In a nationwide poll, N people were interviewed. If 1/4 of

Q1 {N}
-------------------------------------------
YES {N/4} NO {3N/4}
--------------------- -----------------
yes Q2 no Q2 yesQ2 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??

Can anyone, please, explain, why result is E? And post OA.
I am getting completely different result: 2/3N.
If there are 1/4N people answered yes to q1 and 1/3 of those answered yes to q2. Thus, people who answered yes to q2 is 1/12. and total no of people ans yes is 1/12+1/4=1/3N.

So, those who answered NO: N-1/3N=2/3N. What do I do wrong? help appreciated.

One of the GMAT tricks. Do not overcomplicate - they ask for the mumber of people who did not answer "yes" to BOTH questions, while you are calculating "not yes for ANY of the 2 questions"

E should be correct

Ok, thanks. So does question asks ("of those") meaning of all people?

Nope. It's 1/3 of that 1/4 who answered yes to 1st question.

The math goes like this:

1/4 - yes to Q1
1/3 of 1/4 - yes to Q2 and Q1. 1/3 of 1/4 is 1/12 of the total number of people

The question asks simply how many people did are not included into that fraction, so we substract 1/12 from 1 as a whole, thus get 11/12

So first we figure out what proportion of N did answer yes to both questions. 1/3 answered yes to #1 and of those 1/4 answered yes to #2. Thus 1/3 times 1/4=1/12N answered yes to both. Now it is simple subtraction to find those who did not vote yes on both. 11/12N. So the answer should be E.

If you found these comments helpful, please give kudos.
Thanks,
Skip

Bunuel, can you please look at this question. I personally got E for the answer. But after giving it some thought, I started to doubt it. My reasoning goes like this:

Total: 36

Yes to 1: 9
Yes to 1 and Yes to 2: 1/3 * 9 = 3

No to 1: 36-9 = 27
No to 1 No to 2: ?
No to 1 Yes to 2: ?

So, I don't know how we can calculate No 1 No to 2. I guess that's what the question asks.

Thank you.

We require to find the value of shaded region (in pink)

Total students = n

Yes for Q1 \(= \frac{n}{4}\)

Yes for both Q1 & Q2\(= \frac{n}{4} * \frac{1}{3} = \frac{n}{12}\)

Remaining\(= n - \frac{n}{12}\)

\(= \frac{11n}{12}\)

Answer = E

You require to change the row/column arrangement

Refer diagram below:

This is how I did it:

Yes to 2nd No to second Total
Yes to 1st...........10................20.............30
No to 1st................................................90
Total.....................................................120

So, I started by picking a number for the total: I picked 120 as a smart number (3*4=12, which are our denominators).
Then, 1/4 answered yes to the 1st question, so 120/4=30, which means that 90 must have answered no to 1st question (120-30=90); we don't need this, but it is an easy calculation and creates a complete table, just to be able to check for mistakes in the additions.

The problem also states that 1/3 of those who said yes to question one, said yes to question 2. So, 30/3=10, and as before 30-10=20 people said no to question 2.

At this point, we can already solve the question, since we are looking for those that didn't answer "yes" to both questions. From the table, there were 10 people out of 120 that answered yes to both questions, so 120-10=110 people did not answer yes to both questions.

Answer choice E ends up in 110: 11N/12= 11*120/12= 1320/12= 110.

Since 1/4 of the people answered yes to question 1, (1/4)N answered yes to question 1. Since 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N answered yes to both questions 1 and 2.

Thus N - (1/12)N = 12N/12 - N/12 = 11N/12 DID NOT answer yes to both questions.

Answer: E

Multiplying the fractions is the fastest, I think, but you can also pick a number for N that is divisible by 4 and 3. Usually LCM works best.

Let N = 12

\(\frac{1}{4}\) of the people answered "yes" to question #1.

\(\frac{1}{4}\) of 12 = 3.

So 3 said yes to question #1.

"[A]nd of those" [people who answered yes to question 1], \(\frac{1}{3}\) answered "yes" to question #2.

\(\frac{1}{3}\) of 3 is 1 --> That one person is the only person who said "yes" to both questions.

That means 12 - 1 = 11 who did NOT answer yes to both.

11 out of 12 did NOT say "yes" to both: \(\frac{11}{12}\)N

Answer E

hi, how can (1/12)N become yes to both questions 1 and 2....... 1/3 of (1/4)N people answered yes to question 2, (1/4)N x 1/3 = (1/12)N so N/12 should be for the second question only

eka9045, Hopefully this will suffice!


rnn, You have displayed a decent understanding of the question.
However, let's deep-dive!

The logic utilized:

Let's start small -

If 30% of people ate ice-cream, how many people did NOT eat ice-cream?
Clearly, By complement rule, we can say: Complement = Total - Given.
------> \(100 - 30 = 70\)%

if X = 0.3, then what is the value of NOT X?
Clearly, By complement rule, we can say: Complement = Total - Given.
------> it's \(0.7\).
Now, sum it up: If X is given as y%, then the value of NOT X = 100% - y%

The complement-logic is utilised in this question.

Do NOT worry about some-lame-random-number N. We will take care of it!

Argument

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?

Let's break the argument down to its core -

Given: If 1/4 of them answered "yes" to question 1

N = the Total Number of people interviewed.

If N/4 answered YES, then how many did NOT answer yes?
Clearly, By complement rule, we can say: Complement = Total - Given.

Total = N | Given = \(N/4\)
Thus, the people who did NOT answer the 1st question as Yes: Complement = \(N - N/4 = 3N/4\)

Findings from Q1: Yes = N/4 | No = 3N/4

Given: of those, 1/3 answered "yes" to question 2

of those links to the people who already answered to the Q1 as Yes, i.e., \(N/4\)
Thus, of N/4 people,

1/3 of \(N/4\) answered "yes" to Q2
If 1/3 of \(N/4\) answered "yes" to Q2, then how many people of \(N/4\) did NOT answer yes?
Clearly, By complement rule, we can say: Complement = Total - Given.

Total = N/4 | Given = 1/3 of \(N/4\)
Thus, the people who did NOT answer the 2nd question as Yes: Complement = \(N/4 - (1/3)(N/4) = (2/3)(N/4)\)
Remember, the people in this set already marked YES to Q1 -

Findings from Q1 and Q2: (Q1)Yes, (Q2)Yes = (1/3)(N/4) | (Q1)Yes, (Q2)No = (2/3)(N/4)

Question: Which of the following expressions represents the number of people interviewed who did NOT answer "yes" to both questions?

Find the number of people interviewed who did NOT answer "yes" to both questions:
Clearly, By complement rule, we can say: Complement = Total - Given.

Meaning: The number of people who did NOT answer "yes" to both questions = Total - who answered YES to both questions

Total = N | who answered YES to both questions = (Q1)Yes, (Q2)Yes = (1/3)(N/4)

The number of people who did NOT answer "yes" to both questions = \(N - N/12 = 11N/12\)

Total people interviewed: N

Answered YES to question 1: \(\frac{1}{4}^{th} \)
Answered YES to question 2: \(\frac{1}{3}^{th}\)

The number of people interviewed who did NOT answer "yes" to both questions: 1 - Number of people who answered 'YES' to both the questions.

=> N - (\(\frac{1}{4} * \frac{1}{3}\))N

=> N - (\(\frac{N}{12}\))

=> \(\frac{11N}{12}\)

Answer E

Hey guys

Let's use a really easy number in place of N here for a second

It needs to be divisible by 4 and 3 because the fractions used are \(\frac{1}{4}\) and \(\frac{1}{3}\)

Let's use 120

\(\frac{1}{4}\) answered yes to the first question:

\(\frac{1}{4}\)(120) = 30

\(\frac{1}{3}\) of those people answered yes to the second question:

\(\frac{1}{3}\)(30) = 10

So \(\frac{10}{120}\) answered yes to both questions

That means \(\frac{110}{120}\) did not answer yes to both questions

This is what the question is asking for

\(\frac{110}{120} = \frac{11}{12\\
}\) of the total number of people N did not answer yes to both questions:

\(\frac{11}{12}\)N

The answer is (E)

Answer: Option E

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