Nationwide Poll

[shankar.ashwin]

In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

A) N/7

B) 6N/7

C) 5N/12

D) 7N/12

E) 11N/12

[Proleefeek111]

In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

A) N/7

B) 6N/7

C) 5N/12

D) 7N/12

E) 11N/12

First divide entity into 4 equal parts so each part = N/4

Divide one of those parts into 3 equal parts so each part = N/12

Since N/12 says 'Yes' to both questions (N - N/12 = 11N/12) said 'No' to atleast 1 question or DID NOT say YES to both questions. Hence E

[Anurag@Gurome]

In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

A) N/7

B) 6N/7

C) 5N/12

D) 7N/12

E) 11N/12

Number of people who answered "yes" to Q1 = N/4
Of the people who answered "yes" to Q1, number of people who answered "yes" to Q2 = (1/3)(N/4) = N/12
So, number of people who answered "yes" to Q1 and Q2, both = N/12
Therefore, number of people who did not answered "yes" to Q1 and Q2, both = 1- N/12 = 11N/12

The correct answer is E.

[GMATGuruNY]

In a nationwide poll, N people were interviewed. If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

A) N/7

B) 6N/7

C) 5N/12

D) 7N/12

E) 11N/12

Let N=12.
Number who answered YES to question 1 = (1/4)*12 = 3.
Of these 3 people, the number who also answered YES to question 2 = (1/3)*3 = 1.
Since only 1 person answered YES to both questions, the number who did not answer YES to both questions = 12-1 = 11. This is our target.

Now we plug N=12 into the answers to see which yields our target of 11.

Only answer choice E works:
11N/12 = 11(12)/12 = 11.

The correct answer is E.