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# Of the 300 subjects who participated in an experiment using

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

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08 Jun 2012, 00:16
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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
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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08 Jun 2012, 00:43
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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
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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08 Jun 2012, 00:57
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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,
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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15 Aug 2013, 07:26
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100 = 40 + 30 + 75 - 35 - 2 x ALL ----(standard formula)
ALL = 5%

Exactly 3 = 5% Of 300 = 15
Exactly 2 = 35% of 300 = 105

Total = Exactly 1 + Exactly 2 + Exactly 3
300 = Exactly 1+ 15 + 105
Exactly 1= 180 Ans.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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11 Feb 2013, 04:43
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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.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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25 May 2013, 06:40
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people who experienced

1 symptom only - a

2 symptom only- b =35% (given)

3 symptom only- c

no symptoms- 0
a+b+c=100%

a+35%+c = 100% -----> (1)

also

Group 1= 40%

Group 2= 30%

Group 3= 75%

Total = Group1 + Group 2 + Group 3 - (people with 2 symptoms only) - 2*(people with 3 symptpoms only) + Neither

Total = Group1 + Group 2 + Group 3 - (b) - 2*(c) + 0

Total = 40% +30%+75%-35% - 2*(c) + 0= 100%

110%-2c=100%

c=5% -----> (2)

from (1) and (2)

a + 35% + 5% = 100%

a= 60%= 60%(300)= 180. Answer D
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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28 May 2013, 21:44
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x+y+z+p+q+r+w = 300 ---- (a)
x+p+w+q = 120 (40% of 300) ----(1)
p+q+w+r = 90 (30 % of 300)----(2)
similarly q+w+r+z = 225----(3)

Need to find x+y+z=?

Adding equations (1), (2) and (3)
we get x+y+z+2(p+q+r+w)+w=435
subtract equation (a) from above equation
we get p+q+r+2w = 135
given p+q+r = 105 (35% of 300)

so w =15 and p+q+r+w = 120

substitute value of above equation in (a) gets x+y+z = 180
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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19 Aug 2013, 11:55
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macjas wrote:
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

100%=40%+30%+75%-35%-2*x
or, 2x=10%
or, x=5%
Experienced only one of these effects=100%-35%-5%=60%
By the way, 100%=300
or, 1%=300/100
or, 60%=300*60/100=180
So, the best answer is (D). posted By mannan mian
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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15 Aug 2013, 13:25
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macjas wrote:
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

exactly two = A+B+C-2(A n B n C)-(A u B u C)
OR, 35 = 40+30+75 - 2(A n B n C) - 100
OR, (A n B n C) = 5% = 5% OF 300 = 15

Exactly 3 = 15
Exactly 2 = 35% of 300 = 105
So exactly one = 300 -(15+105) = 180 (Answer)
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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11 Feb 2013, 02:27
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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?

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

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18 Aug 2013, 04:53
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Galiya wrote:
Quote:
So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3?
dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?

The reason is simple; you do not want to include any of the common elements. In this case there are three elements;

So when you add A and B you are counting the exactly 2 common elements twice once with A and once with B ; so considering other combinations we subtract 2gr overlaps twice and not thrice.
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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12 Feb 2013, 01:46
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It helped a great deal! Thanks Bunuel! As always, your input is priceless!!
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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28 May 2013, 15:09
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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

got 195 i didnt add all and take that as the total but instead left 300 as the total
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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15 Aug 2013, 10:18
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Quote:
So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3?
dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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16 Aug 2013, 01:00
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Galiya wrote:
Quote:
So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

i dont understand why Vandygrad multiplies 2 gr overlaps by 2 and 3 gr overlaps by 3?
dont we need to minus 3 times "exactly 2 gr" overlaps and once "3 gr" overlaps?

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

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24 Jul 2014, 02:44
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Refer diagram below:

Given that
p + q + r = 105

a + b + c + x + p + q+ r = 300

We require to find value of (a + b + c)

a + b + c = 195 - x .................... (1)

---------------------------------------------
a + p + x + q = 120

b + p + x + r = 90

c + q + x + r + = 225
--------------------------------------------
Adding above 3 equations

a + b + c + 2(p + q + r) + 3x = 435

a + b + c = 225 - 3x ................... (2)

Equating RHS of equation (1) & (2)

225 - 3x = 195 - x

2x = 30

x = 15

a + b + c = 195 - 15 = 180

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

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20 Mar 2015, 22:04
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40 + 30 +75 -35 -2x +0 = 100 ==> x = 5
Therefore, % experienced more than one = 5+35 = 40%
So, % experienced only one = 60% or 300*60% = 180
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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13 Sep 2013, 09:28
the venn diagram is so much easier than the formula
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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13 Sep 2013, 09:32
legitpro wrote:
the venn diagram is so much easier than the formula

But that is how the formula is derived .
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Re: Of the 300 subjects who participated in an experiment using [#permalink]

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05 Oct 2013, 16:00
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 someone explain how we get the formula highlighted in red above? Why do we multiply the 2-group overlaps and 3-group overlaps by 2 and 3 respectively? I didn't get that part. Thanks.
Re: Of the 300 subjects who participated in an experiment using   [#permalink] 05 Oct 2013, 16:00

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