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In a nationwide poll, N people were interviewed. If 1/4

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In a nationwide poll, N people were interviewed. If 1/4

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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

OA=E

Source: Veritas Prep

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M7MBA wrote:
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

OA=E

Source: Veritas Prep
People to answered Yes to Q-1 = N/4

People who answered Yes to both Q-1 and Q-2 = (1/3)*(N/4) = N/12

i.e. People who did NOT answer yes to BOTH Q-1 and Q-2 = N - (N/12) = 11N/12

Answer: Option E

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M7MBA wrote:
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.
Number who also answered yes to question 2 = (1/3)3 = 1.
Number who didn't 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 E works:
(11/12)N = (11/12)12 = 11.

The correct answer is E.

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