The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short...

[BTGmoderatorLU]

Source: Economist GMAT

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

The OA is E

[Scott@TargetTestPrep]

Source: Economist GMAT

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

The OA is E

At first, there would appear to be 4 possible categories of respondents:

(1) Those who did not enjoy and did not understand
(2) Those who did not enjoy but understood
(3) Those who did enjoy but did not understand
(4) Those who did enjoy and understood

However, the wording of the question indicates that all 120 individuals who did not enjoy the painting did not understand it (category (1)). And all of those who enjoyed the painting also did understand it (category (4)) Thus, there appear to be no individuals in categories 2 or 3.

This simplifies the calculation of the total number of respondents. We see that ¾ of the respondents are in category (4), so ¼ of the respondents are in category 1, and we know that there were 120 individuals in category 1. If we let T = the total number of individuals who answered the questionnaire, then we have:

¼ * T = 120

T = 480.

Answer: E

[deloitte247]

Let the total number of visitors who filled the questionnaire = x
People who enjoyed watching the painting = people who understood the painting
People who understood the painting = 3x/4
Therefore, people who do not understand the painting = people who do not enjoy watching the painting
People who do not enjoy watching the painting = 120
$$Therefore,\ \frac{1x}{4}=120;\ and\ x=120\cdot4=480$$
Hence, 480 visitors answered the questionnaire.

Answer = option E