CAT 2022 Set-1 | Data Interpretation and Logical Reasoning | Question: 18

Question

Comprehension:
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.

What fraction of the class are interested in attending a $2$-day event?

• A. $1.9 / 13$
• B. $2 / 3$
• C. $7 / 10$
• D. $7 / 13$