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1. In a rock band, three people play guitar, four sing, and two do both. Six have no talent for singing or guitar, so they do something else. How many members are in the band?
2. The staff at a daycare observed their 64 students eating habits. They observed that 59 children ate green beans, 56 ate cauliflower, 60 ate broccoli, 55 ate green beans and cauliflower, 54 ate cauliflower and broccoli, 56 ate green beans and broccoli, and 53 ate all three. How many children did not eat any of these vegetables? How many ate green beans but not cauliflower? How many children ate only cauliflower? How many ate exactly two types of vegetables?
3. A group of second-graders were surveyed about their favorite field trips. Each child was to write on a slip of paper which trip was his or her favorite (many children named more than one). The survey revealed that 52 wrote down the trip to the river, 50 wrote down the trip to the police station and 44 said the trip to the hardware store. Nineteen had police station and the river. Thirty-two had both the river and the hardware store, and 25 had the police station and the hardware store. Seventeen students liked all three and one did not like any of them. How many children were surveyed?
4. At a family reunion, every niece was a cousin. Half of all aunts were cousins. Half of all cousins were nieces. There were 50 aunts and 30 nieces. No aunt was a niece. How many cousins were neither nieces nor aunts?
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