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Sets

by Neo Anderson » Mon Apr 23, 2012 11:31 pm
The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire, indicating whether they had enjoyed looking at the picture, and whether they felt they had understood it. According to the results of the survey, all 120 visitors who did not enjoy the painting, also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?
a)90
b)200
c)120
d)360
e)480

OA after some time!
Please dont just say the answer, methodology and explanation are as important!
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by killer1387 » Tue Apr 24, 2012 12:11 am
Its 480;

let total who filled the questionnaire is x
120 dint enjoy then x-120 enjoyed.

also 3x/4= both who enjoyed and understood

total = x-120+x-120- 3x/4 + 120 = x
=> 5x/4 - 120 = x
=> x/4 = 120
=> x = 480

Hope this helps..!!
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by Neo Anderson » Tue Apr 24, 2012 1:39 am
Its 480;

let total who filled the questionnaire is x
120 dint enjoy then x-120 enjoyed.

also 3x/4= both who enjoyed and understood

total = x-120+x-120- 3x/4 + 120 = x
=> 5x/4 - 120 = x
=> x/4 = 120
=> x = 480

Hope this helps..!!
after posting the question i realized that 'All' in this line is the most important word,
all 120 visitors who did not enjoy the painting, also did not feel they had understood the painting
which i missed whilst trying to solve initially!

thanks anyway!
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by [email protected] » Tue Apr 24, 2012 4:53 am
Honestly, I did not understand the following step of killer 1387:

total = x-120+x-120- 3x/4 + 120 = x


But anyways I got the solution as E as follows:

Let me give you a precise equation:

There are 2 circles representing equal number let say a = b

so the equation would be:

a + a - 3/4 x + 120 = x {let the total people who filled out the questionaire be x}

solving the above, we get

2a + 120 = 7/4x (hence two variables)

therefore, 8a - 7x = -480

Now try putting all the values from A to E and see what the answer of a comes out to be...

For all the options except for E, 'a' turns out to be less than the common between both of them i.e a as well as b.

That is never possible in Sets. Suppose in AUB = n(A) + n(B) - n(A intersection B)

In this n(A) or n(B) can never be less than n(A intersection B)...

The same thing is happening in the above example and hence I chose the answer as E.

I really do not know how killer 1387 solved the equation having 2 unknown variables i.e x and a

Hope this post really helped you guyzzzzz!!!
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by killer1387 » Tue Apr 24, 2012 7:07 am
[email protected] wrote:Honestly, I did not understand the following step of killer 1387:

total = x-120+x-120- 3x/4 + 120 = x
I proceeded by using two circle that you talked of.
question does says 120 of x doesnt enjoy /understand this means x-120 did enjoyed = no. of people who understand.
Also its given the common guys are = 3x/4

hence total would be
(x-120)+(x-120)- 3x/4 + 120 and this is x.(Note: i have subtracted 3x/4 because its common in both fields)

Hope this clears..!!
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