanks.

Not Bunuel, but lets try

The answer lies in the highlighted part of the question

Only Electricity is 4 times of (No Gas No electricity)

So, if "x" = No Gas No electricity, then 4x = Only electricity

Please refer the Venn diagram above; it explains perfect

In this problem, the term "atleast 100" is the confusion creator which is repeated 5 times; although "100" is not required for any calculation.

Re: A polling company found that, of 300 households surveyed [#permalink]

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04 Oct 2015, 15:02

Hello from the GMAT Club BumpBot!

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Re: A polling company found that, of 300 households surveyed [#permalink]

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06 Nov 2016, 03:14

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).

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