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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
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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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02 May 2015, 12:19
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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24 Sep 2015, 23:21
Bunuel , will you please solve it via matrix table?
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Re: In a nationwide poll, N people were interviewed. If 1/4 of  [#permalink]

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25 Sep 2015, 00:43
saroshgilani wrote:
Bunuel , will you please solve it via matrix table?

Check HERE and HERE.

Hope it helps.
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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.

Answer: E
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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

can somebody please explain me

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.

Answer: E

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

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

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