PS OG Question: A big fight at home on this issue

Question

Hi all I think OG has lost it with this question. I don't agree that their answer is right. I think its not possible to find the answer with the options.. We have had a big fight over this at my home.. One thinks the answer is right, I think its wrong:

So here goes the question..

Q) 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

I think it is none of these.. Please explain as to why it is 11N/12

Here is my table from the above data..:

-----------Q1yes------Q1no-------Total
Q2yes------N/12
Q2no-------N/6
Total-------N/4--------3N/4----------N

Please explain.. before we have a third world war at home!

I tyhink it isall interpretation of this question.. confusing! I am going to be online for the next 30 mins.. want to solve this before the war goes too far

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willget800 · Answer

Oh I saw that the table did not draw up fine.. Although it looked fine in my view...

Will post it again..

celiaXDN · Answer

First 1/4 got the first one right

Second, 1/3 of the 1/4, which is 1/12 got the second right. This is also the percentage of people who got both questions right.

So the percentage of those who don't get both right is 1-1/12 =11/12

jinesh · Answer

Willget.... I took quite some time understanding this problem...and when i did..i cursed myself...for wasting so much time on this silly problem it goes like this.... it says...1/3 of the ppl for the question1 right...ok fine.... but then it says...1/4 of that 1/3 also got the 2nd question rite... 1/4*1/3 = 1/12 so this 1/12 includes total of ppl who got both question 1 and 2 rite... so no of ppl who got both wrong = 1-1/12 = 11/12 thats it ..... u can go and compromise with that person...he/she is rite !!

willget800 · Answer

Now I see it.. but somehow the question posed did not make me think like that.. I thought it meants noq1 and noq2.. anyways i did compromise...

SunShine · Answer

I think the best way to solve this problemis to take an exaple;

let's say there are 120 people, 1/4 say yes to Q1 that is 30 people. so 90 people say NO to Q1.

of these 30 people 1/3 say yes to Q2, that is 10 people. so 20 People say NO to Q2.

so total number of prople who did not answer YES to BOTH question is 90+20 =110

and so 110/120 =11/12

forlorn · Answer

the key here is that this phrase can be ambiguous. is this question asking for the number of people who answered No-No or is it asking for people who didn't answer Yes-Yes (as in number of people who answered Yes-No, No-Yes, and No-No)

this is just a bad question depends on how u read the sentence the meaning is different:
 who did not, answer yes to both. (YN,NY,NN)
 who did not answer yes, to both. (NN)

but since there is no answer choice with 'not enough information', one will have to assume the test makers meant the first case. It is unfortunate though if you just happen to take the second meaning, because you will end up wasting a lot of time just to realize that you took the wrong fork created by an ambiguous question.

I suppose the moral of the story is to identify when ambiguities exist before commiting too much time to one interpretation.

PS OG Question: A big fight at home on this issue

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