Answer:
A = 123
B = 39
C = 379
Explanation:
If 569 freshmen like at least one of these 3 types os music, it means that the sum of the numbers inside the 3 circles have to be 569, and it also means that the difference between these freshmen (those inside the 3 circles) and the total freshmen surveyed don't like any of these type of music, so:
692 – 569 = 123 freshmen that don't like these 3 types of music, and this is the slot A
Now, for the slot B, we have to sum all the numbers inside the circles and see how much left to be equal to 569 (the total of freshmen that like at least one of the 3 type of music):
87 + 106 + 63 + 163 + 87 + 24 + B = 569
530 + B = 569
B = 569 – 530
B = 39
And now, the slot C is the number of freshman that don't like rock, so we have to sum all the numbers outside the circle purple:
87 + 106 + 63 + A = C
We know that A = 123, so:
C = 87 + 106 + 63 + 123
C = 379