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Of the 600 residents of Clermontville, 35% watch the [#permalink]
10 Sep 2004, 22:04

Of the 600 residents of Clermontville, 35% watch the television show Island Survival,
40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents
watch at least one of these three shows and 18% watch exactly 2 of these shows, then
how many Clermontville residents watch all of the shows?
(A) 150
(B) 108
(C) 42
(D) 21
(E) -21

Sometimes I get confused in these type of questions.Is there a different formulae when there are 3 groups instead of 2.

Is the answer 21. If I am right - I will fill in with the venn diagram. Dont use the AUB, BUC formulae - I always get it wrong using that. Venn diagram solves most issues.

I just did the same theory as Rahul.
There is an difference when two parties or three parties are involved.
Rahul gave an perfect and fast explanation to solve problems like this on the real test.

guys
How you have solved by venn diagram..can you demonstrate. What is the formulae in general terms. I mean ..something like
A+B+C- AB -BC -AC + ABC...
Iam not sure of the formulae..
I thought it would be -x instead of -2x..
Why are we putting 2x???
Oh gosh..And I thought I have everything clear in my mind.

OA is 21.
Even I dont know why are they using -2x .. I got the answer as 42.
I feel we are seriously missing something here..I am now sure that Iam not clear on these questions.
I hope that Ian is here, and can clarify the concepts for this in his trademark way.

I = Island Survival = 35
L = Lovelost Lawyers = 40
M = Medical Emergency = 50
X = Those who like ONLY Island Survival
Y = Those who like ONLY Lovelost Lawyers
Z = Those who like ONLY Medical Emergency
We are looking for A
This is given --> IL+IM+LM = 18
We know that:
X = 35-IL-IM-A
Y = 40-IL-LM-A
Z = 50-IM-LM-A
X+Y+Z = (35-IL-IM-A) + (40-IL-LM-A) + (50-IM-LM-A)
X+Y+Z = 125-2IL-2LM-2IM-3A
X+Y+Z = 125-2(IL+LM+IM)-3A
X+Y+Z = 125-2(18)-3A
3A=89-(X+Y+Z) We also know that:
X+Y+Z+IL+LM+IM+A = 100
X+Y+Z+(18)+A=100
X+Y+Z+A=82
A=82-(X+Y+Z)

Isolate variable A:
3A = 89-(X+Y+Z) A = 82-(X+Y+Z) Substract line 2 from line 1 to get rid of terms in brackets:
2A = 7
A = 3.5
3.5% of 600 is 21

Eureka! This may take a bit longer to type than to sketch on a venn diagram. It is actually feasible in 2 min! There may be some faster way but this is how I've done it.

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