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

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Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
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GMAT Date: 02-11-2015
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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, 03:55
1
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, 03:57
1
...................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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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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02 May 2015, 12:19
1
Total number of people = N
Total number of people who answered Yes to Q1 is 1/4 i.e. N/4
Out of "those", number of people who answered Yes to Q2 is 1/3
Here "Those" refers to the people who answered Yes to Q1.
Therefore number of people who answered Yes to Q1 and Yes to Q2 is N(1/4 * 1/3) = N/12
Number of people who answered No to both questions is thus N-(N/12) = 11N/12.
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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28 Feb 2017, 03:51
People who answered yes to question 1 = N/4
People among them who answered yes to question 1 who answer yes to question 2 = N/4*⅓ = N/12
People who did not answer yes to both question = N - people who answered YES to both question
= N -N/12 = 11 N/12. Option E
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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02 Mar 2017, 18:12
1
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

Since 1/4 of the people answered yes to question 1, (1/4)N answered yes to question 1. Since 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N answered yes to both questions 1 and 2.

Thus N - (1/12)N = 12N/12 - N/12 = 11N/12 DID NOT answer yes to both questions.

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

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15 Aug 2017, 13:08
PareshGmat wrote:
scofield1521 wrote:
I tried to do this question by making a table. But I was not able to get the answer!! have someone solved using table?
----------------------------------
| ----- | YQ1 | NQ1 |
----------------------------------
| YQ2 |
----------------------------------
| NQ2 |
----------------------------------
Total |

You require to change the row/column arrangement

Refer diagram below:

Attachment:
matrix.png

what does .........and of those, 1/3 answered "yes" to question 2,, i thought of this as N/4 * 1/3 = N/12 for 2nd question

so total Yes will be N/4 + N/12 = 4N/12 ..... please how total yes will be N/12
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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15 Aug 2017, 13:10
ScottTargetTestPrep wrote:
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

Since 1/4 of the people answered yes to question 1, (1/4)N answered yes to question 1. Since 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N answered yes to both questions 1 and 2.

Thus N - (1/12)N = 12N/12 - N/12 = 11N/12 DID NOT answer yes to both questions.

when you mentioned "Since 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N answered yes to both questions 1 and 2."

how (1/12)N becomes answered yes to both questions 1 and 2....... 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N so N/12 shub be for second question only
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In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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16 Aug 2017, 08:18
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

Multiplying the fractions is the fastest, I think, but you can also pick a number for N that is divisible by 4 and 3. Usually LCM works best.

Let N = 12

$$\frac{1}{4}$$ of the people answered "yes" to question #1.

$$\frac{1}{4}$$ of 12 = 3.

So 3 said yes to question #1.

"[A]nd of those" [people who answered yes to question 1], $$\frac{1}{3}$$ answered "yes" to question #2.

$$\frac{1}{3}$$ of 3 is 1 --> That one person is the only person who said "yes" to both questions.

That means 12 - 1 = 11 who did NOT answer yes to both.

11 out of 12 did NOT say "yes" to both: $$\frac{11}{12}$$N

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

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15 Jul 2019, 01:13
Bunuel wrote:
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.

Is their any other way of solving such questions? I didn't understand it completely.
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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15 Jul 2019, 07:39
hi, how can (1/12)N become yes to both questions 1 and 2....... 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N so N/12 should be for the second question only
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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23 Jul 2019, 14:24
eka9045 wrote:
Is their any other way of solving such questions? I didn't understand it completely.
eka9045, Hopefully this will suffice!

rnn wrote:
hi, how can (1/12)N become yes to both questions 1 and 2....... 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N so N/12 should be for the second question only

rnn, You have displayed a decent understanding of the question.
However, let's deep-dive!

The logic utilized:
Let's start small -
If 30% of people ate ice-cream, how many people did NOT eat ice-cream?
Clearly, By complement rule, we can say: Complement = Total - Given.
------> $$100 - 30 = 70$$%

if X = 0.3, then what is the value of NOT X?
Clearly, By complement rule, we can say: Complement = Total - Given.
------> it's $$0.7$$.
Now, sum it up: If X is given as y%, then the value of NOT X = 100% - y%
The complement-logic is utilised in this question.

Do NOT worry about some-lame-random-number N. We will take care of it!

Argument
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?

Let's break the argument down to its core -
Given: If 1/4 of them answered "yes" to question 1
N = the Total Number of people interviewed.
Clearly, By complement rule, we can say: Complement = Total - Given.
Total = N | Given = $$N/4$$
Thus, the people who did NOT answer the 1st question as Yes: Complement = $$N - N/4 = 3N/4$$
Findings from Q1: Yes = N/4 | No = 3N/4

Given: of those, 1/3 answered "yes" to question 2
of those links to the people who already answered to the Q1 as Yes, i.e., $$N/4$$
Thus, of N/4 people,
1/3 of $$N/4$$ answered "yes" to Q2
If 1/3 of $$N/4$$ answered "yes" to Q2, then how many people of $$N/4$$ did NOT answer yes?
Clearly, By complement rule, we can say: Complement = Total - Given.
Total = N/4 | Given = 1/3 of $$N/4$$
Thus, the people who did NOT answer the 2nd question as Yes: Complement = $$N/4 - (1/3)(N/4) = (2/3)(N/4)$$
Remember, the people in this set already marked YES to Q1 -
Findings from Q1 and Q2: (Q1)Yes, (Q2)Yes = (1/3)(N/4) | (Q1)Yes, (Q2)No = (2/3)(N/4)

Question: Which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?
Find the number of people interviewed who did NOT answer "yes" to both questions:
Clearly, By complement rule, we can say: Complement = Total - Given.
Meaning: The number of people who did NOT answer "yes" to both questions = Total - who answered YES to both questions
Total = N | who answered YES to both questions = (Q1)Yes, (Q2)Yes = (1/3)(N/4)

The number of people who did NOT answer "yes" to both questions = $$N - N/12 = 11N/12$$
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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14 Nov 2019, 06:59
Let’s say N = 24 people. This is a nice number as its divisible by 4 and 3.

Q1 Yes: 6
Q2 Yes: 2

How many people said
Yes/No
No/Yes
No/No

These are all possible outcomes besides Yes/Yes, or 2/24.

1-2/24
1-1/12
11/12N
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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14 Nov 2019, 07:27
can anyone plz explain me this question?
why we are subtracting only 1/12?
why its not like 3/4+11/12=5/3
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Posts: 59561
Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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14 Nov 2019, 07:32
Pooja132 wrote:
can anyone plz explain me this question?
why we are subtracting only 1/12?
why its not like 3/4+11/12=5/3

Re: In a nationwide poll, N people were interviewed. If 1/4 of   [#permalink] 14 Nov 2019, 07:32

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