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megafan
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A polling company found that, of 300 households surveyed, 12 04 Mar 2013, 14:30
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72% (02:29) correct 28% (03:05) wrong based on 489 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
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Bunuel
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A polling company found that, of 300 households surveyed, 12 04 Mar 2013, 16:56
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megafan
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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{Total} = 300;
{Both gasoline and electricity} = 120;
{Only gasoline} = 60;
{Neither gasoline nor electricity} = x;
{Only electricity} = 4x.

{Total} = {Only gasoline} + {Only electricity} + {Both gasoline and electricity} + {Neither gasoline nor electricity}

300 = 60 + 4x + 120 + x
x = {Neither gasoline nor electricity} = 24

Answer: A.

Hope it's clear.
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A polling company found that, of 300 households surveyed, 12 04 Mar 2013, 17:02
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Bunuel


{Total} = {Only gasoline} + {Only electricity} + {Both gasoline and electricity} + {Neither gasoline nor electricity}
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Shouldn't it be minus (-) Both? I thought the relationship was Total = onlyA + onlyB - Both + Neither
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A polling company found that, of 300 households surveyed, 12 04 Mar 2013, 17:22
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Bunuel


{Total} = {Only gasoline} + {Only electricity} + {Both gasoline and electricity} + {Neither gasoline nor electricity}

Shouldn't it be minus (-) Both? I thought the relationship was Total = onlyA + onlyB - Both + Neither
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Nope. It's {Total} = {Group 1} + {Group 2} - {Both} + {Neither}.

Look at the diagram below:
Attachment:
Venn diagram.png
Venn diagram.png [ 6.05 KiB | Viewed 10679 times ]
When we add {Group 1} and {Group 2} (entire circles), we count blue section (Both) twice, thus we should subtract it.

But if we have {Only group 1} and {Only group 2}, then it's {Total} = {Only group 1} + {Only group 2} + {Both} + {Neither}.

Hope it's clear.
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A polling company found that, of 300 households surveyed, 12 29 Jun 2013, 04:42
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electricity Not electricity
Gasoline 120 60 180
Not gasoline 4a a 120
300(total)

4a +a=5a=120
a=24
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A polling company found that, of 300 households surveyed, 12 17 Aug 2013, 09:05
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Three solutions from my Side :

Approach 1 is given by 2-set matrix in the attached JPEG.

Approach 2:

Total = Only E + Only G + Both + Neither

= 60+120+4x+x (Where we have to find X)

X=24

Approach 3 is through Venn Diagrams find attached

120+60+x+4x=300

=> x=24

Rgds,
TGC !
Attachments

sol2.JPG
sol2.JPG [ 13.52 KiB | Viewed 9778 times ]

sol.JPG
sol.JPG [ 17.02 KiB | Viewed 9774 times ]

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A polling company found that, of 300 households surveyed, 12 17 Aug 2013, 09:40
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megafan
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
Show more
For every household that did not spend at least $100 per month on gasoline or electricity = P ,
4 spent at least $100 per month on electricity but not on gasoline = 4P

Spent = 300 - P
again spent = 60+120+4P

Now,
300 - P = 60+120+4P
or, 5P = 120
or, P = 24 (Answer)
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A polling company found that, of 300 households surveyed, 12 15 Sep 2025, 00:12
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