A clearer wording might be as follows:
In a statewide poll, Y people were asked two questions, the only answers to which were "yes" or "no." If 3/4 of the people answered "no" to question 1, and of those, 2/3 answered "yes" to question 2, which of the following expressions represents the number of people interviewed who did not answer "no" to both questions?
(A) Y/12
(B) Y/4
(C) Y/2
(D) 3Y/4
(E) 11Y/12
Let the total number of people = 12.
3/4 of them answered "no" to question 1.
Thus, the number who answered "no" to question 1 = (3/4)(12) = 9.
Of those, 2/3 answered "yes" to question 2.
Thus, of the 9 people who answered "no" to question 1, 1/3 also answered "no" to question 2:
(1/3)(9) = 3.
Which of the following expressions represents the number of people interviewed who did not answer "no" to both questions?
Since only 3 people answered "no" to both questions, the number of people who did NOT answer "no" to both questions = 12-3 = 9. This is our target.
Now plug Y=12 into the answer choices to see which yields our target of 9.
Only
D works:
3Y/4 = (3*12)/4 = 9.
The correct answer is
D.
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