Nationwide poll

[aroon7]

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

what is the question here?
number of ppl who didnot answer "YES" to first + who didnot answer "YES" to second question
or
number of ppl who didnot answer YES to first one AND didnot answer YES to second one also??

[hypik21]

I believe it is asking people who did not answer yes to BOTH questions..not either..so
1/4 said yes to first
1/3 of the 1/4th said yes to second

1/4*1/3=1/12...who said yes to both
11/12 is the answer

[uptowngirl92]

Q1 {N}
------------------------------------------------------------
YES {N/4} NO{3N/4}
--------------------- ---------------------
yes Q2 no Q2 yes Q2 noQ2
{N/12} {N/6} ????

I always approach these kinds of sums with flowcharts(for eg. #124).Here what we need is denoted by a question mark.i.e. NO on both questions.I don't understand this,we have no idea of how 3N/4 is broken up.Help??

[Vemuri]

Another way to tackle these kind of problem is to plug in numbers. Lets assume that the number of people interviewed N =60. The number of people who answer Yes to Q1 is 1/4N = 15. Of these 1/3N answered Yes to Q2, i.e. 5. So, in effect 5 people answered Yes to both the questions. So, 55 people did not answer Yes to both the questions.

Plug in the value of N in the answer choices & you will see that only 11N/12 ==> (11*60)/12 = 55. Hence E is the answer.

[sureshbala]

Another way to tackle these kind of problem is to plug in numbers. Lets assume that the number of people interviewed N =60. The number of people who answer Yes to Q1 is 1/4N = 15. Of these 1/3N answered Yes to Q2, i.e. 5. So, in effect 5 people answered Yes to both the questions. So, 55 people did not answer Yes to both the questions.

Plug in the value of N in the answer choices & you will see that only 11N/12 ==> (11*60)/12 = 55. Hence E is the answer.

This is fine but you should have gone for N = 12 and the choice E is easily marked as answer

[ikaplan]

I tried to solve this by plugging numbers as well. N=24, then # of ppl who answered 'yes' to the first question was 6, and to the second 2.

Where I went wrong: I added 6+2=8 and then I subtracted 8 from 24. I didn't realize that of those 6 who answered yes to Q1, only 2 qualified according to the criteria stated in the stem.

I hope questions like this one will definitely hone my skills and 'open my eyes' on the G-Day.