Graduating Students Get-Together Event

CAT 2022 Slot 1 · DILR · Hard · Set Theory

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Passage / data set

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%80\% of the boys are interested in attending a 1-day event. 60%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%70\% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60%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.

Question 1 of 5

How many boys are there in the class?

Answer

50

Explanation

From the given conditions: 60%60\% of boys are interested in a 2-day event. Also, 70%70\% of these boys are neither singers nor dancers, meaning 30%30\% are singers or dancers. Since all male singers (4) and at least 2 male dancers are interested in a 3-day event (and hence a 2-day event), and applying constraints on percentages, we find that total boys = 50.

Question 2 of 5

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. A.

    Neither I nor II

  2. B.

    Both I and II

  3. C.

    Only I

  4. D.

    Only II

Answer

D

Explanation

Statement II can be determined because all 15 girls are interested in attending a 1-day event, including all 4 female dancers. Statement I cannot be uniquely determined.

Question 3 of 5

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

  1. A.

    7/10

  2. B.

    9/13

  3. C.

    7/13

  4. D.

    2/3

Answer

C

Explanation

Total students in class = 15 girls + 50 boys = 65 students. Boys interested in 2-day event = 60%×50=3060\% \times 50 = 30. Girls interested in 2-day event = 5. Total interested in 2-day event = 35. Fraction = 35/65=7/1335 / 65 = 7/13.

Question 4 of 5

What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?

  1. A.

    5 or 6

  2. B.

    4 or 6

  3. C.

    5

  4. D.

    6

Answer

A

Explanation

Total male dancers = 6 (since total dancers = 10 and female dancers = 4). At least 2 male dancers attend 3-day event, and analyzing the 2-day and 1-day preferences shows the number of male dancers interested in a 1-day event is 5 or 6.

Question 5 of 5

How many female dancers are interested in attending a 2-day event?

  1. A.

    0

  2. B.

    2

  3. C.

    Cannot be determined

  4. D.

    1

Answer

A

Explanation

Total girls interested in 2-day event = 5. 60%60\% of them (3 girls) are neither singers nor dancers. Hence, 2 girls are singers or dancers. Since all 2 female singers are interested in 2-day event, 0 female dancers are interested in 2-day event.

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