Question

John is curious about the type of music his classmates enjoy and decides to survey 125 of his classmates. In his survey, 63 students enjoy both hip hop and pop music, 13 enjoy only pop music, and a total of 90 enjoy hip hop. How many of his classmates do not enjoy hip hop or pop?

Answer 1

Total 22 students do not enjoy hip hop or pop.

Explanation:

It is given that total number of students is 125.

A : Total number of students, who enjoy hip hop

B : Total number of students, who enjoy pop

A∩B : Total number of students, who enjoy both hip hop and pop music.

From the given information it is clear that

`A=90`

`A\cap B=63`

`A'\cap B=13`

`A'\cap=B-A\cap B`

`13=B-63`

`B=76`

Total number of students, who enjoy at least one of the music.

`A\cupB=A+B-A\cap B`

`A\cupB=90+76-63`

`A\cupB=103`

Total number of students, who do not enjoy any music.

`125-A\cupB=125-103=22`

Therefore total 22 students do not enjoy hip hop or pop.