Answer:
50
Explanation:
A Venn diagram is very helpful for this picture and I've included one in the attached.
If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.
However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.
Since 200 people like both rock and country, these people are part of the 350 people that like rock.
We can find the number of people who like rock only by subtracting 200 from 350:
350 - 200 = 150 (Rock only)
Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.
We can find the number of people who like country only by subtracting 200 from 300:
300 - 200 = 100 (Country only)
Currently, we have 450/500 as 150 + 200 + 100 = 450.
Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:
500 - 450 = 50 (Neither rock nor country)
We can check that the numbers we found equal 500:
Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed
150 + 200 + 100 + 50 = 500
500 = 500
(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)