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OG 13 #178 - Virtual Reality

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OG 13 #178 - Virtual Reality

by wied81 » Tue May 01, 2012 12:51 pm
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.
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by mathbyvemuri » Tue May 01, 2012 5:53 pm
Hi wied81,
Please check, some information is missing in the Question
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by shantanu86 » Tue May 01, 2012 8:25 pm
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.
Hi wied81,

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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by GMATGuruNY » Wed May 02, 2012 4:22 am
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.
Here is a useful 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 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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by wied81 » Wed May 02, 2012 6:23 am
Thanks Mitch, that really helps.
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by theCEO » Sun Jul 01, 2012 6:38 am
GMATGuruNY wrote:
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.
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.

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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by GMATGuruNY » Sun Jul 01, 2012 7:06 am
theCEO wrote: Nice! Don't mean to be picky but typo in one of the steps.
Fixed the typo. Thanks for pointing it out!
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by talueng » Sun Nov 18, 2012 4:49 am
GMATGuruNY wrote: Here is the formula for 3 overlapping groups:

T = A + B + C - (AB + AC + BC) - 2(ABC)
Thanks, this is really useful. So, for 2 overlapping groups, it would be:
T = A + B - AB ?
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by GMATGuruNY » Sun Nov 18, 2012 5:00 am
talueng wrote:
GMATGuruNY wrote: Here is the formula for 3 overlapping groups:

T = A + B + C - (AB + AC + BC) - 2(ABC)
Thanks, this is really useful. So, for 2 overlapping groups, it would be:
T = A + B - AB ?
If every element must be a member of A, B or both:
T = A + B - AB.

If some elements belong to NEITHER group:
T = A + B - AB + N.
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by Gmatprep13 » Sun Dec 02, 2012 9:07 am
GMATGuruNY wrote:
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.
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.

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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by GMATGuruNY » Sun Dec 02, 2012 2:24 pm
Gmatprep13 wrote:
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.
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.
In the formula above, AB, AC and BC do not represent multiplication.
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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by Duaabasheer » Mon Dec 03, 2012 11:44 pm
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
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by zeza » Sun Dec 30, 2012 11:15 am
GMATGuruNY wrote:
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.
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.

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.
Can I ask why are we subtracting by 2x all 3 groups (... -2(ABC))?
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by Param800 » Mon Dec 31, 2012 8:30 am
Image

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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by alexander.vien » Mon Dec 31, 2012 12:14 pm
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.
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