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by tapanmittal » Fri Jun 19, 2015 1:52 am
In a statewide poll, Y people were asked two questions, the only
answers to which were "yes" or "no." If 3
4 of them answered "no"
to question 1, and 2
3 of those 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
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Source: — Problem Solving |

by Ian Stewart » Fri Jun 19, 2015 2:01 am
I assume those are meant to be fractions, so 3/4 answer no to the first question, and 2/3 of those answer yes to the second question.

Then (3/4)Y people answer no to the first question. If 2/3 of these answer yes to the second question, the rest, or 1/3, must answer no. So (1/3)(3/4)Y = (1/4)Y answer no to both questions. The rest of the people, or Y - (1/4)Y = (3/4)Y, must have answered yes to at least one question.
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by GMATGuruNY » Fri Jun 19, 2015 2:36 am
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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by tapanmittal » Fri Jun 19, 2015 3:38 am
Thanks GMATGuruNY..I was missing on the keywords highlighted in red by you :)
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by Matt@VeritasPrep » Tue Jun 23, 2015 6:24 pm
I'm thinking Y - (No to Both), which is

Y - (3/4)*(1/3)*Y, or

Y - (1/4)Y, or (3/4)Y
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