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05 May 2021, 07:15
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
73% (02:30) correct
27%
(03:14)
wrong
based on 310
sessions
History
Date
Time
Result
Not Attempted Yet
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. 120
C. 160
D. 360
E. 480
A. 90
B. 120
C. 160
D. 360
E. 480
05 May 2021, 13:13
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IMO Answer = 480 (E)
We are given the following details,
1. People who didn't enjoy the painting at all = 120
2. With respect to point 1 It can also be expressed as,
120= People who didn't enjoy + People who understood - (People who enjoyed and understood)
3. People who enjoyed and understood = 3/4 Total
4. Now, we can use 1,2,3 to get the following equation
120= 120 + People who understood - 3/4T
Thus, People who understood=3/4T
5. People who enjoyed = People who understood = 3/4T
6. Using the formula for combined sets
Total= People who enjoyed + People who understood - People who understood and enjoyed + Neither understood nor enjoyed
Thus,
T = 2.(3/4)T - (3/4)T + 120
-120 = (3/2)T - (3/4)T - (4/4)
-120 = -(T/4)
T = 120*4 = 480
Posted from my mobile device
We are given the following details,
1. People who didn't enjoy the painting at all = 120
2. With respect to point 1 It can also be expressed as,
120= People who didn't enjoy + People who understood - (People who enjoyed and understood)
3. People who enjoyed and understood = 3/4 Total
4. Now, we can use 1,2,3 to get the following equation
120= 120 + People who understood - 3/4T
Thus, People who understood=3/4T
5. People who enjoyed = People who understood = 3/4T
6. Using the formula for combined sets
Total= People who enjoyed + People who understood - People who understood and enjoyed + Neither understood nor enjoyed
Thus,
T = 2.(3/4)T - (3/4)T + 120
-120 = (3/2)T - (3/4)T - (4/4)
-120 = -(T/4)
T = 120*4 = 480
Posted from my mobile device
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13 May 2021, 03:50
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Bunuel
Please refer the table below :
Attachment:
table.png [ 11.55 KiB | Viewed 5130 times ]
From the table we can see total visitors \(= 120 +x\)
Also \(\frac{3}{4} (120+x) = x\)
Hence \(x= 360\)
Hence total visitors : \(120 + 360 = 480\)
Ans-E
Hope it's clear.
