A polling company found that, of 300 households surveyed

Question

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.

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

cyberjadugar · Accepted Answer

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,

daviesj · Answer

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.

shrouded1 · Answer

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)

Bunuel · Answer

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.

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.

stne · Answer

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 ??

Bunuel · Answer

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.

PathFinder007 · Answer

HI Bunuel,

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

Please clarify.

Thanks.

PareshGmat · Answer

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

JeffTargetTestPrep · Answer

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

testcracker · Answer

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

Archit3110 · Answer

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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A polling company found that, of 300 households surveyed

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