for these type of questions drawing venn diagrams
let studying only Aeronautics ,Biotech and Cryogenic be a,b,c
studying both A and B but not c=d
studying both B and C but not a=e
studying both A and C but not b=f
studying all 3 be x
to maximise x everything else must be minimised
Now for 3rd question given cryogenics =100 => And B but not C =100
in order to do this the situation would be
d= x+1 (exactly two>exactly three ) (we maximised d and not e and f cause we wanted to minimise a and b)
e=0,f=0
only A,a =b+1, only b =b, cause A > B (x+x+1+b+1>x+x+1+b )
now C>A=> (x+a+d+1>x+a+d)=>only c= d+a+1=> total C =x+x+1+b+2
we have 2 equations
x+x+1+b+2=100
2x+b=97---------------(2)
2x+b+3 +x+1+2b+1=20
3x +3b =195-----------(1)
solving x=32
Will change this only when I get into a B skool of my choice....