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Louis14
Joined: 01 Nov 2019
Last visit: 04 Nov 2023
Posts: 249
Given Kudos: 472
Schools: NUS MiF "22 (A) LSE MFin "22 (S) HEC MFin "22
GMAT 1: 680 Q48 V34
GPA: 3.56
03 Mar 2020, 16:13
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I'm right at the end of my GMAT prep, and apparently just when I thought there couldn't be any thing left that I haven't prepared for, the specter of 3 sets Venn Diagram questions said, "hold my bear" 
Based on my research, I've realized that there are two formulas to tackle these daunting questions:
Formula One: Total=A+B+C−(AnB+AnC+BnC)+AnBnC+Neither
Formula Two: Total=A+B+C− {Sum of Exactly 2 groups members} −2∗AnBnC+Neither
Could anyone please explain when to use which formula?
Thanks.
Based on my research, I've realized that there are two formulas to tackle these daunting questions:
Formula One: Total=A+B+C−(AnB+AnC+BnC)+AnBnC+Neither
Formula Two: Total=A+B+C− {Sum of Exactly 2 groups members} −2∗AnBnC+Neither
Could anyone please explain when to use which formula?
Thanks.
shameekv1989
GMAT 3: 720 Q50 V38
Posts: 820
03 Mar 2020, 16:36
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Louis14
Hey Louis14, All the best with your final preparations.
For this you basically need to understand why you subtract twice in one formula and why add in the other.
A - Exactly one group members in A + Exactly 2 Group Members in AB and AC + Exactly 3 group members in ABC
B - Exactly one group members in B + Exactly 2 Group Members in AB and BC + Exactly 3 group members in ABC
C - Exactly one group members in C + Exactly 2 Group Members in AC and BC + Exactly 3 group members in ABC
Thus when you add A+B+C = Exactly one group members individually in A, B and C + 2 (2 group members of AB, BC and AC) + 3 (3 group members of ABC)
Finally you want Total = Exactly one group members of A, B and C + Exactly 2 group members of AB, BC and AC + Exactly 3 group members of ABC
Thus as you can see when you add A+B+C you have added an extra (Exactly 2 group members of AB, BC and AC) and have added 2 extras of (Exactly 3 group members of ABC) - This is to say when those AB, BC and AC sets given to you do not include 3 group members.
Thus you subtract the extras to get the final total.
Formula 2 is valid when AB, BC and AC sets include those 3 group members of ABC. If that is the case :-
2 group members of AB and AC; 2 group members of AB and BC; 2 group members of AC and BC will include 3 group members in them as well. Thus when you are subtracting once from A+B+C, you are essentially subtracting 3 the (3 group members). But you need one time the 3 group members of ABC to count them in the total. Hence you add once the 3 group members.
I don't how clear was the above explanation, but I hope it does give a lil better understanding.
04 Mar 2020, 00:09
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