Let me elaborate
Let b represent the number of students part of both cooking and painting ( the common part of a two circle venn diagram)
b= 53 is given
Students for only cooking be a (Thereby total cooking students is a+53)
Students for only painting be c ( Thereby total painting students is c+53)
and n be the students - for neither cooking nor painting
( One may see the diagram in the previous message, hope the above elaboration helps)
Now we are asked how many are not a part of painting i.e a+n
Let us evaluate statement 1
It gives us b+c = 72 ---> c=19, but nothing on n -- Hence not sufficient
For statement 2
a+b =59, giving a=6, but we still dont have n -- hence not sufficient
Even if we combine both, not sufficient as we have nothing on n- Hence in my opinion - answer is E..
In nutshell my submission is we are asked how many are
NOT part of painting.
Until we know how many are not a part of both, we dont have sufficient data. Hence E is the answer.
Let me know your thoughts
P.S - I did study your solution and since the above is what I thought posted it.
Your replies are prompt. I appreciate that!
Bunuel
I don’t clearly see the notations you used, but here’s the logic:
We’re given b = 53 and asked to find a.
(1) gives b + c = 72, which only lets us find c = 19 but not a, so not sufficient.
(2) gives a + b = 59, and with b = 53, we get a = 6, so sufficient.
So the answer is B.
P.S. You quoted my solution but it seems you ignored it altogether and didn’t study it at all.