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

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100 = 40 + 30 + 75 - (35 +3x) + x

x = 5

Attachments Capture.JPG [ 17.05 KiB | Viewed 2788 times ]

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

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

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kabirchaudhry92 wrote:
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".

While the above is not how I would have done the question, it is actually correct. The question is asking us for the number of people who experienced exactly one effect, which is the total minus the 2-group overlaps minus the 3-group overlaps. Because we can write the total as:

Total = Group 1 + Group 2 + Group 3 - 2-group overlaps - 3-group overlaps * 2

if we subtract from this total the 2-group overlaps and the 3-group overlaps, we get:

Group 1 + Group 2 + Group 3 - 2-group overlaps - 3-group overlaps * 2 - (2-group overlaps + 3-group overlaps)

which is equal to

Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3

For those who are thinking about how to do questions like this most efficiently, here are my GMAT Timing Tips for this question (the links have growing lists of questions that you can use to practice these tips):

Three-set Venn Diagrams: I recommend starting three-set Venn Diagram questions by drawing the diagram. We can write in all of the numbers we have been given, realizing that we are told that there are 0 people who have experienced none of the side effects. Then, we need to recognize that the total percent (100%) is equal to the sum of the percents in each group (145%) minus the percent we double counted because there are in exactly two groups (35%) minus 2 times those we double counted because they are in all three groups (I would call this X3, because we need to solve for this). We would find that X3 = 5%.

Write down what the question is asking: While this applies to all Quant questions, it is especially important here. If we wrote down that we needed to solve for the total (100%) minus those in exactly two groups (35%) minus those in all three groups (X3) and convert this percent to a number of people (total number is 300), we can quickly answer the correct question when we finish solving for the number in all three groups. For example, I would have written what I was solving for as: (100% - 35% - X3) of 300 = ?

Please let me know if you have any questions about my tips, and if you would like me to post a video solution.
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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1
Bunuel wrote:
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.

Hi dave13,
In case your doubt regarding this question is not cleared here it is .
First I will explain the derivation of both the formulas and then you can find its application.

refer to advanced-overlapping-sets-problems-144260.html for the pictorial representation.

Only A= a, only B=b, only C=c ,
only A&B =d, only A&C =e , only B&C=f, These are exactly two group overlaps.
A&B&C = g all three group over laps
Two group overlaps d+g , e+g,f+g.

Now Each element is of certain value that adds up to total of the group. ie
a+b+c+d+e+f+g+n=T, where n=none .
Now Set A= a+d+e+g, We will take into account all the elements the construct the Set which is the value of Only A+only A&B+only A&C+A&B&C. This is how set A is build.
Set B= b+d+f+g We will take into account all the elements the construct the Set which is the value of Only B+only A&B +onlyB&C+A&B&C
Set C=c+e+f+g We will take into account all the elements the construct the Set which is the value of Only C+only A&C +onlyB&C+A&B&C

Well there are two Basic Formulas for three overlapping sets

T= A+B+C- (sum of exactly two over-lapping sets)-2(all three) +none
lets understand how is it constructed

First part
A+B+C= (a+d+e+g)+(b+d+f+g)+(c+e+f+g )

A+B+C=a+b+c+2d+2e+2f+3g. To cancel out the additional (d,e,f and the two g's that we got subtract them so that our final result is T= a+b+c+ d+f+e+g+n

Second part Removing the additional d,e,f and 2g
This can be done in two ways where each way gives us a formula

Method 1

Remove the exactly two group elements and remove twice of element that belongs to all three groups )
Elements that belong to exactly two group are d,e,f and element that belongs to all three groups is "g"

T= a+b+c+2d+2e+2f+3g- d-f-e-2g
T=a+b+c+d+e+f+g
add the final element "n" to get the total T
T=a+b+c+d+e+f+g+n
Hence the formula
T= (a+d+e+g)+(b+d+f+g)+(c+e+f+g )-(d+e+f)-2(g)+n
T= A+B+C- (sum of exactly two over-lapping sets)-2(all three) +none

Method 2
Removing can also be done by removing the two overlap groups ,
So the elements of the this group are (d+g,e+g,f+g)
T= a+b+c+2d+2e+2f+3g -d-g-e-g-f-g
T= a+b+c+d+e+f We dont have element"g" which completes the total
So to undo this effecy we add an element "g" which is nothing but element belonging to all three sets
T=a+b+c+d+e+f+g+n
SO this gives us the second formula.
T= A+B+C- (sum of two over-lapping sets)+all three +none
T= (a+d+e+g)+(b+d+f+g)+(c+e+f+g ) - ( d+g+e+g+f+g)+(g)+n

No Coming back to the question

We are given certain information , is 40 % of 300 = 120, 30% of 300= 90 and 75%of 300=225 and 35 % of 300=105.
let Sweaty Palms be A= a+d+g+e=120,
Vomiting be B=b+d+f+g= 90,&
Dizziness be C=c+e+f+g=225,
also exactly two of the three effects be " sum of exactly two over-lap groups"= d+f+e= 105.
We are asked to find a+b+c=?

So first I will use the formula T= A+B+C- (sum of exactly two over-lapping sets)- 2(all three) +none and calculate all three.

Why do we need to calculate that since T=a+b+c+d+e+f+g, we are given the values of d+f+e but not g. If we can calculate value of g we can find a+b+c= T-(d+e+f+g)
Let all three symptoms be x then,
120+90+225-105-2(x)+0=300
2(x)=30
so x=15
Now to calculate a+b+c i will use the first formula
T=a+b+c+d+e+f+g+n
we know that d+e+f= 105, and g=15
300=a+b+c+105+15
a+b+c=300-(105+15)
a+b+c= 180.

Let me know if there is something you need more help on, will try my best.
Probus
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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1
First, let’s find the number of participants that experience the listed symptoms.

Since $$40\%$$ reporting sweaty palms, that’s $$\frac{40}{100} \times 300=120$$ participants experiencing this symptom. Similarly, there are

$$\frac{30}{100} \times 300=90$$ participants reporting vomiting and $$\frac{75}{100} \times 300=225$$ who reported experiencing dizziness.

Also, $$\frac{35}{100} \times 300=105$$ have experienced two of the effects.

We can construct a Venn diagram to better visualize the problem.

Attachment: venn 1.jpg [ 17.68 KiB | Viewed 1356 times ]

The intersections between two circles represent the participants who have experienced two symptoms. I’ve shaded it in purple to better understand it.

Attachment: venn 2.jpg [ 17.58 KiB | Viewed 1356 times ]

If we let $$x$$ be the number of participants who experienced all three, we have

Attachment: venn 3.JPG [ 16.58 KiB | Viewed 1356 times ]

If you add up all the number of reports, we have $$225+120+90=435$$. That’s clearly more than the number of participants and the reason behind this is that people who reported two effects were also accounted for in the individual effect report.

For example, participants who reported vomiting AND dizziness are accounted for twice since their report will be counted in the group reporting Dizziness and in the group reporting vomiting. In addition, people who reported three symptoms were counted thrice.

This means that there is an extra $$105$$ and extra $$2x$$ in the count. So, if this gets subtracted from the total, then it must now be $$300$$.

$$435-105-2x=300$$
$$330-2x=300$$
$$30=2x$$
$$x=15$$

So, we have exactly $$105$$ people reporting two symptoms and $$15$$ people who have reported all three.

This means that there are $$300-105-15=180$$ participants who only experience one symptom.

Hence, The final answer is .

Originally posted by EMPOWERMathExpert on 03 Oct 2018, 05:08.
Last edited by EMPOWERMathExpert on 07 Oct 2018, 18:16, edited 1 time in total.
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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1
this is hard. for some problem, number of persons who experience 2 symptom , not ONLY TWO EFFECT, is given and the formular is different.
N=a+b+c-(ab+bc+ca)+abc if ab,bc,ca is the number of person who experience 2 symptoms
N=a+b+c-(ab+bc+ca ) -2abc, if ab,bc,ca is the number of persons who suffer ONLY 2 symptoms

this is the point for 3 circle problems
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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This question can be solved using a Venn diagram.

Attachment: vvv.png [ 15.94 KiB | Viewed 1273 times ]

Number of:
Sweaty $$= 40\% = A$$
Vomiting $$= 30\% = B$$
Dizziness $$= 75\% = C$$

Now we need to use formula for Venn diagram.

$$A∪B∪C=A+B+C-(A∩B+B∩C+C∩A)+2 \times A∩B∩C$$

$$A+B+C→one \ symptom$$

$$A∩B+B∩C+C∩A→total \ number \ of \ patients \ with \ 2 \ symptoms$$

$$A∩B∩C→3 \ symptoms$$

$$300=300(40\%)+300(30\%)+300(75\%)-300(35\%)-2(x) \\ 300=120+90+225-105-2x \\ x=15$$

$$15$$ people had $$3$$ symptoms. Now we can use this to find the number of people with 2 symptoms.

$$300=120+90+225-y+3(15) \\ y=180$$

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

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I prefer to solve this question conceptually.

Total Students (Ts) = 300
Number of students with sweaty plans = 40% of 300 = 120
Number of students with vomiting issues = 30% of 300 = 90
Number of students with dizziness issues = 75% of 300 = 225
Total number of students with issues = 120 + 90 + 225 = 435

So we have 300 students with 435 students experiencing issues that means a total of 135 students with multiple symptoms.

Now we have been told 105 students had dual symptoms that mean these students have been counted twice and can be removed
Hence 435 – 105 = 330

So now we have an extra count of 30 students who are a part of the group with 3 symptoms. We divide the extra value by 2 i.e. 15 students have 3 symptoms.

Now we have enough information to calculate the: Number of students with only 1 symptom
= Ts – Number of students with 2 symptoms – Number of students with 3 students
= 300 – 105 – 15
= 180

Hence D is the correct answer.
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Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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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

Let S+V+D+A+B+C+X = 300 --(1)
S+A+B+X = 120 {Sweat} --(4)
V+A+C+X = 90 {Vomiting} --(5)
D+B+C+X = 225 {Dizzy} --(6)
A+B+C = 105 --(2) {exactly 2 symptoms}
(1)-(2),
S+V+D+X = 195 --(3)
(4)+(5)+(6),
S+V+D+3x = 225

Let U = S+V+D
U+3X = 225 --(7)
U+X = 195 {subtituting (2) in (1)} --(8)
Solving (7) & (8), we get,
[color=#ec008c]U = 180
(option D)

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

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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

My reasoning:

Since everything is in percent form we don't need to convert anything into numerical values until the end (looking at the answer choices).

After reading through the passage, you can see every value is given to you except the percent of people who experienced ALL THREE symptoms. We'll need to find that out.

So %Dizziness + %Vomitting + %Sweaty Palms - %both - 2*%three = 100%

40 + 30 + 75 - 35 - 2*three = 100

Three = 5

Working backwards to get the number of people who experienced only one symptom, we will subtract out all the values of both and three.

40 + 30 + 75 - 2*35 - 3*5 = 60

60% of 300 = 180 (Answer choice D)
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Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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New solution using total person & total symptom equations:

1. # of symptoms = V + D + M = 300*(.3+.75+.4) = 435. (I)
#of symptoms = 1*(people with 1 symptom: o) + 2*(people with 2 symptoms: w) + 3*(people with 3 symptoms: r) (II)
Rewriting (II)
435=1*o+2*.35*300+3*r -> 225=o+3r

2. Population equation: 300 = o + w + r -> o+r=195 (III)

3. Solving for r using (II) and (III): r=15

4. solving for o using (III): o = 195-15=180.
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GMAT 1: 640 Q47 V32 Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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Step 1: Assume
a- one only
b- two overlap
c- three overlap
---------------------------------------------------
Step 2: There are two equations which are to be used in this questionNet total:
a + b + c = 300.
Gross total :
a + 2b + 3c = 435 [300*.4 + 300*.30 + 300*.75 = 120 + 90 + 225 = 435]
----------------------------------------------------
Step 3. Solve for values:

We are given b = .35*300= 105 , now solve the two equations for a and c to get
c= 15
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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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

In the last step why did we do 2-group overlaps * 2 - 3-group overlaps * 3
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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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

I think I have a simpler, a bit non-traditional way of looking at it (refer to the diagram attached)

40% + 30% + 75% = 145%, which is 45% more than 100%, and this 45% is attributed to all the elements which are counted more than once, i.e. d + e + f + 2g = 45% - (1)

We are given in the question stem that d + e + f = 35% - (2), and from (1) and (2), we get 2g = 10% and g = 5%

NOW, a + b + c + d + e + f + g = 100% (since all of the subjects experienced at least one of these effects)

a + b + c + 35% + 5% = 100%, which gives us a + b + c (subjects who experienced only one of these effects) = 60%, and 60% of 300 = 180 and our answer is (D) HIT KUDOS IF YOU FIND THIS SOLUTION HELPFUL Intern  B
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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EMPOWERMathExpert, can this question be solved also with a tic tac toe board as Rich has shown in the EmpowerGMAT course?
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Re: Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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I have got the correct answer but it took me approx 5mins.
Is it worth investing this much amount of time?
Is there any method by which it could be done within 2-3mins?
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Of the 300 subjects who participated in an experiment using virtual-re  [#permalink]

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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

Given: 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.

Asked: 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?

Total = G1 + G2 + G3 - (2 out of 3) - 2* ( All 3) + Neither
300 = 120 + 90 + 225 - 105 - 2x + 0
2x = 435 - 300 - 105 = 30
x = 15

Number of the subjects experienced only one of these effects = Total - (2 out of 3) - (all 3) = 300 - 105 - 15 = 180

IMO D Of the 300 subjects who participated in an experiment using virtual-re   [#permalink] 26 Aug 2019, 08:43

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