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The number of people who prefer to listen only 'Jazz' = 6 × 35 - 5 = 205

Let the total number of people who prefer to listen only 'Jazz' = 41x

ATQ, 41x = 205

⇒ x = 5

The total number of people who prefer to listen only 'folk' = 56x = 280

The total number of people who prefer to listen only 'Rock' = 79x = 395

Let the total number of people who prefer to listen all three genres = 4y

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 75% × 4y = 3y

The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' = 50

The number of people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz' = 35

The total number of people who prefer to listen exactly two type of 'music' genres = 130

ATQ, 3y + 50 + 35 = 130 ⇒ y = 15

The total number of people who prefer to listen all three genres = 4y = 60

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 3y = 45

The number of people who prefer to listen 'Folk' = 280 + 35 + 60 + 45 = 420

The number of people who prefer to listen 'Rock' = 395 + 35 + 60 + 50 = 540

The number of people who prefer to listen 'Jazz' = 205 + 45 + 60 + 50 = 360

The number of people who prefer to listen all three types of 'music' genres = 60

Hence, the correct answer is 60.

The number of people who prefer to listen only 'Jazz' = 6 × 35 - 5 = 205

Let the total number of people who prefer to listen only 'Jazz' = 41x

ATQ, 41x = 205

⇒ x = 5

The total number of people who prefer to listen only 'folk' = 56x = 280

The total number of people who prefer to listen only 'Rock' = 79x = 395

Let the total number of people who prefer to listen all three genres = 4y

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 75% × 4y = 3y

The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' = 50

The number of people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz' = 35

The total number of people who prefer to listen exactly two type of 'music' genres = 130

ATQ, 3y + 50 + 35 = 130

⇒ y = 15

The total number of people who prefer to listen all three genres = 4y = 60

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 3y = 45

The number of people who prefer to listen 'Folk' = 280 + 35 + 60 + 45 = 420

The number of people who prefer to listen 'Rock' = 395 + 35 + 60 + 50 = 540

The number of people who prefer to listen 'Jazz' = 205 + 45 + 60 + 50 = 360

The total number of people who prefer to listen to only 'Folk' and to only 'Rock' = 280 + 395 = 675

Hence, the correct answer is 675.

The number of people who prefer to listen only 'Jazz' = 6 × 35 - 5 = 205

Let the total number of people who prefer to listen only 'Jazz' = 41x

ATQ, 41x = 205

⇒ x = 5

The total number of people who prefer to listen only 'folk' = 56x = 280

The total number of people who prefer to listen only 'Rock' = 79x = 395

Let the total number of people who prefer to listen all three genres = 4y

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 75% × 4y = 3y

The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' = 50

The number of people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz' = 35

The total number of people who prefer to listen exactly two type of 'music' genres = 130

ATQ, 3y + 50 + 35 = 130

⇒ y = 15

The total number of people who prefer to listen all three genres = 4y = 60

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 3y = 45

The number of people who prefer to listen 'Folk' = 280 + 35 + 60 + 45 = 420

The number of people who prefer to listen 'Rock' = 395 + 35 + 60 + 50 = 540

The number of people who prefer to listen 'Jazz' = 205 + 45 + 60 + 50 = 360

The number of people who prefer to listen exactly one type of 'music' genre = 280 + 395 + 205 = 880

The number of people who prefer to listen exactly two types of 'music' genres = 50 + 35 + 45 = 130

Required difference = 880 - 130 = 750

Hence, the correct answer is 750.

The number of people who prefer to listen only 'Jazz' = 6 × 35 - 5 = 205

Let the total number of people who prefer to listen only 'Jazz' = 41x

ATQ, 41x = 205

⇒ x = 5

The total number of people who prefer to listen only 'folk' = 56x = 280

The total number of people who prefer to listen only 'Rock' = 79x = 395

Let the total number of people who prefer to listen all three genres = 4y

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 75% × 4y = 3y

The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' = 50

The number of people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz' = 35

The total number of people who prefer to listen exactly two type of 'music' genres = 130

ATQ, 3y + 50 + 35 = 130

⇒ y = 15

The total number of people who prefer to listen all three genres = 4y = 60

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 3y = 45

The number of people who prefer to listen 'Folk' = 280 + 35 + 60 + 45 = 420

The number of people who prefer to listen 'Rock' = 395 + 35 + 60 + 50 = 540

The number of people who prefer to listen 'Jazz' = 205 + 45 + 60 + 50 = 360

The total number of people who prefer to listen 'Rock' = 540

Hence, the correct answer is 540.

The number of people who prefer to listen only 'Jazz' = 6 × 35 - 5 = 205

Let the total number of people who prefer to listen only 'Jazz' = 41x

ATQ, 41x = 205

⇒ x = 5

The total number of people who prefer to listen only 'folk' = 56x = 280

The total number of people who prefer to listen only 'Rock' = 79x = 395

Let the total number of people who prefer to listen all three genres = 4y

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 75% × 4y = 3y

The number of people who prefer to listen both 'Rock' and 'Jazz' but not 'Folk' = 50

The number of people who prefer to listen both 'Folk' and 'Rock' but not 'Jazz' = 35

The total number of people who prefer to listen exactly two type of 'music' genres = 130

ATQ, 3y + 50 + 35 = 130

⇒ y = 15

The total number of people who prefer to listen all three genres = 4y = 60

The number of people who prefer to listen both 'Folk' and 'Jazz' but not 'Rock' = 3y = 45

The number of people who prefer to listen 'Folk' = 280 + 35 + 60 + 45 = 420

The number of people who prefer to listen 'Rock' = 395 + 35 + 60 + 50 = 540

The number of people who prefer to listen 'Jazz' = 205 + 45 + 60 + 50 = 360

Ratio between the number of people who prefer to listen 'Folk' and to 'Jazz' = 420 : 360 = 7 : 6

Hence, the correct answer is 7 : 6.

Given that:

There are seven persons, who were born in different years - 1961, 1968, 1972, 1988, 1993, 1999, and 2013. All the age calculations are done taking the base year as 2020.

So, their ages are:

 

1) D was born in a leap year but not in the year 1988.

So, here there are 3 leap years - 1968, 1972 and 1988 (all are divisible by 4)

So, 2 cases will generate D can born either in 1968 or 1972:

 

2) Only three persons were born between D and F.

3. C is the eldest person among them all.

So, C was born in 1961:

 

4) The difference between the ages of G and D is 4 years.

 

 

5) B was born in an odd-numbered year but not in 1993 nor he was the last one to be born.

Here, B was born in 1999, neither in 1993 nor in 2013 (at last).

6. The sum of the ages of A and F is a multiple of 13.

Here, age is 32 + 7 = 39 (39 is a multiple of 13).

So in there 2 statements Case I will be eliminate:

Here we have case II:

 

E was born in the year 1993.

Given that:

There are seven persons, who were born in different years - 1961, 1968, 1972, 1988, 1993, 1999, and 2013. All the age calculations are done taking the base year as 2020.

So, their ages are:

 

1) D was born in a leap year but not in the year 1988.

So, here there are 3 leap years - 1968, 1972 and 1988 (all are divisible by 4)

So, 2 cases will generate D can born either in 1968 or 1972:

 

2) Only three persons were born between D and F. 

3. C is the eldest person among them all.

So, C was born in 1961:

 

4) The difference between the ages of G and D is 4 years.

 

 

5) B was born in an odd-numbered year but not in 1993 nor he was the last one to be born.

Here, B was born in 1999, neither in 1993 nor in 2013 (at last).

6. The sum of the ages of A and F is a multiple of 13.

Here, age is 32 + 7 = 39 (39 is a multiple of 13).

So in there 2 statements Case I will be eliminate:

Here we have case II:

 

The sum of the ages of C and B is → 59 + 21 = 80 years.

Given that:

There are seven persons, who were born in different years - 1961, 1968, 1972, 1988, 1993, 1999, and 2013. All the age calculations are done taking the base year as 2020.

So, their ages are:

 

1) D was born in a leap year but not in the year 1988.

So, here there are 3 leap years - 1968, 1972 and 1988 (all are divisible by 4)

So, 2 cases will generate D can born either in 1968 or 1972:

 

2) Only three persons were born between D and F. 

3. C is the eldest person among them all.

So, C was born in 1961:

 

4) The difference between the ages of G and D is 4 years.

 

 

5) B was born in an odd-numbered year but not in 1993 nor he was the last one to be born.

Here, B was born in 1999, neither in 1993 nor in 2013 (at last).

6. The sum of the ages of A and F is a multiple of 13.

Here, age is 32 + 7 = 39 (39 is a multiple of 13).

So in there 2 statements Case I will be eliminate:

Here we have case II:

 

No one is born between G and D, so none.

Given that:

There are seven persons, who were born in different years - 1961, 1968, 1972, 1988, 1993, 1999, and 2013. All the age calculations are done taking the base year as 2020.

So, their ages are:

 

1) D was born in a leap year but not in the year 1988.

So, here there are 3 leap years - 1968, 1972 and 1988 (all are divisible by 4)

So, 2 cases will generate D can born either in 1968 or 1972:

 

2) Only three persons were born between D and F. 

3. C is the eldest person among them all.

So, C was born in 1961:

 

4) The difference between the ages of G and D is 4 years.

 

 

5) B was born in an odd-numbered year but not in 1993 nor he was the last one to be born.

Here, B was born in 1999, neither in 1993 nor in 2013 (at last).

6. The sum of the ages of A and F is a multiple of 13.

Here, age is 32 + 7 = 39 (39 is a multiple of 13).

So in there 2 statements Case I will be eliminate:

Here we have case II:

 

G does not belong to the group as G was born in the even - numbered years.

Given that:

There are seven persons, who were born in different years - 1961, 1968, 1972, 1988, 1993, 1999, and 2013. All the age calculations are done taking the base year as 2020.

So, their ages are:

 

1) D was born in a leap year but not in the year 1988.

So, here there are 3 leap years - 1968, 1972 and 1988 (all are divisible by 4)

So, 2 cases will generate D can born either in 1968 or 1972:

 

2) Only three persons were born between D and F. 

3. C is the eldest person among them all.

So, C was born in 1961:

 

4) The difference between the ages of G and D is 4 years.

 

 

5) B was born in an odd-numbered year but not in 1993 nor he was the last one to be born.

Here, B was born in 1999, neither in 1993 nor in 2013 (at last).

6. The sum of the ages of A and F is a multiple of 13.

Here, age is 32 + 7 = 39 (39 is a multiple of 13).

So in there 2 statements Case I will be eliminate:

Here we have case II:

 

B was born in 1999.