triple groups

Don't give up on Venn diagrams. I've attached mine to show you what my approach is.

Without using "%" everywhere, I expressed the following equations:

100 = (S + M + B) + (x + y + 30) - 2(m) ............. Eq 1

Where
S + M + B = Pple who only study one subject
x + y + 30 = Pple who study two or more subjects
m = Pple who study all three subjects (NOTE: Need to subtract 2(m) from Eq 1 because it is over-counted in [x + y + 30])

Also,
56 = S + x + 30 - m............. Eq 2
44 = M + 30 + y - m............. Eq 3
40 = B + x + y - m............... Eq 4

Add up Equations 2, 3 & 4, you get:
140 = S + M + B + 2(x + y + 30) - 3m............. Eq 5

Combine Eq 1 and 5 by substraction: (Eq 5)- (Eq 1)
40 = x + y + 30 - m
(x + y - m) = 10

Since we're trying to isolate B, substitute x + y - m = 10 into Eq 4, which gives you 30.

Remember 30 is the percentage of total students, so 30% of 400 = 120.

if you are stcuk with a complicated venn diagram ... do the POE

the answer can not me more than 40%... becuase this is total number of staudents who read biology.....

Option D and E are out ....

we have to look for a max numebr... if i'm in middle of the venn diagram and cant find the answer... i can be sure ... that its not A...

now if you are really short of time ... take a guess and you have a 50:50 chance ..... or put the values ... and check your answer ....

yes it is clear- I am wired not in the triple ven way. I am good at double matric charts and even triple venns but this one got me off my rocker. The logical approach of max and min values works better here. (for me atleast) thanks folks!