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Of the 600 residents of Clermontville, 35% watch the [#permalink]
10 Sep 2004, 23:04
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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?
Sometimes I get confused in these type of questions.Is there a different formulae when there are 3 groups instead of 2.
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
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.