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

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

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02 Nov 2003, 13:41
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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
[Reveal] Spoiler: OA
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20 Sep 2009, 08:13
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Those who answered yes to both questions = 1/4 x 1/3 = 1/12
So, answer = 1 - 1/12 = 11/12
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06 Oct 2010, 03:27
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nonameee 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

Bunuel, can you please look at this question. I personally got E for the answer. But after giving it some thought, I started to doubt it. My reasoning goes like this:

Total: 36

Yes to 1: 9
Yes to 1 and Yes to 2: 1/3 * 9 = 3

No to 1: 36-9 = 27
No to 1 No to 2: ?
No to 1 Yes to 2: ?

So, I don't know how we can calculate No 1 No to 2. I guess that's what the question asks.

Thank you.

No, the question asks for {No,No}, {No,Yes}, {Yes,No} any combination but {Yes,Yes}: "the number of people interviewed who did NOT answer "yes" to both questions".

If we use your example then: 1/4th of 36 or 9 people answered YES to question 1. Of those, 1/3 answered "yes" to question 2, so 1/3rd of 9 or 3 people answered YES to BOTH question 1 and 2. So YES to both questions answered 3/36=1/12 of N people interviewed and 1-1/12=11/12 of N people interviewed did NOT answer "yes" to both questions.

Hope it's clear.
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Re: In a nationwide poll, N people were interviewed. If 1/4 of [#permalink]

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24 Jul 2014, 00:50
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We require to find the value of shaded region (in pink)

Total students = n

Yes for Q1 $$= \frac{n}{4}$$

Yes for both Q1 & Q2$$= \frac{n}{4} * \frac{1}{3} = \frac{n}{12}$$

Remaining$$= n - \frac{n}{12}$$

$$= \frac{11n}{12}$$

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20 Sep 2009, 04:13
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barakhaiev wrote:
Can anyone, please, explain, why result is E? And post OA.
I am getting completely different result: 2/3N.
If there are 1/4N people answered yes to q1 and 1/3 of those answered yes to q2. Thus, people who answered yes to q2 is 1/12. and total no of people ans yes is 1/12+1/4=1/3N.

So, those who answered NO: N-1/3N=2/3N. What do I do wrong? help appreciated.

One of the GMAT tricks. Do not overcomplicate - they ask for the mumber of people who did not answer "yes" to BOTH questions, while you are calculating "not yes for ANY of the 2 questions"

E should be correct
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22 Sep 2009, 12:56
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barakhaiev wrote:
Ok, thanks. So does question asks ("of those") meaning of all people?

Nope. It's 1/3 of that 1/4 who answered yes to 1st question.

The math goes like this:

1/4 - yes to Q1
1/3 of 1/4 - yes to Q2 and Q1. 1/3 of 1/4 is 1/12 of the total number of people

The question asks simply how many people did are not included into that fraction, so we substract 1/12 from 1 as a whole, thus get 11/12
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11 May 2010, 07:29
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I solved it in a different approach (with a calculated guess):

N/4 says Yes to Q1. So, 3N/4 will say No to Q1.So, the final number has to be >=3N/4.

On looking the choices B and E remains. We cant have 7 in the denominator, so E is the answer

sudzpwc 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

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19 May 2010, 19:30
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So first we figure out what proportion of N did answer yes to both questions. 1/3 answered yes to #1 and of those 1/4 answered yes to #2. Thus 1/3 times 1/4=1/12N answered yes to both. Now it is simple subtraction to find those who did not vote yes on both. 11/12N. So the answer should be E.

Thanks,
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Re: In a nationwide poll, N people were interviewed. If 1/4 of [#permalink]

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03 Jan 2015, 02:55
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This is how I did it:

Yes to 2nd No to second Total
Yes to 1st...........10................20.............30
No to 1st................................................90
Total.....................................................120

So, I started by picking a number for the total: I picked 120 as a smart number (3*4=12, which are our denominators).
Then, 1/4 answered yes to the 1st question, so 120/4=30, which means that 90 must have answered no to 1st question (120-30=90); we don't need this, but it is an easy calculation and creates a complete table, just to be able to check for mistakes in the additions.

The problem also states that 1/3 of those who said yes to question one, said yes to question 2. So, 30/3=10, and as before 30-10=20 people said no to question 2.

At this point, we can already solve the question, since we are looking for those that didn't answer "yes" to both questions. From the table, there were 10 people out of 120 that answered yes to both questions, so 120-10=110 people did not answer yes to both questions.

Answer choice E ends up in 110: 11N/12= 11*120/12= 1320/12= 110.
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Re: In a nationwide poll, N people were interviewed. If 1/4 of [#permalink]

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03 Jan 2015, 02:57
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...................Yes to 2nd.........No to second........Total
Yes to 1st...........10.....................20..................30
No to 1st..........................................................90
Total...............................................................120

Just readding the table because it wasn't visible before. Hope it will be clear now!
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13 May 2009, 03:44
Q1 {N}
-------------------------------------------
YES {N/4} NO {3N/4}
--------------------- -----------------
yes Q2 no Q2 yesQ2 noQ2
{N/12} {N/6} ???

I always approach these kinds of sums with flowcharts(for eg. #124).Here what we need is denoted by a question mark.i.e. NO on both questions.I don't understand this,we have no idea of how 3N/4 is broken up.Help??
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13 May 2009, 05:36
You dug this up from the lost pages.

Anyway, E

Q1 Yes No
1/4N 3/4N (1-1/4)
Q2 1/4*1/3N 1-1/4*1/3N

i.e No to both the questions = 11N/12
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20 Sep 2009, 02:12
sudzpwc 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

Can anyone, please, explain, why result is E? And post OA.
I am getting completely different result: 2/3N.
If there are 1/4N people answered yes to q1 and 1/3 of those answered yes to q2. Thus, people who answered yes to q2 is 1/12. and total no of people ans yes is 1/12+1/4=1/3N.

So, those who answered NO: N-1/3N=2/3N. What do I do wrong? help appreciated.
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22 Sep 2009, 11:52
barakhaiev wrote:
Can anyone, please, explain, why result is E? And post OA.
I am getting completely different result: 2/3N.
If there are 1/4N people answered yes to q1 and 1/3 of those answered yes to q2. Thus, people who answered yes to q2 is 1/12. and total no of people ans yes is 1/12+1/4=1/3N.

So, those who answered NO: N-1/3N=2/3N. What do I do wrong? help appreciated.

One of the GMAT tricks. Do not overcomplicate - they ask for the mumber of people who did not answer "yes" to BOTH questions, while you are calculating "not yes for ANY of the 2 questions"

E should be correct

Ok, thanks. So does question asks ("of those") meaning of all people?
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23 Sep 2009, 04:37
barakhaiev wrote:
Ok, thanks. So does question asks ("of those") meaning of all people?

Nope. It's 1/3 of that 1/4 who answered yes to 1st question.

The math goes like this:

1/4 - yes to Q1
1/3 of 1/4 - yes to Q2 and Q1. 1/3 of 1/4 is 1/12 of the total number of people

The question asks simply how many people did are not included into that fraction, so we substract 1/12 from 1 as a whole, thus get 11/12

I got it...tricky.

Thank you very much for clarifying it, arkadiyua!
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23 Sep 2009, 10:46
Yes i too go with the answer of 11N/12. The trick here is the number of people who have not answered YES to both questions is not the same as the number of people who have answered NO to both questions. It could be that they had answered YES to only one of the questions or NO to both questions.
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24 Oct 2009, 22:32
E for me

But this question is somewhat unclear to me. There might be people who answer no in the question 1 but answer yes in the question 2.
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06 Oct 2010, 03:03
Bunuel, can you please look at this question. I personally got E for the answer. But after giving it some thought, I started to doubt it. My reasoning goes like this:

Total: 36

Yes to 1: 9
Yes to 1 and Yes to 2: 1/3 * 9 = 3

No to 1: 36-9 = 27
No to 1 No to 2: ?
No to 1 Yes to 2: ?

So, I don't know how we can calculate No 1 No to 2. I guess that's what the question asks.

Thank you.
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06 Oct 2010, 03:45
Yes, thanks a lot. I got the question wrong.
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Re: In a nationwide poll, N people were interviewed. If 1/4 of [#permalink]

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20 Dec 2012, 21:45
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How many of N said yes to question 1? N/4
1/3 of that said Yes to question 2: N/12

$$N - \frac{1}{4}*\frac{1}{3} = N - \frac{N}{12}= \frac{11N}{12}$$

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Re: In a nationwide poll, N people were interviewed. If 1/4 of   [#permalink] 20 Dec 2012, 21:45

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