178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
OG 13 #178 - Virtual Reality
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Hi wied81,
Please check, some information is missing in the Question
Please check, some information is missing in the Question
RaviSankar Vemuri
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Hi wied81,wied81 wrote:178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
The answer is clearly [spoiler][D][/spoiler] , 180
I solved it using Vein Diagrams.
Please google and use this approach for solving set related questions, instead of relying on formulas.
This approach should help you tremendously!!
If you feel like it, hit thanks
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Here is a useful formula for 3 overlapping groups:wied81 wrote:178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of the groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let T = 100%.
Sweaty palms = 40.
Vomiting = 30.
Dizziness = 75.
Exactly 2 of the groups = 35.
Let x = the percentage in all 3 groups.
Plugging these values into the formula, we get:
100 = 40 + 30 + 75 - 35 - 2x
100 = 110 - 2x
x=5.
Since 35% are in 2 of the groups and 5% are in all 3 groups, the percentage in exactly one of the groups = 100-35-5 = 60.
Number in exactly one of the groups = .6(300) = 180.
The correct answer is D.
Last edited by GMATGuruNY on Thu Dec 03, 2015 9:49 am, edited 3 times in total.
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GMATGuruNY wrote:Here is the formula for 3 overlapping groups:wied81 wrote:178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let T = 100%.
Sweaty palms = 40.
Vomiting = 30.
Dizziness = 75.
Exactly 2 of the groups = 35.
Let x = the percentage in all 3 groups.
Plugging these values into the formula, we get:
100 = 40 + 35 + 75 - 35 - 2x
100 = 110 - 2x
x=5.
Since 35% are in 2 of the groups and 5% are in all 3 groups, the percentage in exactly one of the groups = 100-35-5 = 60.
Number in exactly one of the groups = .6(300) = 180.
The correct answer is D.
Nice! Don't mean to be picky but typo in one of the steps.
100 = 40 + 35 + 75 - 35 - 2x: +35 should be +30
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Fixed the typo. Thanks for pointing it out!theCEO wrote: Nice! Don't mean to be picky but typo in one of the steps.
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If every element must be a member of A, B or both:talueng wrote:Thanks, this is really useful. So, for 2 overlapping groups, it would be:GMATGuruNY wrote: Here is the formula for 3 overlapping groups:
T = A + B + C - (AB + AC + BC) - 2(ABC)
T = A + B - AB ?
T = A + B - AB.
If some elements belong to NEITHER group:
T = A + B - AB + N.
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GMATGuruNY wrote:Here is the formula for 3 overlapping groups:wied81 wrote:178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let T = 100%.
Sweaty palms = 40.
Vomiting = 30.
Dizziness = 75.
Exactly 2 of the groups = 35.
Let x = the percentage in all 3 groups.
Plugging these values into the formula, we get:
100 = 40 + 30 + 75 - 35 - 2x
100 = 110 - 2x
x=5.
Since 35% are in 2 of the groups and 5% are in all 3 groups, the percentage in exactly one of the groups = 100-35-5 = 60.
Number in exactly one of the groups = .6(300) = 180.
The correct answer is D.
Hi GMAT Guru NY, I am lost. How does AB + AC + BC = 35 in the above. If you are multiply A(B) to get AB alone you would get 1200.
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In the formula above, AB, AC and BC do not represent multiplication.Gmatprep13 wrote:Hi GMAT Guru NY, I am lost. How does AB + AC + BC = 35 in the above. If you are multiply A(B) to get AB alone you would get 1200.Here is the formula for 3 overlapping groups:
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
Rather:
AB = the number of elements that are in both group A and group B (but NOT in group C).
AC = the number of elements that are in both group A and group C (but NOT in group B).
BC = the number of elements that are in both group B and group C (but NOT in group A).
Thus:
AB + AC + BC = the number of elements that are in exactly TWO of the 3 groups.
In the problem above, since 35 percent of the subjects experienced exactly 2 of the effects, AB + AC + BC = 35.
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Hello!
I had a similar question about this problem- I recognized that i had to draw a Venn diagram and subtract the overlaps. Here were my steps for solving this problem:
1) Drew venn diagram, identified areas of overlap and that some people have experienced 2 symptoms and others 3
2) Calculated the % of people who experienced each symptom:
Sweaty Palms: 120
Vomiting: 90
Dizziness: 225.......... Adding to a sum of 435
3) Calculated the % of people who experienced TWO symptoms: 105
4) Used the following equation to calculate the % of people who experienced THREE symptoms (x) :
435 - 105- x = 300
x=30
5) This led me to believe that the number of those who experienced only ONE symptom is 300-105-30= 165.
I have no clue where I went wrong.. this makes perfect sense in my head.
Any help is welcomed thanks in advance.
Duaa
I had a similar question about this problem- I recognized that i had to draw a Venn diagram and subtract the overlaps. Here were my steps for solving this problem:
1) Drew venn diagram, identified areas of overlap and that some people have experienced 2 symptoms and others 3
2) Calculated the % of people who experienced each symptom:
Sweaty Palms: 120
Vomiting: 90
Dizziness: 225.......... Adding to a sum of 435
3) Calculated the % of people who experienced TWO symptoms: 105
4) Used the following equation to calculate the % of people who experienced THREE symptoms (x) :
435 - 105- x = 300
x=30
5) This led me to believe that the number of those who experienced only ONE symptom is 300-105-30= 165.
I have no clue where I went wrong.. this makes perfect sense in my head.
Any help is welcomed thanks in advance.
Duaa
Can I ask why are we subtracting by 2x all 3 groups (... -2(ABC))?GMATGuruNY wrote:Here is the formula for 3 overlapping groups:wied81 wrote:178. 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
OA: D
I know that for 'both, neither' PS questions containing two variables it is nice to use the 'Group A + Group B + Neither - Both = Total' formula but for PS questions containing three variables, as this one does, is there a similar formula? These questions take up a big chunk of time, for me personally, and it would be nice to be able to plug in a formula if applicable.
Thanks in advance for any guidance.
T = A + B + C - (AB + AC + BC) - 2(ABC)
The big idea with overlapping group problems is to SUBTRACT THE OVERLAPS.
When we add together everyone in A, everyone in B, and everyone in C:
Those in exactly 2 of groups (AB+AC+BC) are counted twice, so they need to be subtracted from the total ONCE.
Those in all 3 groups (ABC) are counted 3 times, so they need to be subtracted from the total TWICE.
By subtracting the overlaps, we ensure that no one is overcounted.
In the problem above:
Let T = 100%.
Sweaty palms = 40.
Vomiting = 30.
Dizziness = 75.
Exactly 2 of the groups = 35.
Let x = the percentage in all 3 groups.
Plugging these values into the formula, we get:
100 = 40 + 30 + 75 - 35 - 2x
100 = 110 - 2x
x=5.
Since 35% are in 2 of the groups and 5% are in all 3 groups, the percentage in exactly one of the groups = 100-35-5 = 60.
Number in exactly one of the groups = .6(300) = 180.
The correct answer is D.
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Let me try to explain you why we are subtracting 2 * ( ABC )
So, our formula is this--
TOTAL = A + B + C - ( Sum of EXACTLY 2 group overlap)- 2*( all three) + Neither
Notice that EXACTLY (only) 2-group overlaps is not the same as 2-group overlaps:
Elements which are common only for A and B are in section d (so elements which are common ONLY for A and B refer to the elements which are in A and B but not in C);
Elements which are common only for A and C are in section e;
Elements which are common only for B and C are in section f.
Let's see how this formula is derived. Again: when we add three groups A, B, and C some sections are counted more than once. For instance: sections d, e, and f are counted twice and section g thrice. Hence we need to subtract sections d, e, and f ONCE (to count section g only once) and subtract section g TWICE (again to count section g only once).
When we subtract Sum of EXACTLY 2 group overlap from A + B + C we subtract sections d,e,and f once ( fine) and next we need to subtract ONLY section g TWICE.
For 3 set probability questions, I have developed ( or gathered ) these three basic formulas and I am able to solve any tough problem with it.
FIRST FORMULA -
TOTAL = A + B + C - ( Sum of 2 group overlap) + ( All three ) + Neither
SECOND FORMULA -
TOTAL = A + B + C - ( Sum of EXACTLY 2 group overlap)- 2*( all three) + Neither
THIRD FORMULA-
TOTAL = ( Exactly one group ) + ( Exactly 2 groups) + ( All three ) + Neither
I hope this clarifies your doubt
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Using the forumla for 3 overlapping sets this problem is not as difficult as it may seem.
(Set A) + (Set B) + (Set C) - (Total in 2 of 3 sets) - 2(Total in all 3 sets) + Neither
First off, notice the problem says everyone belongs to at least 1 of the groups. That eliminates the "Neither". Calculate the number of people for each of the individual groups -
Group A = 120
Group B = 90
Group C = 225
Total in 2 of the 3 groups = 105
Since we know the total is 300, we can setup the equation: 120 + 90 + 225 - 105 - 2(# in all 3 groups) = 300.
This simplifies to 330 - 2(# in all 3 groups) = 300 - for this to be true, 15 people must be in all 3 groups.
Theoretically, if we add the number of people in two groups (105) and the number in all three (15) and subtract it from the total, we can find the number of people that are in only 1 group.
300 - 120 = 180 people in only 1 group
The correct answer is D.
(Set A) + (Set B) + (Set C) - (Total in 2 of 3 sets) - 2(Total in all 3 sets) + Neither
First off, notice the problem says everyone belongs to at least 1 of the groups. That eliminates the "Neither". Calculate the number of people for each of the individual groups -
Group A = 120
Group B = 90
Group C = 225
Total in 2 of the 3 groups = 105
Since we know the total is 300, we can setup the equation: 120 + 90 + 225 - 105 - 2(# in all 3 groups) = 300.
This simplifies to 330 - 2(# in all 3 groups) = 300 - for this to be true, 15 people must be in all 3 groups.
Theoretically, if we add the number of people in two groups (105) and the number in all three (15) and subtract it from the total, we can find the number of people that are in only 1 group.
300 - 120 = 180 people in only 1 group
The correct answer is D.