BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Venn diagram with 3 intersecting sets

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 21
Joined: Mon Jul 01, 2019 8:40 am

Venn diagram with 3 intersecting sets

by Darkknightreturning » Sat Jul 20, 2019 11:24 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

The formula for 3 intersecting sets is Total=A+B+C−(AUB+AUC+BUC)+AnBnC + Neither
While solving some questions I came across the formula : Total = A + B + C - (sum of 2-group overlaps) - 2*(all three) + Neither
Is this correct? When 2 group overlaps are considered, aren't we substracting the all 3 intersection area already? $$$$
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Wed Jul 24, 2019 8:53 pm
Darkknightreturning wrote:The formula for 3 intersecting sets is Total=A+B+C−(AUB+AUC+BUC)+AnBnC + Neither
While solving some questions I came across the formula : Total = A + B + C - (sum of 2-group overlaps) - 2*(all three) + Neither
Is this correct? When 2 group overlaps are considered, aren't we substracting the all 3 intersection area already? $$$$
Both of them are correct. Let's understand each of them.

1. Total = A + B + C − (AUB + AUC + BUC) + AnBnC + Neither

In the above notations, AnBnC represents 'all three', AUB represents A and C, AUB represents A and C, and BUC represents B and C. Note that AnBnC is a part of all AUB, AUC, and BUC; thus, AnBnC is subtracted 3 times; it's count is missing, we must include it once, thus, AnBnC is added.

2. Total = A + B + C - (Sum of 2-group overlaps) - 2*(all three) + Neither

In the above notations, (Sum of 2-group overlaps) represents ONLY 2-groups or does not include 'all three' groups. Since in A, B and C, 'all three' is counted 3 times, we must subtract it 2 times so as to count it only once.

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Manhattan | GRE Prep Courses Boston | ACT Prep Courses San Francisco | Seattle IELTS Tutoring | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1