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taneja.niks: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Tue Jun 29, 2010 9:41 am; Thanked: 2 times

by taneja.niks » Fri Sep 24, 2010 11:10 am

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: D
PLEASE EXPLAIN

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Source: Beat The GMAT — Problem Solving | Fri Sep 24, 2010 11:10 am

diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Fri Sep 24, 2010 11:44 am

taneja.niks 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

OA: D
PLEASE EXPLAIN

ummm i will solve the PS this following way
N/4 -> yes (1) => 3N/4 No (1)
n/4*1/3=N/12 yes (2) so N/4-N/12=1N/6 no (2)
the number both answer no is 3N/4-1N/6=7N/12

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Fri Sep 24, 2010 11:53 am

dear taneja
can you please verify OA!!!
sometimes it is misleading

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taneja.niks: Senior | Next Rank: 100 Posts; Posts: 70; Joined: Tue Jun 29, 2010 9:41 am; Thanked: 2 times

by taneja.niks » Fri Sep 24, 2010 11:58 am

sorry the answer is E

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Fri Sep 24, 2010 12:06 pm

taneja.niks wrote:sorry the answer is E

Ya answer should be E.

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diebeatsthegmat: Legendary Member; Posts: 1119; Joined: Fri May 07, 2010 8:50 amFollowed by: 3 members; Thanked: 29 times

by diebeatsthegmat » Fri Sep 24, 2010 1:54 pm

diebeatsthegmat wrote:
taneja.niks 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

OA: D
PLEASE EXPLAIN
ummm i will solve the PS this following way
N/4 -> yes (1) => 3N/4 No (1)
n/4*1/3=N/12 yes (2) so N/4-N/12=1N/6 no (2)
the number both answer no is 3N/4-1N/6=7N/12

oh yeah, dunno what i was thinking at 3 am lol....
N/12 people who answered both yes thus to find the people answered both no it shud be N-N/12=E
h i cant sleep!

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saurabhmahajan: Master | Next Rank: 500 Posts; Posts: 250; Joined: Thu Jan 07, 2010 2:21 am; Thanked: 10 times

by saurabhmahajan » Sat Sep 25, 2010 12:38 am

sorry ... but i still not understood.

please help me with the explanation.

Thanks and regards,
Saurabh Mahajan

I can understand you not winning,but i will not forgive you for not trying.

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fsutanto: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Sun May 30, 2010 2:34 am

by fsutanto » Sat Sep 25, 2010 1:07 am

Saurabh, I would answer it this way...

# of people who answered NO to question 1:
(3/4)N

# of people who answered YES to question 1 AND NO to question 2:
(1/4)N * (1 - 1/3) = (1/4)N * (2/3) = (2/12)N

Summing both the above leads to:
(3/4)N + (2/12)N = (9/12)N + (2/12)N = (11/12)N

So the number of people interviewed who did not answer to BOTH questions is (11/12)N, which is (E).

Trust this explains your question.

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limestone: Master | Next Rank: 500 Posts; Posts: 307; Joined: Sun Jul 11, 2010 7:52 pmFollowed by: 1 member; Thanked: 36 times; GMAT Score:640

by limestone » Sat Sep 25, 2010 3:53 am

To find the No. of people did not answer yes to both question, just find the no. of them that did say yes to both question, then subtract the total no. of people to the no. of who said yes to both.

No. of people said yes to 1st question: 1/4N
Of those said yes to 1st, 1/3 said yes to the second, hence no. of people said yes to both : 1/4N* 1/3 = 1/12*N

Thus no. of people did not say yes to both questions: 1N- 1/12*N = 11/12*N
Pick E.

"There is nothing either good or bad - but thinking makes it so" - Shakespeare.

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