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.

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.

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)

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