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A polling company found that, of 300 households surveyed

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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. 24 B. 30 C. 36 D. 90 E. 96 [Reveal] Spoiler: OA Retired Moderator Joined: 02 Sep 2010 Posts: 805 Location: London Followers: 105 Kudos [?]: 958 [0], given: 25 Re: Gasoline and Electricity [#permalink] Show Tags 06 Oct 2010, 23:52 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

(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 ? _________________ - Stne Kellogg MMM ThreadMaster Joined: 28 Mar 2012 Posts: 314 Location: India GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Followers: 29 Kudos [?]: 399 [3] , given: 23 Re: Gasoline and Electricity [#permalink] Show Tags 20 Jun 2012, 22:06 3 This post received KUDOS 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 4152 times ]

Last edited by cyberjadugar on 09 Jul 2012, 00:08, edited 1 time in total.
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Re: A polling company found that, of 300 households surveyed [#permalink]

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21 Jun 2012, 00:36
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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. _________________ Manager Joined: 27 May 2012 Posts: 218 Followers: 2 Kudos [?]: 71 [0], given: 432 Re: A polling company found that, of 300 households surveyed [#permalink] Show Tags 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};

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

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, 03:51
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: 152 Location: India Concentration: Finance, Human Resources GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) Followers: 10 Kudos [?]: 304 [2] , given: 35 Re: A polling company found that, of 300 households surveyed [#permalink] Show Tags 17 Sep 2012, 05:25 2 This post received KUDOS 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 Senior Manager Joined: 22 Nov 2010 Posts: 288 Location: India GMAT 1: 670 Q49 V33 WE: Consulting (Telecommunications) Followers: 5 Kudos [?]: 138 [0], given: 75 Re: A polling company found that, of 300 households surveyed [#permalink] Show Tags 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};

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

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}.

BR
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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. Please clarify. Thanks. SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1858 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Followers: 47 Kudos [?]: 1937 [0], given: 193 A polling company found that, of 300 households surveyed [#permalink] Show Tags 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};

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

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.

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 [#permalink]

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04 Oct 2015, 15:02
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Re: A polling company found that, of 300 households surveyed [#permalink]

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06 Nov 2016, 03:14
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Re: A polling company found that, of 300 households surveyed   [#permalink] 06 Nov 2016, 03:14
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