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

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Manager
Joined: 14 Mar 2008
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In a nationwide poll, N people were interviewed. If 1/4 of [#permalink]

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04 Apr 2008, 12:49
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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

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Intern
Joined: 27 Mar 2008
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04 Apr 2008, 14:02
The easiest way to address this problem is to give N a value. Looking at the fractions in the problem "1/4" and "1/3" i would use a large number that has a common multiple (12), say 1200.

Working through the questions: 1/4 of 1200 = 300; 1/3 of 300 = 100. So those who did not answer yes to both questions is 1100 (1200 - 100).

Plug 1200 into N in the various answer choices and see which one gives you the answer 1100. Answer in the case is E (11N/12).

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Director
Joined: 14 Jan 2007
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04 Apr 2008, 18:43
It should be 'E'.

The trick in this question is to find out the common interviewees (who answered 'yes' to question 1 and 2 both)

Carefully reading the question stem, If 1/4 of them answered "yes" to question 1, and of those, 1/3 answered "yes" to question 2

Interviewees, who answered 'yes' to question 1 and 2 both are 1/4.1/3 = 1/12
Hence the left out will be the interviewees, who didi not answer 'yes' to both question,,i.e 11/12

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Re: PS: nationwide poll   [#permalink] 04 Apr 2008, 18:43
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