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Of the 300 subjects who participated in an experiment using

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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 14 Dec 2017, 04:49
geometric wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0
300*.1 = 30
300 = 120 + 90 + 225 - 105 - 2*(all three)
2*(all three) = 30
:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180



I did not understand the 2nd part of the answer. how did you derive this formula and when is it supposed to be used? Any help would be appreciated.
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Of the 300 subjects who participated in an experiment using [#permalink]

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New post 02 Jan 2018, 00:47
N(a U b U c) = N(a) + N(b) + N(c) - N(a ∩ b) - N(b ∩ c) - N(c ∩ a) + N(a ∩ b ∩ c)

N(a ∩ b) = (only a, b) + N(a ∩ b ∩ c)
N(c ∩ b) = (only c, b) + N(a ∩ b ∩ c)
N(a ∩ c) = (only c, a) + N(a ∩ b ∩ c)

In percentages:
100 = 40+30+75-35-2N(a ∩ b ∩ c) ----> N(a ∩ b ∩ c) = 5

100 = (exactly one) + (exactly two) + (exactly three) ---> exactly one = 100-35-5 ---> exactly one = 60% ---> 180 people

Hence answer: D
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 02 Jan 2018, 10:23
Bunuel wrote:
iwillbeatthegmat wrote:
vandygrad11 wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0
300*.1 = 30
300 = 120 + 90 + 225 - 105 - 2*(all three)
2*(all three) = 30
:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180


I'm having trouble understanding this formula. Why is the sum of all three overlaps multiplied by two?

Thanks in advance.


Explained here: http://gmatclub.com/forum/advanced-over ... 44260.html

Hope it helps.


Hello Bunuel, can you please explain this 2*(all three) how do we get 15*3 ? I checked the link you provided, but still cant understand this moment. :? thank you :-)
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 02 Jan 2018, 15:13
geometric wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0
300*.1 = 30
300 = 120 + 90 + 225 - 105 - 2*(all three)
2*(all three) = 30
:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180


Why did you multiply 300 by 10% - where do you see such information that all three is 30 :? ....another confusion why here you use figures except of (all three) 300 = 120 + 90 + 225 - 105 - 2*(all three) if all three is unknown then we could use 3x = all three multiplied by 2 = 6x :?

and why are you using two equations ? where as Bunuel in his post provides one formula to apply when we have three groups ? https://gmatclub.com/forum/advanced-ove ... 44260.html which says: Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither :)
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 03 Jan 2018, 05:29
dave13 wrote:
geometric wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0
300*.1 = 30
300 = 120 + 90 + 225 - 105 - 2*(all three)
2*(all three) = 30
:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180


Why did you multiply 300 by 10% - where do you see such information that all three is 30 :? ....another confusion why here you use figures except of (all three) 300 = 120 + 90 + 225 - 105 - 2*(all three) if all three is unknown then we could use 3x = all three multiplied by 2 = 6x :?

and why are you using two equations ? where as Bunuel in his post provides one formula to apply when we have three groups ? https://gmatclub.com/forum/advanced-ove ... 44260.html which says: Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither :)



these overlapping sets overlap both parts of my brain - totally confusing :-)
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Concentration: Finance
GMAT 1: 710 Q50 V36
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 07 Feb 2018, 09:49
Don't bother with actual number until the very end, just keep in percentage form and multiply the number when you find the fraction.

We got: (keep in mind that everything is percentage based)
100 = Group 1 + group 2 + group 3 - (exactly 2) - 2*(exactly 3)
100 = 40 + 30 + 75 - 35 - 2*(exactly 3), solve for this we got (exactly 3) = 5

Here is a very useful formula for these kind of question:
Total number of people = (exactly 1) + (exactly 2) + (exactly 3), it's also equal 100%, hence:
100 = (exactly 1) + 35 + 5
(exactly 1) = 60%, total number of exactly 1 = 300 * 60% = 180
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 09 Feb 2018, 05:03
cyberjadugar wrote:
Quote:
Of the 300 subjects who participated in an experiment using virtual-reality therapy to reduce their fear of heights, 40 percent experienced sweaty palms, 30 percent experienced vomiting, and 75 percent experienced dizziness. If all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects, how many of the subjects experienced only one of these effects?

A. 105
B. 125
C. 130
D. 180
E. 195
Hi,

We know, \(A\cup B\cup C = A+B+C-A\cap B-B\cap C-C\cap A +A\cap B\cap C\)
where
\(A = 40%\)
\(B = 30%\)
\(C = 75%\)
As per the attached Venn diagram,
\(A\cup B\cup C=100%\)

\(A\cap B+B\cap C+C\cap A=\)Exactly two - 3x (assuming \(A\cap B\cap C=x\))
\(=35-3x\)
Thus,
\(100= 40+30+75-(35-3x)+x\)
or \(x = 5%\)

Thus, subjects expriencing only one effect = 100% - (subjects expriencing only two effects) - (subjects expriencing all effects)
or subjects expriencing only one effect = 100 - 35 - 5 = 60%

60% of 300 = 180

Answer is (D)

Regards,


perfect solution.

but remember, there are many form of formulae for this kind. know what formalar is used for what condition
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 19 Apr 2018, 02:36
I found the easiest way to solve the problem is to first find AnBnC and then add it to the sum of EXACTLY two overlapping sets (sum of two overlapping sets ) and then subtract it from the total

So, Tot = A+B+C - (sum of exactly 2 groups overlaps) - 2 (sum of all three = x ) + None
300 = 120+90+225 - 105 -2x + 0 => x = 15

Thus the sum of two groups overlaps = 105 + 15 = 120
Therefore, the subjects experienced only one of these effects = Total - the subjects who experienced more than 1 of these effects
= 300 - 120 = 180
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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New post 30 May 2018, 14:58
Bunuel wrote:
saintforlife wrote:
vandygrad11 wrote:
The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0
300*.1 = 30
300 = 120 + 90 + 225 - 105 - 2*(all three)
2*(all three) = 30
:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer
= 120 + 90 + 225 - 105*2 - 15*3
= 435 - 210 - 45
= 180


Can you please explain why 2 group overlap was multiplied by 2 and 3 group overlap multiplied by 3 ??
The formula stated in the link posted by you states "Total=A+B+C−(sum of EXACTLY 2−group overlaps)−2∗(all three)+Neither".
Not able to understand this step.. Please help
Re: Of the 300 subjects who participated in an experiment using   [#permalink] 30 May 2018, 14:58

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