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In a nationwide poll, P people were asked 2 questions. If 2/5 answered
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Bunuel
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  08 Aug 2016, 08:08
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P
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14101992
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  08 Aug 2016, 09:14
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no of people polled who did not answer “yes” to both questions = P - no of people polled who answered “yes” to both questions

no of people who answered yes for the 2nd question = 1/3 * 2/5 * P = 2/15*P

no of people polled who did not answer “yes” to both questions = P - 2/15*P = 13/15*P

Hence, E will be the answer.
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Senthil1981
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  Updated on: 08 Aug 2016, 09:34
Answer is B 3/5 * P

" If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2 "
As per this 2/5 P answered yes to q1 and 1/3 of those means answered yes to q2, which means 2/5*P includes the set of people who answered yes to both Q.
So it's just P - 2/5*P = 3/5 *P

Correct answer is 13/15
P - 2/5*1/3

Originally posted by Senthil1981 on 08 Aug 2016, 09:19.
Last edited by Senthil1981 on 08 Aug 2016, 09:34, edited 1 time in total.
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  08 Aug 2016, 09:24
Senthil1981
As far as I understand from the question, it says 1/3 of 2/5*P (who answered Q1 as yes) answered Q2 as yes. and 1/3 of 2/5*P will be 2/15*P. And P - 2/15*P = 13/15*P
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Senthil1981
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  Updated on: 08 Aug 2016, 09:36
Hi 14101992, you're right, I missed the "both" part.

Let's check the question once again
In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

2/5 answered yes to Q1, and "of those" also answered yes to Q2, which means 2/5 includes people who answered yes to Q1 and Q2.And the question is how many answered No, so it's just total - who answered yes. P - 2/5 P.

Originally posted by Senthil1981 on 08 Aug 2016, 09:30.
Last edited by Senthil1981 on 08 Aug 2016, 09:36, edited 1 time in total.
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  08 Aug 2016, 09:33
Hi 14101992,

you're right, I missed the both part. Please ignore my reply
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  09 Aug 2016, 11:34
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Bunuel wrote:
In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P



Yes xYes

Q1 2p/5

Q2 2p/15

Total 8p/15

8p/15 answered Yes for both the Qs. Therefore, number of people who answered xYes to both the Qs = p - 8p/15 = 13p/15

option E is the correct answer.
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  09 Aug 2016, 22:31
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What we need ? Total number of folks who dint say yes to both Q1 and Q2 in terms of P

ie : Q1N*Q2Y + Q1Y*Q2N + Q1N*Q2N

Q1N*Q2Y + Q1N*Q2N = 3/5P
Q1Y*Q2N = 4/15P

3/5 + 4/15 = 13/15P (E)

I wanted to draw a table with Q1Y Q2Y and Q1N and Q2N but could not align it properly
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  12 Aug 2016, 05:02
Answer E - 13P/15 is the correct answer
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In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  12 Aug 2016, 11:54
Bunuel wrote:
In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P


Take 300 as the total number of people (as it should be a multiple of 15, 2/5*1/3=2/15 hence for convenience we take 300 as P) Now 120 said Yes to 1 & out of them 40 said Yes to 2, so in the first case we are left with 180, and second case we are left with 120-40=80. The total who didnot say yes to both will be 180+80=260
Feed the value of P in the options. Only 13P/15 gives you 260. Hence E
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  12 Aug 2016, 21:36
yes to q 1 = 2P/5
yes to q1 and q2 = 1/3(2P/5) = 2P/15
no to q1 and q2 = P- (2P/15) = 13P/15
E
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  12 Jan 2018, 09:56
Bunuel wrote:
In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P


Hello Bunuel,
I don't seem to understand this.
Per the solutions, answer E will include some of the people who said yes to question 1 and that will make it wrong.
Unless my reasoning is not correct
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ScottTargetTestPrep
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  10 Aug 2018, 17:45
Expert Reply
Bunuel wrote:
In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P


The number of people who answered yes to both questions is (2/5)P x 1/3 = (2/15)P, so (13/15)P did not answer yes to both questions.

Answer: E
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CEdward
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Re: In a nationwide poll, P people were asked 2 questions. If 2/5 answered [#permalink] New post  23 Jan 2021, 14:02
Totally overthought this one. 6.5 minutes. I had the answer staring at me for a good 3.5 minutes.

In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes” to question 1, and of those 1/3 also answered “yes” to question 2, which of the following represents the number of people polled who did not answer “yes” to both questions?

A. 2/15*P
B. 3/5*P
C. 3/4*P
D. 5/6*P
E. 13/15*P

2P/5 = YES Q1
1/3(2P/5) = YES (Q2)

It follows that
2/3(2P/5) = NO (Q2)

2P/5 = YES Q1 ---> 3P/5 NO (Q1)

3P/5 + 2/3(2P/5) = 13/15

Answer is E.
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