Event Planning

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(CAT 2022)


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:

1. 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.
2. 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.
3. 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.
4. 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.
5. 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.


1) How many boys are there in the class?

2) Which of the following can be determined from the given information?
I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.
II. The number of female dancers who are interested in attending a 1-day event.
  1. Neither I nor II
  2. Both I and II
  3. Only I
  4. Only II
3) What fraction of the class are interested in attending a 2-day event?
  1. 7/10
  2. 9/13
  3. 7/13
  4. 2/3
4) What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?
  1. 5 or 6
  2. 4 or 6
  3. 5
  4. 6
5) How many female dancers are interested in attending a 2-day event?
  1. 0
  2. 2
  3. Cannot be determined
  4. 1



For answers CLICK HERE.

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