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by shankar.ashwin » Sat Oct 08, 2011 2:33 am
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
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by Proleefeek111 » Sat Oct 08, 2011 3:29 am
shankar.ashwin 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
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
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by Anurag@Gurome » Sat Oct 08, 2011 4:01 am
shankar.ashwin 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
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.
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by GMATGuruNY » Sat Oct 08, 2011 4:15 am
shankar.ashwin 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.
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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