Question

653 incoming freshmen were surveyed in all
398 of the freshmen like classical
322 of the freshmen like jazz
185 of the freshmen like both jazz and classical
253 of the freshmen like both jazz and rock
291 of the freshmen like both classical and rock
142 of the freshmen like all three types of music (jazz, classical, rock)
49 of the freshmen dont like any of these three types of music (jazz, classical, rock)
construct a venn diagram illustrating these results. then answer the question.
image: venn diagram with \all freshmen in the survey\, \like jazz\, \like classical\, \like rock\ circles
how many of the freshmen like jazz, but like neither classical nor rock?
\boxed{} freshmen

Explanation:

Step1: Find the number of freshmen who like jazz and rock only.

The number of freshmen who like both jazz and rock is 253, and the number who like all three is 142. So, the number who like jazz and rock only is $253 - 142 = 111$.

Step2: Find the number of freshmen who like jazz and classical only.

The number of freshmen who like both jazz and classical is 185, and the number who like all three is 142. So, the number who like jazz and classical only is $185 - 142 = 43$.

Step3: Calculate the number of freshmen who like jazz but neither classical nor rock.

The total number of freshmen who like jazz is 322. We subtract the number who like jazz and rock only, jazz and classical only, and all three. So, it is $322 - 111 - 43 - 142 = 26$.

Answer:

26