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

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gmatter2012: Master | Next Rank: 500 Posts; Posts: 138; Joined: Sat May 05, 2012 7:03 pm; Thanked: 1 times

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

by gmatter2012 » Wed Jun 20, 2012 9:32 pm

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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Source: Beat The GMAT — Problem Solving | Wed Jun 20, 2012 9:32 pm

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jun 20, 2012 10:21 pm

gmatter2012 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?

Total = 300
Both gasoline and electricity, B = 120
Only gasoline, G = 60

Say, number of only electricity = E and number of none = N
Hence, E = 4N

Now, (G + E + B + N) = 300
---> (60 + E + 120 + N) = 300
---> (60 + 4N + 120 + N) = 300
---> 5N = (300 - 180) = 120
---> N = 24

The correct answer is A.

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gmatter2012: Master | Next Rank: 500 Posts; Posts: 138; Joined: Sat May 05, 2012 7:03 pm; Thanked: 1 times

by gmatter2012 » Wed Jun 20, 2012 11:03 pm

Anurag Thank you.

I was just a little confused about " and for every household that did not spend at least $100 per month on gasoline or electricity "

Does Did not spend on E OR G = Universal - ( spend on E or G )

basically I want to know how to find E or G here ,
I knew that A or B can be found in two ways :

1) only A + only B + AnB
2) A + B - AnB
I

so how to apply this concept here, to find E or G

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Wed Jun 20, 2012 11:19 pm

gmatter2012 wrote:Anurag Thank you.
Does Did not spend on E OR G = Universal - ( spend on E or G )

Yes.
And spent on E or G = (spent only on G) + (spent only on E) + (spent on both)

gmatter2012 wrote:I knew that A or B can be found in two ways :

1) only A + only B + AnB
2) A + B - AnB

This is true only when all of the elements belong either to A or B or both.
But when there are elements that do not belong to neither of them then,

1. Universal = only A + only B + both A and B + neither A nor B
OR
2. Universal = A + B - both A and B + neither A nor B

Hope that helps.

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gmatter2012: Master | Next Rank: 500 Posts; Posts: 138; Joined: Sat May 05, 2012 7:03 pm; Thanked: 1 times

by gmatter2012 » Wed Jun 20, 2012 11:49 pm

Anurag@Gurome wrote:
gmatter2012 wrote:Anurag Thank you.
Does Did not spend on E OR G = Universal - ( spend on E or G )
Yes.
And spent on E or G = (spent only on G) + (spent only on E) + (spent on both)

gmatter2012 wrote:I knew that A or B can be found in two ways :

1) only A + only B + AnB
2) A + B - AnB
This is true only when all of the elements belong either to A or B or both.
But when there are elements that do not belong to neither of them then,
1. Universal = only A + only B + both A and B + neither A nor B
OR
2. Universal = A + B - both A and B + neither A nor B
Hope that helps.

so E or G = E U G = [only E + Only G + Both + None ]

so "OR" means "Union" right?

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Thu Jun 21, 2012 12:41 am

gmatter2012 wrote:so E or G = E U G = [only E + Only G + Both + None ]

so "OR" means "Union" right?

Yes, OR means UNION.
But when you say "E or G" then how come "none" comes into picture?

I think you are mixing up universal with union.
They are not same. Union of two sets does not contain the elements which are in neither of them but universal contains everything.

See the following Venn diagram.

The union of A and B, i.e. (A U B) is the shaded region.
But the universal set contains everything inside the rectangle , i.e. the shaded region (A U B) and the white region (elements those are neither in A nor in B)

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by Scott@TargetTestPrep » Mon Jan 15, 2018 11:57 am

gmatter2012 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

Answer: A

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