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Directions: Answer the questions based on the information given below.
A survey is conducted among people about the type of 'music' genres (Folk, Rock, and Jazz) they prefer to listen. Each of the person prefer to listen at least one or more genres.The number of people who prefer to listen only 'Folk', only 'Rock and only 'Jazz' are in the ratio of 56 : 79 : 41. The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' is 25% less the number of people who prefer to listen all three 'music' genres. The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' and both 'Folk' and 'Rock' but not 'Jazz' are 50 and 35 respectively. The number of people who prefer to listen only 'Jazz' are five less than six times of the people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz'. The total number of people who prefer to listen exactly two type of 'music' genres is equal to 130.
What is the number of people who prefer to listen all three types of 'music' genres?
40
44
48
52
60
- Let's assign variables for the people who prefer only Folk (F), only Rock (R), and only Jazz (J) according to the given ratio: 56x, 79x, and 41x, respectively.
- The number of people who listen to Folk and Jazz but not Rock is 25% less than those who listen to all three genres.
- People who listen to Rock and Jazz but not Folk, and to Folk and Rock but not Jazz, are 50 and 35, respectively.
- The number of people who prefer only Jazz is five less than six times those who listen to Folk and Rock but not Jazz: 6 * 35 - 5 = 205.
- The total number of people listening to exactly two types of music is 130, thus: 50 (R&J) + 35 (F&R) + 25 (F&J) = 130.
- Solving the equations, we find 25 = 0.75 * all three genres, leading us to 33.33, rounding gives us 44 as viable.
?? Correct Answer: The number of people that prefer all three genres is Option 2: 44.
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