Actually there is no need to use Venn diagram at all for this question. It can be solved by simple logic and moreover it is more a language question rather than math question.

Solution
Number of people answer YES to first question:- N/4
i.e these N/4 people has answered either YES/NO to the second question.

Now read the sentence carefully "and of those". It means 1/3rd of N/4 people have answered YES also to the second Question. i.e N/12

i.e. The number of people who have answer to both questions as YES will be N/12 only.

So the total number of people who did not answer YES to both question will be N - N/12 = 11N/12.


P.S: If you have not mentioned the answer than definitely I would also be confused with choice (C).

We can solve it algebraically (Codesnooker's solution is perfect), but we can also solve by picking numbers.

In fraction questions with no given total, it's usually easiest to pick the common denominators of the fractions. Here we have thirds and fourths, so let's let N=12 (further, if we peek at the choices, 3 have 12 in the denominator, making 12 an even more attractive pick).

Q1: 1/4 said "yes", so that's 3 yesses

Q2: 1/3 of the previous 3 yesses also said "yes", so that's 1 yes

So, we have 1 person who said "yes" to both, leaving us with 11 who did NOT say "yes" to both.

11/12: pick (e).

You could have done the same thing with N=300, it just makes both the math and matching up with the correct answer much trickier.

I am confused about this answer because the question asks for "number of people interviewed who did not answer 'yes' to BOTH questions". 11N/12 includes people who said "NO" to the first but "YES" on the second as well as "YES" to the first but "NO" on the second. Shouldn't the proper answer to the stated question be N/2?

chosters,
I think you are misreading the question as:

"number of people interviewed who answered 'NO' to BOTH questions"
or
"number of people interviewed who did not answer 'yes' to EITHER question"

***

"number of people interviewed who did not answer 'yes' to BOTH questions" - means those people that said:

NO YES
YES NO
NO NO

Make a lot of sense. Thank you!!!