CAT 2022 Slot 1 — DILR Question 6
Directions for next 5 queestions.
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.
How many boys are there in the class?
Answer & solution
Answer: 50
There are boys and girls in the class. Each of the boy or girl is either a dance or singer or none of these but not both.
There are 6 singers in the class, 4 of them are boys.
⇒ There are 4 male singers and 2 female singers
There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer
⇒ There are 6 male dances and 4 female dancers
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From (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.
Since all 4 male singers are interested in a 3-day event, they all must also be interested in a 2-day and a 1-day event.
Since 2 male dancers are interested in a 3-day event, male dancers interested in a 2-day event must be greater than or equal to 2.
âââââââ
From (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.
From (3): 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. Hence, 30% of those who are interested in a 2-day event are dancers or singers.
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Now, (2 + b) = 30% of 60% of (10 + x)
⇒ 2 + b + 4 = × × (10 + x)
⇒ 6 + b = × (10 + x)
Here b has to be an integer, hence (10 + x) should be completely divisible by 50.
∴ x should be 40 or 90 or 140 and so on.
But since b cannot be greater than 4, x should be 40 and b = 3.
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From (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.
This is only possible when 2 female singers while no female dance is interested in a 2-day event.
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From (3): 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
⇒ 0 + 2 = × (0 + 2 + females interested in a 2-day event who are neither singer nor dancer)
females interested in a 2-day event who are neither singer nor dancer = 3
âââââââ
∴ There are 50 boys in the class.
Hence, 50.