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A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 192 like rock,156 like country, and 118 like jazz. Moreover, 18 like rock and country, 20 like rock and jazz, 24 like country and jazz, and 6 like all three types of music. How many students surveyed liked rock only?

a) 148

b) 160

c) 142

d) 192

e) 154

f) None of the above.

Respuesta :

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Answer:

160

Step-by-step explanation:

Total students were 500.

We define our grupes:

Rock = A

country = B

Jazz = C

The groups are given by,

A=192

B=156

C=118

From the combination we have:

[tex]A \cap B=18[/tex]

[tex]A\cap C=20[/tex]

[tex]B\cap C=24[/tex]

[tex]A\cap B\cap C=6[/tex]

Students who liked Rock only are:

[tex]X=A-A\cap C-A\cap B+A\cap B\cap C[/tex]

[tex]X=92-20-18+6[/tex]

[tex]X=160[/tex]