Hi,

In the question stem it says - no student majors in all
three subjects . But in statement B it says 40 of the students do not major in any of the three
subjects . Arent they contrary to each other ?

No, they are not contrary. The question is just fine.
If we represent majors in Maths,Computer Science and Biology as M,C,B then
no student majors in all three subjects -> n(M n C n B) = 0
40 of the students do not major in any of the three subjects -> n( M U C U B) = 250 - 40.
Coming to the problem,
Each student who majors in mathematics also majors in computer science -> M is a subset of C i.e. set M lies entirely in C, when we draw a Venn diagram.
So, n(M n C) = n(M) and n(M U C) = n(C)
So, n(M U C U B) = n(C U B)
As no student majors in all three subjects, there should be any elements common to M and B.
So, n(M n B) = 0
Let n(M n B) = x.
Number of students student who major in 2 of the 3 subjects is given by
n(M n B) + n(M n C) + n(B n C) = 0 + n(M) + n(B n C)
So, we need to find n(M) + n(B n C)
Given that 90 of the students major only in biology -> n(only B) = 90
From(1):
n(Only C) = 50
This means n(C) - n(M) - n(C n B) = 50.
So, n(M) + n(B n C) = n(C) - 50.

From(2):
n(C U B U M) = 210.
So, n(C) + n(only B) = 210.
So, n (C) = 210 - 90 = 120.

From(1) and (2):
n(M) + n(B n C) = n(C) - 50 = 120-50 = 70

Hence, C

Hey I couldn't draw this as a Venn diagram and upload this. Please draw a Venn diagram, then it will be easy to understand.
Draw it in such a way, M lies entirely in C and there will be no common part for M and B although C and B can overlap.

A good starting diagram of the situation could look like this



We must find x + y.

You must remember that "None" is a possibility.
The 0 in the center and the 90 come from the question prompt directly, and the other two 0's come from the fact that every Math major MUST also be a CS major. So, no one can be Math only, and no one can be just Math and Bio.

To answer the original question: The prompt says that no one is in the very center, but Statement 2 is addressing the "None" region.

The answer is C because we need both the CS-only number and the "None" number in order to get everything but x+y. Once we have that total of everything else (90 + 50 + 40 = 180), we can get x + y = 250 - 180 = 70.

Hope this helps.