A survey asked 816 college freshmen whether they had been to a movie or eaten in a restaurant during the past week. The following information was obtained: 395 freshmen had been to neither a movie nor a restaurant, and 263 had been to a movie. If 86 of those who had been to a movie had not been to a restaurant, how many of the surveyed freshmen had been to the following?(a) both a movie and a restaurant(b) a movie or a restaurant(c) a restaurant(d) a restaurant but not a movie
Question
A survey asked 816 college freshmen whether they had been to a movie or eaten in a restaurant during the past week. The following information was obtained: 395 freshmen had been to neither a movie nor a restaurant, and 263 had been to a movie. If 86 of those who had been to a movie had not been to a restaurant, how many of the surveyed freshmen had been to the following?(a) both a movie and a restaurant(b) a movie or a restaurant(c) a restaurant(d) a restaurant but not a movie
Solution
(a) Both a movie and a restaurant: The number of freshmen who had been to a movie is 263. Out of these, 86 had not been to a restaurant. Therefore, the number of freshmen who had been to both a movie and a restaurant is 263 - 86 = 177.
(b) A movie or a restaurant: The total number of surveyed freshmen is 816. Out of these, 395 had been to neither a movie nor a restaurant. Therefore, the number of freshmen who had been to either a movie or a restaurant is 816 - 395 = 421.
(c) A restaurant: The number of freshmen who had been to a movie but not a restaurant is 86. The number of freshmen who had been to both a movie and a restaurant is 177. Therefore, the number of freshmen who had been to a restaurant is 421 (from part b) - 86 = 335.
(d) A restaurant but not a movie: The number of freshmen who had been to a restaurant is 335 (from part c). Out of these, 177 had also been to a movie. Therefore, the number of freshmen who had been to a restaurant but not a movie is 335 - 177 = 158.
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