Nationwide Poll

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yvonne0923: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Mon Mar 07, 2011 8:43 pmFollowed by: 1 member; Thanked: 1 times

by yvonne0923 » Fri May 13, 2011 5:59 pm

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. 7/N
B. 6N/7
C. 5N/12
D. 7N/12
E. 11N/12

_________________________________________________________________________________________________

I don't get the answer E for this problem, since N/4 is the number of people who answered "yes" for the 1st question, and 1/3*N/4 = N/12 is the number of people who answered "yes" for the 2nd question. Then I used 1-(N/4)-(N/12) = 2N/3, which is the number of people who did not answer "yes" to both questions.
But why the answer is E?
anyone has idea about this?

Thanks.[/spoiler]

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Source: Beat The GMAT — Problem Solving | Fri May 13, 2011 5:59 pm

vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 amFollowed by: 14 members; Thanked: 105 times

by vikram4689 » Fri May 13, 2011 7:08 pm

Answer is E

Reason ,
No of people answered yes to Q1 & Q2 = (N/4)/3 = N/12
No of people who did not answered yes to Q1 & Q2 = N - N/12 = 11N/12

You missed the "of those" part in ques

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yvonne0923: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Mon Mar 07, 2011 8:43 pmFollowed by: 1 member; Thanked: 1 times

by yvonne0923 » Fri May 13, 2011 9:14 pm

vikram4689 wrote:Answer is E

Reason ,
No of people answered yes to Q1 & Q2 = (N/4)/3 = N/12
No of people who did not answered yes to Q1 & Q2 = N - N/12 = 11N/12

You missed the "of those" part in ques

N/12 is only for the number of people answered yes for Q2, but for Q1,we have to add up N/4.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat May 14, 2011 12:52 am

yvonne0923 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. 7/N
B. 6N/7
C. 5N/12
D. 7N/12
E. 11N/12

_________________________________________________________________________________________________

I don't get the answer E for this problem, since N/4 is the number of people who answered "yes" for the 1st question, and 1/3*N/4 = N/12 is the number of people who answered "yes" for the 2nd question. Then I used 1-(N/4)-(N/12) = 2N/3, which is the number of people who did not answer "yes" to both questions.
But why the answer is E?
anyone has idea about this?

Thanks.[/spoiler]

Let N=12.
Number who answered yes to question 1 = (1/4)*12 = 3.
Number who also answered yes to question 2 = (1/3)*3 = 1.
Number who didn't answer yes to both questions = 12-1 = 11. This is our target.

Now we plug N=12 into the answers to see which yields our target of 11.

Only answer choice E works:
(11/12)*N = (11/12)*12 = 11.

The correct answer is E.

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vikram4689: Legendary Member; Posts: 1325; Joined: Sun Nov 01, 2009 6:24 amFollowed by: 14 members; Thanked: 105 times

by vikram4689 » Sat May 14, 2011 8:45 am

mate you are not understanding the language of ques. "of those" means from the no. of people already described.therefore N/12 is no of people answered yes to q1 and q2

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buoyant: Master | Next Rank: 500 Posts; Posts: 106; Joined: Sat Mar 02, 2013 4:29 pm; Thanked: 4 times

by buoyant » Sat Dec 07, 2013 11:20 am

GMATGuruNY wrote: Let N=12.
Number who answered yes to question 1 = (1/4)*12 = 3.
Number who also answered yes to question 2 = (1/3)*3 = 1.
Number who didn't answer yes to both questions = 12-1 = 11. This is our target.

Now we plug N=12 into the answers to see which yields our target of 11.

Only answer choice E works:
(11/12)*N = (11/12)*12 = 11.

The correct answer is E.

Hi Mitch,

Could you please solve this question in Matrix method?
I am not getting the answer in that method. I am just stuck.

Thanks!

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Sat Dec 07, 2013 1:45 pm

Q1: 1/4 yes
Q1 & Q2: 1/4 * 1/3 = 1/12 yes

1 - 1/12 = 11/12 no

Answer E. 11N/12

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buoyant: Master | Next Rank: 500 Posts; Posts: 106; Joined: Sat Mar 02, 2013 4:29 pm; Thanked: 4 times

by buoyant » Sat Dec 07, 2013 6:40 pm

i created a matrix table..
2 columns : "yes to question 1 (y1)" and "not yes to question 1 (~y1)"
2 rows : "yes to question 2 (y2)" and "not yes to question 2 (~y2)"

given y1= N/4
y1 and y2 = 1/3 * N/4= N/12
So, ~y1= N-N/4=3N/4 and (y1~y2) = N/4-N/12= N/6

No idea, how to proceed from here to find (~y1~y2) .....

Please help.

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