What is the number of people who prefer to listen all three types of 39 music 39 genres ........

Quantitative Aptitude (SBI-PO) Case Studies

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?

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Explanation:

Let’s break this down step by step with what we know:

- The folks who ONLY like Folk, Rock, and Jazz are split in a 56:79:41 ratio. Let’s call those F, R, and J.

- People who like both Folk and Jazz, but NOT Rock, are 25% less than the “all three genres” group (let’s call “all three” A). So that category is 0.75A.

- Both Rock & Jazz but not Folk: 50 people.

- Both Folk & Rock but not Jazz: 35 people.

- Only Jazz is five less than six times the “Folk & Rock but not Jazz.” So, Only Jazz = 6×35 – 5 = 210 – 5 = 205.

- The total of the “exactly two genres” people is 130, so 0.75A (Folk&Jazz, not Rock) + 50 (Rock&Jazz, not Folk) + 35 (Folk&Rock, not Jazz) = 130.

- That adds up to: 0.75A + 50 + 35 = 130, so 0.75A = 45 ? A = 60.

Put simply, the answer is 60. That's option 5.

Here’s what all the clues tell you:

- Only Jazz is 205, matches the calculation.

- The counts for “exactly two genres” also fit when A = 60.

- All info clicks into alignment with A = 60.

- ?? Correct Answer: Option 5, 60.