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# A polling company found that, of 300 households surveyed

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Manager
Joined: 24 Jun 2010
Posts: 133
Concentration: Strategy, Technology
A polling company found that, of 300 households surveyed  [#permalink]

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06 Oct 2010, 18:35
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45% (medium)

Question Stats:

71% (02:30) correct 29% (03:02) wrong based on 300 sessions

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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 ##### Most Helpful Community Reply Current Student Joined: 29 Mar 2012 Posts: 295 Location: India GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: Gasoline and Electricity [#permalink] ### Show Tags Updated on: 09 Jul 2012, 01:08 5 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

Regards,
Attachments

Venn.jpg [ 22.47 KiB | Viewed 5859 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.
##### General Discussion
Retired Moderator
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Location: London
Re: Gasoline and Electricity  [#permalink]

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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

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

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21 Jun 2012, 01:36
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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 {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. _________________ Director Joined: 27 May 2012 Posts: 898 Re: A polling company found that, of 300 households surveyed [#permalink] ### Show Tags 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};

$$300 = 60 + 4x + 120 + x$$ --> $$x=24$$.

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  [#permalink]

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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. _________________ Manager Status: Never ever give up on yourself.Period. Joined: 23 Aug 2012 Posts: 133 Location: India Concentration: Finance, Human Resources GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) Re: A polling company found that, of 300 households surveyed [#permalink] ### Show Tags 17 Sep 2012, 06:25 4 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. _________________ Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html Manager Joined: 10 Mar 2014 Posts: 180 Re: A polling company found that, of 300 households surveyed [#permalink] ### Show Tags 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};

$$300 = 60 + 4x + 120 + x$$ --> $$x=24$$.

Hope it's clear.

HI Bunuel,

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

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

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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 _________________ Kindly press "+1 Kudos" to appreciate Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2817 Re: A polling company found that, of 300 households surveyed [#permalink] ### Show Tags 14 Nov 2017, 07:20 1 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

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

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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 GMAT Club Legend Joined: 18 Aug 2017 Posts: 4976 Location: India Concentration: Sustainability, Marketing GPA: 4 WE: Marketing (Energy and Utilities) Re: A polling company found that, of 300 households surveyed [#permalink] ### Show Tags 22 Jun 2019, 02:26 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

CAN BE SOLVED USING 2X2 MATRIX

---- -----100$ELECT-----N 100$ ELEC------TOTAL
100$GAS---120-----------60---------------180 N100$GAS---4X------------X----------120
TOTAL ---120+4X----------60+5X------300
SO 4X+X=120
X=24 IMO A
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Re: A polling company found that, of 300 households surveyed   [#permalink] 22 Jun 2019, 02:26
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