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# Of the 300 subjects who participated in an experiment using

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

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08 Jun 2012, 01:16
37
179
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Difficulty:

95% (hard)

Question Stats:

62% (03:15) correct 38% (03:21) wrong based on 2559 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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11 Feb 2013, 05:43
13
11
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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08 Jun 2012, 01:43
57
1
52
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
##### General Discussion
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Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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08 Jun 2012, 01:57
44
28
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,
Attachments

Venn.jpg [ 21.47 KiB | Viewed 79680 times ]

Intern
Joined: 08 May 2012
Posts: 6
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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11 Feb 2013, 03:27
5
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?

Intern
Joined: 08 May 2012
Posts: 6
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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12 Feb 2013, 02:46
1
It helped a great deal! Thanks Bunuel! As always, your input is priceless!!
Intern
Joined: 28 Apr 2013
Posts: 2
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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25 May 2013, 07:40
9
7
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
Manager
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Posts: 50
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Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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28 May 2013, 16:09
1
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
Intern
Joined: 02 May 2013
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WE: Engineering (Aerospace and Defense)
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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28 May 2013, 22:44
14
5
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
Attachments

Venn.JPG [ 13.05 KiB | Viewed 75339 times ]

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

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15 Aug 2013, 08:26
39
18
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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15 Aug 2013, 11:18
1
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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Joined: 10 Jul 2013
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Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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15 Aug 2013, 14:25
3
2
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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16 Aug 2013, 02:00
1
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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18 Aug 2013, 05:53
2
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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19 Aug 2013, 12:55
6
4
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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13 Sep 2013, 10:28
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, 10:32
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, 17:00
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.
Math Expert
Joined: 02 Sep 2009
Posts: 49496
Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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05 Oct 2013, 17:01
saintforlife 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 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.

Hope it helps.
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Joined: 13 Feb 2011
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Re: Of the 300 subjects who participated in an experiment using  [#permalink]

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01 Jul 2014, 10:10
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,

One correction: In 100= 40+30+75-(35-3x)+x, it should be (35+3x)
Re: Of the 300 subjects who participated in an experiment using &nbs [#permalink] 01 Jul 2014, 10:10

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