Of the 200 students at College T majoring in one or more of

Question

Official Guide Venn Diagrams

Here's a question from OG13 #222, pg 184...and a few notes you should know about Venn Diagrams for the GMAT.
 https://www.gmatpill.com/problemsolving/og/222/222-small.jpg

https://www.youtube.com/watch?v=iHJyQBWh-E0

General Outline

You'll often see venn diagrams associated with word problems that involve an overlapping 
segment between two parts. In the example above, we have a group of students in one
 major and a group of students in another major.

Divide the Problem

Two Circles:   Each of these majors (chemistry and biology) are represented with the
 two circles.

Overlapped Portion:    Some people double-major - that's the overlapping shaded region. 
This is the portion that belongs to both circles. In the question above, this means students 
who major in both chemistry and biology.

Outside square Area:   Perhaps some students do not major in either chemistry or 
biology - this is represented by the portion outside of the two circles but within the box.

It is NOT necessarily equivalent to:

1 - circle1 - circle 2

You cannot simply subtract the value of each circle to find the area of this outside area. 
If the circles overlap, you would be double counting the overlapping region in your 
calculation. So do not fall into this trip!

Translate and Use the Hints  
In the above question, you are given information that "at least 30 students are not 
majoring in either chemistry or biology"---the keyword is "at least."

We don't know exactly how many students are in this "outside" area, but we know 
that at least 30 of them are there. So utilize this 30 to help you find the extreme 
range of how many students are double majoring.

Out of the 200 students, 30 of them are not involved with chemistry or biology.

So that must mean the remaining 170 are involved with chemistry or biology to some extent.

But comparing this 170 relevant students with the 130 chemistry majors and the 150
biology majors seems to show the numbers don't add up.

The combined 130 chem and 150 bio majors = 280 majors, which is a lot more than the
relevant students. So what exactly does this mean?

Please view the video for further explanation on how to set this problem up and 
think through it. Track your OG progress  here .

rajathpanta · Answer

Hi,

Here is my take.

Pls see the attached diagram.

Since it says atleast 30 it means that bio not major and chemistry not major can vary from 30 to 50.
This implies major in both can vary from 110 to 130

epiphany1 · Answer

Of the 200 students at College T majoring in one or
more of the sciences, 130 are majoring in chemistry
and 150 are majoring in biology. If at least 30 of the
students are not majoring in either chemistry or
biology, then the number of students majoring in both
chemistry and biology could be any number from
(A) 20 to 50
(B) 40 to 70
(C) 50 to 130
(D) 110 to 130
(E) 110 to 150

Of the 200 students at College T majoring in one or more of

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