If 60 percent of respondents answered Yes to the first question of a

Question

If 60 percent of respondents answered Yes to the first question of a survey, 35 percent answered Yes to the second question, and 15 percent answered No to both questions, what percent of the respondents answered Yes to both questions?

A. 10%
B. 25%
C. 40%
D. 55%
E. 70%

A. 10%
B. 25%
C. 40%
D. 55%
E. 70%

pushpitkc · Answer

Let's assume 100 people took the Survey.

Exactly (60)60% answered YES for the first question -> 40 answered NO for the first question
Since (35)35% answered YES for the 2nd question -> 65 answered NO for the second question.

As a total of 15 answered NO for both the questions, 40 + 65 - 15 = 90 answered NO for both
the questions. This also means that 100 - 90 or 10 people answered YES to both the questions.

Therefore, the percentage of respondents who answered YES for both questions is  \frac{10}{100} =  10%(Option A)

gmat1393 · Answer

Assuming the class size as 100 we get the Answer as 10 as per below.

carouselambra · Answer

Hi  Bunuel   yashikaaggarwal

Could you please help? I understood the solution after looking at the above posts but I was trying via double matrix.
Below is my working and I want to understand what is wrong.

Q1 - Yes - 60% , so 40% would have said no
Q2- Yes - 35% , so 65% would have said no

But we know that,No (Q1+Q2) = 15%
 Will this not translate into 85% people answering 'Yes' to both questions? 
Thereafter, we can check, 95% of 85 will give us the number of folks who answered 'Yes' to both questions.

MathRevolution · Answer

First question - YES - 60%

Second question - YES - 35%

Both Question - No - 15% : Both question 'YES': 100 - 15 = 85%

Percent of the respondents answered Yes to both questions: 60 + 35 - 85 = 10

Answer A

carouselambra · Answer

Whoops. That was a bad miss. Thanks

hkkat · Answer

assume we have 100 people

Yes to first question: 100 x 60% = 60
Yes to second question: 100 x 35% = 35

100 = 60 + 35 -both +15
10= both

the equation is:
 Total = A + B – Both + Neither

so the answer is A

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