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# Of the 300 subjects who participated in an experiment using

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Intern
Joined: 02 Nov 2017
Posts: 14
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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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.
Intern
Joined: 30 Jan 2017
Posts: 3
Of the 300 subjects who participated in an experiment using [#permalink]

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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

Senior Manager
Joined: 09 Mar 2016
Posts: 333
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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02 Jan 2018, 10:23
Bunuel wrote:
iwillbeatthegmat 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?

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
Senior Manager
Joined: 09 Mar 2016
Posts: 333
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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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
Senior Manager
Joined: 09 Mar 2016
Posts: 333
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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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
Intern
Joined: 28 Jan 2018
Posts: 39
Location: Netherlands
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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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
Senior Manager
Joined: 29 Jun 2017
Posts: 265
Re: Of the 300 subjects who participated in an experiment using [#permalink]

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09 Feb 2018, 05:03
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

Regards,

perfect solution.

but remember, there are many form of formulae for this kind. know what formalar is used for what condition
Re: Of the 300 subjects who participated in an experiment using   [#permalink] 09 Feb 2018, 05:03

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