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In a college 66 students enjoy rock music, 62 enjoy pop music, 58 enjoy jazz music, 16 enjoy both rock and pop music, 27 enjoy both pop and jazz music
Question

In a college 66 students enjoy rock music, 62 enjoy pop music, 58 enjoy jazz music, 16 enjoy both rock and pop music, 27 enjoy both pop and jazz music, and 13 enjoy both jazz and rock music. No one enjoys all three music. Find how many enjoy at least one type of music.

A.

110

B.

120

C.

130

D.

140

Correct option is C

Given:
In a college 66 students enjoy rock music, 62 enjoy pop music, 58 enjoy jazz music, 16 enjoy both rock and pop music, 27 enjoy both pop and jazz music, and 13 enjoy both jazz and rock music.
No one enjoys all three music.
From the given information possible Venn diagram will be.
Solution:
Total = (Rock) + (Pop) + (Jazz) – (Rock and Pop) – (Pop and Jazz) – (Jazz and Rock)
= 66 + 62 + 58 – 16 – 27 – 13
= 186 – 56
= 130
130 enjoy at least one type of music.
Thus, correct option is (c).

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