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Official guide 11th Ed. PS question # 180

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Official guide 11th Ed. PS question # 180

by mlane25269 » Fri Jun 27, 2008 4:52 pm
Hi,

I'm hoping someone can tell what I'm doing wrong on this question. The question reads:

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


OA is "E" and I solved this problem by picking numbers and making N=12 and theoretically I would think that the number of people did not answer yes would = 8 because 1/4 of N = 3 and 1/3 of 3 = 1 for a total of 4 who answered yes to both questions. So 8 should be the value for the number of people who did not answer yes to both questions but when I plug N = 12 into answer E I don't get a value of 8.

What am I doing wrong?
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by AleksandrM » Fri Jun 27, 2008 5:46 pm
Pick a number for N.

I chose 24.

1/4 of 24 = 6. So you have 6 that said YES and 18 that said NO.

1/3 of the 6 = 2. So you have 2 that said YES and 4 that said NO.

You have 18 + 4 = 22 that did NOT answer yes to both questions.

Now, look at the answer choices:

24/7 will give you a fraction

6 x 24/7 will give you a fraction

5 x 24/12 = 10

7 x 24/12 = 14

11 x 24/12 = 22 Bingo!
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by tanviet » Fri Jun 27, 2008 6:17 pm
N/4 is number who anwser Q 1

1/3 of N/4 is N/12 . there is N/12 persons who answer Q2

N/12 is also the number who answer both question

so, N-N/12=11N/12 is the number who do not answer to both question

read the problem carefully, friends
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by mlane25269 » Fri Jun 27, 2008 9:05 pm
Ahhh that makes sense now...thanks!
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by TNgri » Mon Feb 09, 2009 4:43 pm
Can you please explain me people how you are solving this problem.
I did not understand how we just simply do N-N/12.

Problem states: ... N people, 1/4 of them answered "Y" to Q1, and of those, 1/3 answered "Y" to Q2.
Question: Which of the following expressions represents the number of people interviewed who did not answer "yes" TO BOTH QUESTIONS.

In my understanding, they are 3/4 who answered "N" to Q1, then narrowing down, the part of 3/4 who answered again "N" but to Q2. In other words, part of people who answered only N.
When we deduct N-N/12 we find people who did not answered 2Y, but who anwered either YN, or NY.

Please see attached image describing the problem.
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