A polling company found that, of 300 households surveyed, 12

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

(A) 24
(B) 30
(C) 36
(D) 90
(E) 96

Bunuel · Accepted Answer

{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.

megafan · Answer

Shouldn't it be minus (-) Both? I thought the relationship was Total = onlyA + onlyB - Both + Neither

Bunuel · Answer

Nope. It's {Total} = {Group 1} + {Group 2} - {Both} + {Neither}. Look at the diagram below: Venn diagram.png 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.

prbhtsngr · Answer

electricity Not electricity 
Gasoline 120 60 180
Not gasoline 4a a 120
 300(total)

4a +a=5a=120
a=24

TGC · Answer

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 !

Asifpirlo · Answer

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)

bumpbot · Answer

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A polling company found that, of 300 households surveyed, 12

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