There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2...
Question
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.
Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.
The following facts are also known:
- All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
- Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
- 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
- No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
- The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.
What fraction of the class are interested in attending a 2-day event?