# Lesson: 3-Criteria Venn Diagrams

## Comment on 3-Criteria Venn Diagrams

### Thank you sir, your

Thank you sir, your explanations are clear and are the best I've ever got to have. The last question with 3 criteria seems to be very long to take out..﻿

### This question type is a real

This question type is a real time-killer. Fortunately, they are exceedingly rare on the GRE.

### I suppose another easiest

I suppose another easiest approach to solve this rare type of question directly could be something like this:

As we are given that: Total number of students, say T = 100.
Similarly, using symbols P,S and M to denote the number of physics, sociology and Music students respectively.
We have,
n(P) = 40, n(S) = 60, n(M) = 80.
Also,
n(PnS) = 7, n(SnM) = 46, n(PnM) = 36 and n(PuSuM) = 100.

now applying the venn diagram rule for 3 sets we get,

n(T) = n(P) + n(S) + n(M) - n(PnS) - n(SnM) - n(MnP) + n(PnSnM) + Complement of n(PuSuM)
Now, plugging in the corresponding values we get,
100 = 40 + 60 + 80 - 7 - 46 - 36 + 6 + (no. of students taking none of the courses)

Solving, we have-
The number of students taking none of the courses to be 3.