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Of the 300 subjects who participated in an experiment using virtual-re

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New post 08 Jun 2012, 01:16
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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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Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New post 11 Feb 2013, 05:43
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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: ADVANCED OVERLAPPING SETS PROBLEMS

19. Overlapping Sets



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

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New post 08 Jun 2012, 01:43
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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 virtual-re  [#permalink]

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New post 08 Jun 2012, 01:57
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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

Answer is (D)

Regards,
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New post 11 Feb 2013, 03:27
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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.
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New post 25 May 2013, 07:40
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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 virtual-re  [#permalink]

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New post 28 May 2013, 22:44
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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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New post 15 Aug 2013, 08:26
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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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New post 15 Aug 2013, 11:18
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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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New post 15 Aug 2013, 14:25
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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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New post 18 Aug 2013, 05:53
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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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New post 19 Aug 2013, 12:55
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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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New post 24 Jul 2014, 03:44
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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

Answer = D
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New post 20 Mar 2015, 23:04
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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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New post 27 Aug 2015, 23:16
Hi,

Bunuel - I went through the link on advanced overlapping set, but I fail to understand the basis for the second formula used in the solution ->
A+B+C- (2-grp overlays)*2 - (3-grp overlays)*3

Please let me know how this formula was derived?

Thanks.
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New post 05 Oct 2015, 02:59
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mysterygirl wrote:
Hi,
1:
Bunuel - I went through the link on advanced overlapping set, but I fail to understand the basis for the second formula used in the solution ->
A+B+C- (2-grp overlays)*2 - (3-grp overlays)*3

Please let me know how this formula was derived?

Thanks.


For this reply, I'll be referencing Paresh's brilliant answer, because he goes through the effort of breaking down the various components of our three sets.

My advice is don't start off with the formula as a base to understand the question. Key idea here is understanding the question, and parsing the information in the prompt to reach a valid solution. You read the question, you have an idea of what's being given, you've established that it relates to Overlapping Sets. Great, so what do we have?

The question supplies us with these following knowns
Number of Groups: 3
Group 1 (Sweaty Palms: SP): 40% of 300= 4*30=120
Group 2 (Vomiting: V): 30% of 300 = 3*30 = 90
Group 3 (Dizziness: D): 75% of 300 = 7.5*30=225

All people in the study experience atleast 1 of these symptoms, 35% experience exactly 2 of those symptoms.

So where are those people that fall in 35% of the study? Referring to Paresh's Venn Diagram:
They are sectors p+q+r, notice that x was not included? Because x represents people who experienced SP, V, and D. The sectors in bold, represent the people who exactly two symptoms, for clarity

p: Represents people who experienced both SP and V.
q: Represents people who experienced both SP and D
r: Represents people who experienced both D and V.

The unknowns:
1. People who experienced exactly one of these symptoms.
2. People who experienced all three of these symptoms.

You should get into the habit of not mechanically applying the formula, but take a look at the Venn Diagram .

From the first list of unknowns, where is that represented in the Venn Diagram? Well, obviously, it's going to be as follows:
If we only look at SP, this contains more regions than we would want, we want the part of SP the excludes the overlaps.
Here are the following totals for all three groups.

Total SP: A+p+q+x
Total V: B + p + r + x
Total D: C + q + r + x

Now you should be asking yourself, do we want all those sectors? As you probably assumed, the answer is no. Why don't we want all those sectors? Because the sectors of interest are:

Only SP: A
Only V: B
Only D: C

What's left over?
The intersection of SP and V: p + p + x = 2p + x -> P is in both SP and V
The intersection of SP and D: q + q + x = 2q + x -> Q is in both SP and D
The intersection of D and V: r + r + x = 2r + x -> D is in both D and V.

This is what's meant by exactly two groups overlapping, elements common to two sectors and not the third.

It helps to refer to the Venn Diagram, to see exactly how these intersections are derived. It's easy to see those letters and get lost in the learning process, but this is a way to help distill the information, before you intuitively apply the formula (and not mechanically).

Okay now we sum up what we know.

35% of 300 are in p + q + r, so that means means 105 people in the study had exactly two symptoms.

We know that we care to get the people that are in A, B, and C (Refer to Venn Diagram). So using the supplied in formation

Sweaty Palms has 120 people, both from those 120, there are people who fall in p or q, we don't want that.
Vomiting has 90 people, we obviously don't want all 90. Some fall in the Sweaty palms group (p), others fall in the dizziness group (r).
Dizziness has 225 people, I think you can spot the pattern by now. We don't want the entire set of 225, some are in Sweaty Palms (q), others are in Vomiting (r)

The Sectors we do want are in bold:
SP= A + p+q + x
V= B + p + r + x
D = C + q + r + x

It's like we made a full circle, but we'll start plugging in values.

SP + V + D = A + p+q + x + B + p + r + x + C + q + r + x

We know know SP=120, V=90, D=225. We want ONLY A from the Sweaty Palms group, ONLY B from the Vomiting Group, ONLY C from the Diziness group.

Referring the color coded equation above, we do some simple algebraic manipulation to get it in this form.
I moved all the sectors of interest as the first three terms on the RHS.

In the form of sectors:
SP + V +D= A + B + C + p+ p + q + q + r + r + x + x + x
In the form of actual numbers
SP + V+ D= 120 + 90+ 225
SP + V+ D = 435

Now combining the representation that's in the form of sectors, with the representation that's in the form of actual numbers, we get

435 = A + B + C + p+ p + q + q + r + r + x + x + x
You will noticed x is counted three times, because it's where all three groups intersect. x contains people who were dizzy, vomiting, and had sweaty palms. Those poor people

Also, p is counted twice, because p happens to fall in both Sweaty Palms and Vomiting. q happens to be the people the people who were dizzy, and had sweaty palms, and finally r are people who were dizzy and vomiting. While you're reading along, just tick these guys off in the Venn Diagram.

Okay, so we get it in the final form, we're almost there.

435= A + B + C + 2p + 2q + 2r + 3x
435 = A + B + C + 2(p+q+r) + 3x

Now we know Total = 300. We know p+q+r = 105, but it looks like we don't know A + B +C (our areas of interest) AND x. But we can solve for x

Total = A + B + C + x + p + q + r

You might be looking at this, and thinking why is that different from the one we just derived, this one
435 = A + B + C + 2(p+q+r) + 3x

Here were started off the SP, V, D, so within those, some of our sectors were counted twice, and three times as discussed above. The one we will work with now, contains all individual sectors, don't think about groups, just think of the areas they occupy.

Again,

54= A + B + C + x + p + q + r
300 = A + B + C + x + 105
A + B + C= 300-105-x
A + B + C = 195-x

Looks like we're getting somewhere. Back to this formula, were it contains groups that are counted more than once
435 = A + B + C + 2(p+q+r) + 3x
We will sub in the following
p+q + r = 105
A + B + C = 195-x

435= 195-x + 2*(105) + 3x
435=195 + 210 + 2x
435 = 405 + 2x
435- 405 = 2x
30 = 2x
x=15

We know A + B + C = 195-x
and we know x=15
so
A + B + C=195-15
A + B + C=180

Now I hope you can see why those some sectors were counted twice, and others three times. The post you quoted had:
Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3

Group 1: SP; Group 2: V, Group 3: D
2-Group Overlaps: p+q+r
3-group overlaps: x

Taking the totals of of SP and V and D, subtracting the 2-Group Overlaps (p+q+r) two times and subtracting the three groups overlaps three times
leaves us with the unique regions A,B,C

To summarize, A, B, C were our areas of interest within SP, V, and D. To partition them we utilized totals of Sweaty Palms, which contained regions that fell in two other sectors, and one region that was shared by all three sectors. Same from the other Groups of Symptoms.

This should not be your process when solving it, but it helps to break it down while you're studying. So during the actual exam, you'll know how to parse the question, what information to utilize and HOW to utilize it to reach the answer.
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New post 28 Jun 2016, 05:45
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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


This is a 3-circle Venn Diagram problem. Because we do not know the number of unique items in this particular set, we can use the following formula:

Total # of Unique Elements = # in (Group A) + # in (Group B) + # in (Group C) – # in (Groups of Exactly Two) – 2 [#in (Group of Exactly Three)] + # in (Neither)

Next we can label our groups with the information presented.

# in Group A = # who experienced sweaty palms

# in Group B = # who experienced vomiting

# in Group C = # who experienced dizziness

We are given that 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.

We can solve for the number in each group:

# who experienced sweaty palms = 300 x 0.4 = 120

# who experienced vomiting = 300 x 0.3 = 90

# who experienced dizziness = 300 x 0.75 = 225

We are also given that all of the subjects experienced at least one of these effects and 35 percent of the subjects experienced exactly two of these effects.

This means the following:

# in Groups of Exactly Two = 300 x 0.35 = 105

Since all the subjects experienced at least one of the effects it means that the # in (Neither) is equal to zero. We can now plug in all the information we have into our formula, in which T represents # in (Group of Exactly Three).

Total # of Unique Elements = # in (Group A) + # in (Group B) + # in (Group C) – # in (Groups of Exactly Two) – 2 [#in (Group of Exactly Three)] + # in (Neither)

300 = 120 + 90 + 225 – 105 – 2T + 0

300 = 330 – 2T

30 = 2T

15 = T

Now that we have determined a value for T, we are very close to finishing the problem. The question asks how many of the subjects experienced only one of these effects.

To determine this we can set up one final formula.

Total = # who experienced only 1 effect + # who experienced two effects + # who experienced all 3 effects + # who experienced no effects

We can let x represent the # who only experienced 1 effect.

300 = x + 105 + 15 + 0

300 = x + 120

180 = x

Answer is D.
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New post 10 Oct 2016, 08:12
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Hi everyone,

Here's my video explanation of the question. Hope you enjoy!



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

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New post 29 Jun 2017, 18:35
Using Venn diagram,

sweaty palms = a+e+g+d
vomiting = b+e+g+f
dizziness= c+g+d+f
------------
Total = a+b+c+2d+2e+2f+3g which is d+e+f+2g more than the desired form of a+b+c+d+e+f+g
40%+30%+75% all show some condition = 145%
we can see that we have counted some people more than once and they add up to the extra 45%

i.e d+e+f are people counted twice and make up the 35% as given in the question
The remaining 45%-35%=10% must represent people who are triple counted or 2g=10% or g=5%

hence, d+e+f+g=40 or 40%, remaining 60% are the ones who show only one of the three effects or .6*300 = 180
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Re: Of the 300 subjects who participated in an experiment using virtual-re   [#permalink] 29 Jun 2017, 18:35

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