Lesson: 3-Criteria Venn Diagrams

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Can someone explain the formula for three overlapping sets? i don't get it since the video seems to be exhaustive enough to tackle 3 overlapping sets:
Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Thx in advance,
gmat-admin's picture

I've never been a fan of formulas for 3 overlapping sets, and I doubt that the test-makers would create a question that relied on a student memorizing the formula.

Actually, I should say formulaS. There are two:

#1) Total = Group 1 + Group 2 + Group 3 - (sum of all 2 or more overlaps) + (in all 3 groups) + none.

#2) Total = Group 1 + Group 2 + Group 3 - (sum of members in EXACTLY 2 groups) - 2(All three groups) + none

You are using a formula that incorrectly combines formula #1 and formula #2

In this question, we need to use formula #1

We get: 100 = 40 + 60 + 80 - (7 + 46 + 36) + 6 + none
Simplify: 100 = 97 + none

So, none = 3

Hey Bret, with this concept i was able to answear all the questions from the official guide related to this subject apart from question 203. Is there any chance you could help me, please ? The solution from the official guide is not understandable for me and I found another solution on GMAT-club where they used the formula you just wrote about, but is there any other way to solve this question with the concept we learned in this video ?
gmat-admin's picture

That's a VERY tricky question.

ceilidh.erickson provides a nice solution here: http://www.beatthegmat.com/plz-explain-official-guide-ps-q-178-t281640.html

Her response is the 2nd one listed in the thread.

i donno about you Brent but this question seems overly difficult and would take ~5 min time away from the 75 min I have for quant. You think it's worth even trying to understand this thoroughly? Or if I ever come across it just guess best and move on? Is it worth my time?
gmat-admin's picture

This is not a common question type on the GMAT, and I think most students will not see one on test day.
They can be quite time-consuming, so if you're behind time-wise, it's a GREAT candidate for guessing and moving on.

I guess Bennaghmouch is talking about the formula for 2 overlapping sets


@ alicia for me the algebraic approach was the easiest one

Can you please explain this with venn diagram,, i tried but failed.

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
gmat-admin's picture

Hi santhosh1989,

ceilidh.erickson provides a nice solution (using a Venn diagram) here: http://www.beatthegmat.com/plz-explain-official-guide-ps-q-178-t281640.html


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