Last visit was: 18 May 2026, 05:44 It is currently 18 May 2026, 05:44
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2   3 
655-705 (Hard)|   Overlapping Sets|   Word Problems|                                 
User avatar
gabrielta
User avatar
Joined: 23 Jun 2025
Last visit: 15 Oct 2025
Posts: 4
Own Kudos:
3
Given Kudos: 63
Posts: 4
Kudos: 3
Of the 300 subjects who participated in an experiment using virtual-re 16 Aug 2025, 02:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[ltr]A∩B+B∩C+C∩A=A∩B+B∩C+C∩A = Exactly two - 3x (assuming A∩B∩C=xA∩B∩C=x)

You wrote as above, but there is 1 mistake. It must be: A∩B+B∩C+C∩A=A∩B+B∩C+C∩A = Exactly two + 3x (assuming A∩B∩C=xA∩B∩C=x), not -3x[/ltr]

Just for a more perfect response.

Cheers.
cyberjadugar
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,
Show more
User avatar
dhruvie
User avatar
Joined: 07 Sep 2025
Last visit: 09 Feb 2026
Posts: 18
Own Kudos:
4
Given Kudos: 33
Schools: XLRI PGDM'25 (S) ISB '26 (S)
Schools: XLRI PGDM'25 (S) ISB '26 (S)
Posts: 18
Kudos: 4
Of the 300 subjects who participated in an experiment using virtual-re 26 Sep 2025, 06:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can solve via Venn.


macjas
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
Show more

Attachments

image.jpg
image.jpg [ 3.99 MiB | Viewed 233 times ]

User avatar
DanTheGMATMan
User avatar
Joined: 02 Oct 2015
Last visit: 17 May 2026
Posts: 380
Own Kudos:
268
Given Kudos: 9
Expert
Expert reply
Posts: 380
Kudos: 268
Of the 300 subjects who participated in an experiment using virtual-re 21 Oct 2025, 07:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
No charts or venn diagrams:
User avatar
Swishy
User avatar
Joined: 19 Mar 2026
Last visit: 16 May 2026
Posts: 1
Posts: 1
Kudos: 0
Of the 300 subjects who participated in an experiment using virtual-re 03 May 2026, 09:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
To be really honest, I have figured the fastest way to solve these type of questions is what I call the "discrepancy method".

So according to question - there are total 300 subjects.

40% experience sweaty palms - 300 * 40% = 120
30% experience vomiting - 300 * 30% = 90
75% experience dizziness - 300 * 75% = 225

So, totalling these percentages we get = 435. But our original no. of subjects is 300. So there has been discrepancy of 135.

Now, if you visualize, the subjects who experience exactly two symptoms have been counted 2 times, for eg. once in sweaty palms category and other in say vomiting. Where they should be counted only once. So they will increase the discrepancy by * 1.

Similarly, subjects who experience exactly 3 symptoms have been counted 3 times instead of 1. So they will exceed the discrepancy by * 2.

We know from question stem that subject who experience exactly 2 symptoms = 35% of 300 = 105.

So, the extra 135 we are getting is from 105 (subjects with exactly 2 symptoms) * 1 + subjects with 3 symptoms * 2. (Transferring into equation if you want to - 135 = 105 * 1 + x * 2)

Thus, 135 - 105 = 2x
x = 15 = subjects with exactly three symptoms.

Thus, subjects with exactly 1 symptom is 300 - 105 - 15 = 180 subjects.

This method take time to click but once you do, you can solve any type of overlapping sets question in under 2 minutes.
   1   2   3 
Moderators:
Bunuel
Math Expert
110586 posts
Krunaal
Tuck School Moderator
852 posts