Questions: A college radio station surveyed incoming freshmen to gather information about the types of music that they like. Here are the results. Español - 618 incoming freshmen were surveyed in all - 274 of the freshmen like rap - 362 of the freshmen like jazz - 193 of the freshmen like both rap and jazz - 139 of the freshmen like both rap and rock - 123 of the freshmen like both jazz and rock - 91 of the freshmen like all three types of music (rap, jazz, rock) - 113 of the freshmen don't like any of these three types of music (rap, jazz, rock) Construct a Venn diagram illustrating these results. Then answer the question. How many of the freshmen like both jazz and rap, but don't like rock? freshmen

Solution Steps

• Total freshmen surveyed: 618
• Freshmen who like rap: 274
• Freshmen who like jazz: 362
• Freshmen who like rock: 312
• Freshmen who like both rap and jazz: 193
• Freshmen who like both rap and rock: 139
• Freshmen who like both jazz and rock: 123
• Freshmen who like all three types of music: 91
• Freshmen who don't like any of these three types of music: 113

The Venn diagram provided shows the distribution of freshmen who like different combinations of music genres. The numbers in the overlapping regions represent the number of freshmen who like the corresponding combinations of music genres.

• Freshmen who like both jazz and rap: 193
• Freshmen who like all three types of music: 91

To find the number of freshmen who like both jazz and rap but don't like rock, subtract the number of freshmen who like all three types of music from the number of freshmen who like both jazz and rap: \[ 193 - 91 = 102 \]

Final Answer