Answer:
d) 360
Explanation:
To solve this problem, we can use a Venn diagram. Let R, C, and J represent the sets of students who like rock, country, and jazz, respectively. We can fill in the diagram with the given information:
J
/ \
/ \
/ \
RC-----C
\ /
\ /
\ /
R
We know that:
The total number of students surveyed is 500.
9 students like all three types of music, so we can put 9 in the intersection of all three sets (RCJ).
24 like rock and country, so we can put 24 in the intersection of R and C (RC).
29 like rock and jazz, so we can put 29 in the intersection of R and J (RJ).
29 like country and jazz, so we can put 29 in the intersection of C and J (CJ).
We can calculate the number of students who like only one type of music by subtracting the number of students who like two or three types of music from the total number of students surveyed:
Total = R + C + J - RCJ
500 = 204 + 164 + 129 - 9
We can use this equation to solve for R, C, and J:
R = 204 - 24 - 29 - 9 = 142
C = 164 - 24 - 29 - 9 = 102
J = 129 - 29 - 29 - 9 = 62
So there are 142 students who like rock only, 102 students who like country only, and 62 students who like jazz only. Therefore, the total number of students who like exactly one type of music is:
142 + 102 + 62 = 306
Therefore, the answer is (d) 360.