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A polling company found that, of 300 households surveyed
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06 Oct 2010, 18:35
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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. 24 B. 30 C. 36 D. 90 E. 96
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Re: Gasoline and Electricity
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Updated on: 09 Jul 2012, 01:08
Quote: 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,
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Venn.jpg [ 22.47 KiB  Viewed 5068 times ]
Originally posted by cyberjadugar on 20 Jun 2012, 23:06.
Last edited by cyberjadugar on 09 Jul 2012, 01:08, edited 1 time in total.




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Re: Gasoline and Electricity
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07 Oct 2010, 00:52
krazo wrote: Here is one I thought was pretty good...
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 300 = 180 + 5x implies x=24 Answer is (A)
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Re: A polling company found that, of 300 households surveyed
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21 Jun 2012, 01:36
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.
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Re: A polling company found that, of 300 households surveyed
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21 Jun 2012, 04:20
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 ??
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Re: A polling company found that, of 300 households surveyed
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21 Jun 2012, 04:51
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.
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Re: A polling company found that, of 300 households surveyed
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17 Sep 2012, 06:25
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.. ElectricityNonElectricityTotal Gasoline12060180 NonGasln4xx120 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
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07 Aug 2014, 12:06
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. Please clarify. Thanks.



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A polling company found that, of 300 households surveyed
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08 Aug 2014, 00:19
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. May be GMAT trick
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Re: A polling company found that, of 300 households surveyed
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14 Nov 2017, 07:20
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 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
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23 Nov 2017, 16:32
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 now, according to the ratio 120 * 1/5 = 24 thanks




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