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.
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