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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

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 4786 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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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.

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

We can create the following equation:

Total = number who spent at least 100 on gasoline only + number who spent at least 100 on electricity only + number who spend at least 100 on both + number who spent at least 100 on neither

If we let x = number who spent at least 100 on neither, then 4x = number who spent at least 100 on electricity only, and we have:

300 = 60 + 4x + 120 + x

300 = 180 + 5x

120 = 5x

x = 24

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

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23 Nov 2017, 15:32

krazo 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

a ratio between "none and only electricity" is given

so, none and only electricity = (300 - 120 -60) = 120